Gautam Gambhir is one of four Indian batsmen in the current line-up to average more than 50 © Getty Images

Recently I received a trigger mail that the first four Indian batsmen during the recently concluded Napier Test had a batting average above 50. Initially I thought that this would be a very common occurrence. However a preliminary perusal indicated that this was indeed a rare occurrence. So I did a detailed study and the results are presented below.

First a few points on the qualifying criteria.

Initially I thought of using the career batting average. However I discarded that in favour of using a career-to-date batting average because of the following reasons.

- This is the more accurate and correct option and a very interesting one to incorporate.
- Using the career average will move blocks of Tests in and out of the table as a batsman's career average moves either side of 50. For instance, if Gambhir's average moves back to below 50 quite a few Tests will go out of the table. That is not correct.
- Using the batting average is a simple task and can be done by any reader using Cricinfo's Statsguru. However the career-to-date batting average requires the special database I have.
- It allows me to include many a good batsmen such as Inzamam, Gilchrist, Walters, Worrell (in the last innings) et al who have had a fair proportion of their careers at above 50 and finished with a career batting average below 50.

I have only incorporated the following caveats.

During the first 10 Tests of the batsman, if the average exceeds 50, this will be considered only if his career batting average is above 50. This is to take care of the Azharuddin/Phil Hughes/Walters situation. Also if a batsman finished his career with fewer than 1000 runs, a batting average of above 50 will be ignored. This is to take care of batsmen such as Taslim Arif or CF Walters who scored fewer than 1000 runs but finished with averages exceeding 50.

Now let us look at the table.

Tests in which teams had four or more batsmen with 50 plus batting averages

1768 2005 Icc 6 Smith(55.50), Sehwag(55.81), Dravid(58.30),
                Lara(54.09), Kallis(56.88), Inzamam-ul-Haq(50.80)

1661 2003 Aus 5 Hayden(52.01), Ponting(51.12), Waugh(51.07),
                Lehmann(50.79), Gilchrist(58.80)

0194 1930 Eng 4 Hobbs(59.62),Sutcliffe(63.60),Hammond(65.27),Hendren(50.33)
0273 1939 Eng 4 Hutton(63.35),Paynter(63.79),Hammond(61.56),Compton(50.06)
1326 1996 Win 4 Campbell(53.06),Lara(60.06),Adams(68.33),Chanderpaul(50.01)
1340 1996 Win 4 Campbell(50.17),Lara(59.69),Chanderpaul(57.62),Adams(63.83)
1343 1996 Win 4 Campbell(54.65),Lara(58.38),Chanderpaul(54.07),Adams(60.74)
1346 1996 Win 4 Campbell(50.68),Chanderpaul(55.29),Lara(56.41),Adams(61.31)
1595 2002 Aus 4 Hayden(50.59),Waugh(50.27),Martyn(53.38),Gilchrist(60.38)
1663 2003 Aus 4 Hayden(56.77),Ponting(50.97),Waugh(51.20),Gilchrist(61.06)
1671 2003 Aus 4 Hayden(57.69),Ponting(52.73),Waugh(51.25),Gilchrist(60.25)
1673 2003 Aus 4 Hayden(57.34),Ponting(54.61),Waugh(51.17),Gilchrist(58.53)
1678 2003 Aus 4 Hayden(56.80),Ponting(54.07),Gilchrist(58.24),Waugh(51.13)
1680 2004 Aus 4 Hayden(58.56),Ponting(56.36),Waugh(50.98),Gilchrist(57.44)
1685 2004 Aus 4 Hayden(58.08),Ponting(55.64),Lehmann(50.38),Gilchrist(54.71)
1688 2004 Aus 4 Hayden(58.92),Gilchrist(52.88),Lehmann(51.96),Ponting(54.95)
1691 2004 Aus 4 Hayden(58.26),Ponting(54.69),Lehmann(50.67),Gilchrist(54.38)
1706 2004 Aus 4 Hayden(56.60),Ponting(54.72),Lehmann(52.79),Gilchrist(53.91)
1739 2005 Aus 4 Hayden(54.55),Ponting(55.47),Martyn(50.16),Gilchrist(52.68)
1744 2005 Aus 4 Hayden(54.05),Ponting(55.40),Martyn(51.43),Gilchrist(54.90)
1756 2005 Aus 4 Hayden(53.09),Ponting(56.09),Martyn(50.63),Gilchrist(55.28)
1758 2005 Aus 4 Hayden(52.92),Ponting(55.98),Martyn(50.81),Gilchrist(54.73)
1760 2005 Aus 4 Hayden(52.24),Ponting(55.57),Martyn(50.15),Gilchrist(54.67)
1773 2005 Aus 4 Hayden(53.60),Ponting(56.43),Hussey(55.29),Gilchrist(51.89)
1777 2005 Aus 4 Hayden(53.81),Ponting(56.15),Hussey(55.29),Gilchrist(50.91)
1779 2005 Aus 4 Hayden(53.63),Ponting(56.56),Hussey(55.29),Gilchrist(50.33)
1789 2006 Aus 4 Hayden(54.18),Ponting(57.69),Hussey(55.29),Gilchrist(50.18)
1917 2009 Ind 4 Gambhir(50.74),Sehwag(50.82),Dravid(52.39),Tendulkar(54.73)

There is only one instance of six batsmen exceeding 50. This happened in the one-off disaster between Australia and ICC. They are Smith, Sehwag, Dravid, Lara, Kallis and Inzamam. Even though Inzamam finished his career with a batting average of 49.61, his career-to-date batting average before this Test was 50.47. Now we see the benefit of using the career-to-date figures. I don't need to remind readers that the six 50+ batsmen could not save ICC from a humiliating defeat.

Similarly there is also only one instance of five batsmen exceeding 50. This was in Test # 1661 between Australia and Zimbabwe (remember the 380) in which Hayden, Ponting, Steve Waugh, Lehmann and Gilchrist exceeded 50. Lehmann and Gilchrist, at that point in their careers, although Gilchrist closed at 47.61 and Lehmann finished with 44.95. I have confirmed that Lehmann had played in more than 10 Tests for this average.

Then there are quite a number of Australian teams, in all, who have had four players exceeding 50. The core of this group has been Hayden, Ponting and Gilchrist and one from S Waugh, Lehmann or Hussey have completed the four. These teams played a total of 19 Tests during the 2000s.

Surprisingly there are West Indian teams of 1996 which qualify with Lara, Chanderpaul, Sherwin Campbell (with his outstanding start) and Adams (again with his outstanding start) completing the foursome. The fact is that Chanderpaul dropped off but recovered and has over 8500 runs at 50+. However Campbell and Adams really fell off. This team played 4 Tests.

There are two distinct English teams of the 1930s. One has Hobbs, Sutcliffe, Hammond and Hendren. The other one has Hutton, Paynter, Hammond and Compton. Only Hendren amongst this collection of greats has a career batting average of below 50.

The Napier Test comes in finally. It is a peculiar situation at Napier. Gambhir started with an average of 50.74, so the Indian team had Gambhir, Sehwag. Dravid and Tendulkar completing the quartet in the first innings. However Gambhir's average dropped to 49.85 at the end of the first innings. So, strictly speaking, the second innings does not qualify and there were only three 50+ players. Of course Gambhir has gone to 52.03 with his epic 137 and the Basin reserve Test has this quartet starting the innings.

A couple of footnotes

Coming to the original question, thanks to Ashwin Mahesh for that, of the first 4 batsmen having 50+ averages. The Napier Test is a conundrum. The first innings was perfect, with Gambhir on 50.74. Unfortunately the night-watchman came in and Tendulkar batted at no.5. So this does not qualify. In the second innings, there was no problem with the sequence except that Gambhir fell below 50.

However this has been redressed at Basin Reserve where the first four have 50+ averages. It is amazing that, based on these criteria, the Basin reserve will be the first such occasion in Test history. The nearest has been the English team of the 30s. However Hendren batted at no.5 almost always in those matches.

If we take the career averages instead of career-to-date averages, the ICC team is still on top with 5 players in their eleven, Inzamam missing out since his career average falls just below 50. S.Rajesh (Stats-Editor, Cricinfo) has pointed out that Inzamam's average went down below only because of that ICC Test, exclude that, and he averages 50.16. Unfortunately that aberration is still an "official" test. So nothing can be done.

No other team has had 5 such batsmen and a few teams, such as Australia, India and England have four 50+ batsmen. Because of Gambhir's current 50+ average quite a few recent Indian teams make it. However the fallacy of this method will be shown if Gambhir falls below 50. All these Indian teams will go off.

Chandran had raised an interesting query on the Indian team having 6 batsmen whose highest Test score exceeded 200. Wondered whether it is a record. Since this is a related query and an interesting one at that, I have answered the same in the body of this article.

Unfortunately India is one of many teams with 6 batsmen whose highest score is 200+. It so happens that there are two teams which have 7 batsmen whose highest score exceeds 200. The first is a Pakistani team which played 4 tests during 1985. That team had Mudassar, Mohsin, Qasim Omar, Javed, Zaheer, Saleem Malik and Wasim Akram (yes, you read it correctly) whose career HS was 200+.

During 2000-01, 7 Australian teams had Hayden/Slater/Langer/Ponting/S.Waugh/Gilchrist and Gillespie (!?) whose career HS was 200+.

Although I must say that the HS at the time the tests were played were not necessarily 200+ since these HS's might have been achieved subsequently.

	Mohammad Ashraful averages less than 24, and more than 45% of his innings have ended before he has reached ten © AFP

A number of remarks raised in response to my last article on the worst Test batsmen suggested that these poor "batsmen" were in reality bowlers and I should also look at the specialist batsmen to determine who was the worst ever. These comments, led by "Voyager", made a lot of sense and I have completed the study. I must say this is also a fascinating one and my thanks to all who suggested this. I will admit, this specific analysis completely escaped me.

As usual I have set some criteria for selection. Let me outline these first.

1. These should be specialist batsmen. Bowlers (even those who might only have averaged 1-2 wickets per Test) and wicketkeepers have been excluded.

2. A minimum of 25 Test innings should have been played.

3. The Batting Average should be below 20.00 for those who played their entire career before 1925 and below 25.00 for those who played afterwards.

4. The Batting Position Average for the batsman (already presented and discussed by me in these columns) should not be below 6.5. This is to make sure that only specialist batsmen are included. Otherwise bowlers like Kumble, Warne, Vaas et al would come in. The number 6.5 ensures a tilt towards no.6 position than no.7 position.

These entry constraints let 41 batsmen walk under the bar.

Now for the analysis.

I have considered the following three measures for analysis. These are all logical and make sense.

1. The Batting Average, the truest of all measures. The highest weight is given for this measure.

2. The % of single digit scores. This is an improvement on the number of Zeroes I considered earlier and was suggested by Karthik. The lower this % is, the greater credit to the batsman. The range is from 26.7% to 70.0%.

3. The quality of bowling faced. Just in case the less-performing specialist batsmen faced top quality bowling, they have to be given credit. I have also used the weighted bowling average faced, in other words, the exact quality of bowling faced. If Parker faced a Pakistani bowling attack sans Imran, playing, but only as a batsman, this is taken care of. The lower this Average Bowling Quality figure is, the greater credit to the batsman. The range is from 26.6 to 41.5.

The formula is given below.

Index = 
                  (100.0 - Single digit inns %)   (60 - Avge Bowling Quality) 
Batting Average +  ---------------------------  +  -------------------------
                                10                             5

The formula is self-evident. The division by 10 and 5 is to ensure appropriate weights.

Let us look at the tables.

Cty Batsman          Mats Inns NO Runs  HS BPA Batting Scores<10 Bow  Index
                                                Avge    No   %   Qty

Nzl Miller L.S.M      13   25   0  346  47 3.96 13.84   12 48.0% 29.2 25.20
Aus Bonnor G.J        17   30   0  512 128 5.27 17.07   21 70.0% 26.6 26.75
Eng Read J.M          17   29   2  463  57 5.17 17.15   13 44.8% 31.0 28.47
Bng Alok Kapali       17   34   1  584  85 6.06 17.70   13 38.2% 35.8 28.71
Pak Maqsood Ahmed     16   27   1  507  99 4.67 19.50   13 48.1% 33.0 30.08
Nzl Chapple M.E       14   27   1  497  76 4.52 19.12   13 48.1% 31.0 30.11
Aus Horan T.P         15   27   2  471 124 4.00 18.84   12 44.4% 29.4 30.51
Bng Hannan Sarkar     17   33   0  662  76 2.03 20.06   14 42.4% 36.3 30.56
Eng Ikin J.T          18   31   2  606  60 4.81 20.90   12 38.7% 41.5 30.73
Nzl McGregor S.N      25   47   2  892 111 4.11 19.82   18 38.3% 31.6 31.67
Zim Ebrahim D.D       29   55   1 1230  94 2.69 22.78   27 49.1% 39.1 32.05
Zim Gripper T.R       20   38   1  809 112 2.18 21.86   17 44.7% 36.3 32.12
Bng Aminul Islam      13   26   1  530 145 4.31 21.20   10 38.5% 35.5 32.26
Nzl Morgan R.W        20   34   1  734  97 4.82 22.24   16 47.1% 36.3 32.28
Bng Aftab Ahmed       14   27   3  514  82 5.56 21.42   10 37.0% 35.8 32.56
Zim Wishart C.B       27   50   1 1098 114 5.20 22.41   24 48.0% 34.5 32.71
Bng Javed Omar        40   80   2 1720 119 2.12 22.05   33 41.2% 36.1 32.71
Eng Larkins W         13   25   1  493  64 2.72 20.54   10 40.0% 28.9 32.77
Win Morton R.S        15   27   1  573  70 3.89 22.04   13 48.1% 31.9 32.84
Win Simmons P.V       26   47   2 1002 110 2.40 22.27   16 34.0% 36.3 33.60
Nzl Morrison J.F.M    17   29   0  656 117 2.55 22.62   13 44.8% 31.6 33.81
Nzl Bell M.D          18   32   2  729 107 2.16 24.30   17 53.1% 35.6 33.86
Bng Mohammad Ashraful 48   93   4 2125 158 4.59 23.88   42 45.2% 35.1 34.35
Nzl Franklin T.J      21   37   1  828 101 2.00 23.00   10 27.0% 39.1 34.47
Aus Richardson V.Y    19   30   0  706 138 4.97 23.53   13 43.3% 33.5 34.51
Eng Athey C.W.J       23   41   1  919 123 3.22 22.98   16 39.0% 32.4 34.60
Zim Rennie G.J        23   46   1 1023  93 2.89 22.73   16 34.8% 32.9 34.68
Nzl How J.M           18   34   1  771  92 2.00 23.36   10 29.4% 38.7 34.68
Nzl Murray B.A.G      13   26   1  598  90 2.00 23.92   11 42.3% 34.4 34.81
Nzl Pocock B.A        15   29   0  665  85 2.00 22.93   10 34.5% 32.3 35.02
Eng Brearley J.M      39   66   3 1442  91 3.12 22.89   23 34.8% 31.7 35.06
Pak Asif Mujtaba      25   41   3  928  65 4.46 24.42   15 36.6% 37.7 35.23
Bng Al Sahariar       15   30   0  683  71 2.80 22.77    8 26.7% 34.3 35.25
Eng Knight N.V        17   30   0  719 113 3.70 23.97   11 36.7% 34.8 35.35
Win Griffith A.F.G    14   27   1  638 114 2.00 24.54   12 44.4% 32.2 35.64
Pak Mathias W         21   36   3  783  77 5.81 23.73   12 33.3% 32.8 35.83
Win Smith D.S         28   49   2 1165 108 2.31 24.79   16 32.7% 36.2 36.29
Saf Cheetham J.E      24   43   6  883  89 5.74 23.86   13 30.2% 32.2 36.41
Nzl Parker J.M        36   63   2 1498 121 3.67 24.56   24 38.1% 30.6 36.62
Win Williams S.C      31   52   3 1183 128 2.29 24.14   14 26.9% 33.0 36.84
Pak Kardar A.H        23   37   3  847  93 6.16 24.91   12 32.4% 32.8 37.12

Lawrence Miller is an unknown name but is going to become quite well-known, one suspects. He barely gets in having played 25 innings. He played between 1953 and 1958. To boot, he batted in the middle order to start with but opened in the last six Tests. I am amazed that New Zealand cricket was at such a low ebb that they could not replace a batsmen who did not go past 50 in 13 Tests, had a single digit score in half the innings he played (and bowled a total of 2 balls). However I must mention that his top score of 47 helped New Zealand secure their first ever Test win against West Indies. Also that Miller faced good quality bowling almost always.

George Bonnor and John Read played duriing the first few years of Test cricket. Bonnor was more successful with a century and two 50s. Their averages of around 17 should be considered to be slightly higher in view of the time they played in. I have not done any average adjustment.

Now comes the interesting part. Couple of average Bangladeshi batsmen follow them. Some reader mentioned Jack Ikin. He finds a place in the top 10. It can be seen that the bowling he faced was very average quality, the post-war Indians, New Zealanders and West Indian bowlers.

Note how high Mohammad Ashraful and Javed Omar are in the table. They have also played a huge number of Tests. To be the premier batsmen of a modern team and average around 23 reflects the state of Bangladeshi cricket. What is also galling is the high % of single digit dismissals by both these batsmen, both above 40%.

As expected, Mike Brearley takes his place in this table in the lower half. That too because he crossed 10 a few times more than other batsmen and also faced very good bowling almost always.

What surprises me is the presence of Jamie How in this table. For How to be given 18 Tests in today's situation is quite surprising.

New Zealand has most entries in this table, 11. Bangladesh follows with 7. Surprisingly England has a few recent batsmen, viz., Athey, Brearley, Knight and Larkins in this list. Similarly West Indies has Morton, Simmons, D.S.Smith and Williams present. Pakistan has four players incluyding Asif Mujtaba. A.H.Kardar just about makes the list. He captained Pakistan during the difficult early days.

How, along with Pollard, Franklin, Murray are the New Zealanders in this list who have opened, quite unsuccessfully, in all the Tests they have played. The only other ever-present opener is Griffith of West Indies. Martin Bell should also have been there. However he played once in the no.7 position.

Note the absence of a single Indian in this list. For the record, the worst Indian specialist batsman is Eknath Solkar, with an average of just over 25, since his tally 18 wickets in 27 Tests is quite low. But his extraordinary fileding should give him the all-rounder status. As such the crown should go to Ashok Mankad, with an average of around 26, followed by Arun Lal.

For that matter the only Australians are the pre-1930. The nearest a modern Australian comes in is John Dyson, with an average just over 26.

	Chris Martin does everything right except make contact with the ball © Getty Images

A lot of analysis has been done on the best batsmen in Test cricket. Whatever be the methodology used, all analysis lead to the incomparable Don Bradman at the top. The arguments start when some one is anointed the second best, any one of 5 batsmen could fill this place.

Let us leave that topic aside. I have always felt that the other end of batting table presents a fascinating possibility. Who is the worst batsman who ever carried a bat and walked in. Is it Chris Martin, is it one of the Indian spinners, is it a West Indian fast bowler or an unexpected batsman out side this lot? Without further ado, let us delve in.

First a few criteria to be fixed.

The first is that the batsman (okay, I know I am stretching the point) has to have played 25 Test innings, which, for a tail-ender, represents nearly 20 Tests. The next is that the career batting average should be below 10.00. These twin criteria have enabled 70 tail-end batsmen to be selected.

Let me also mention that I would not do just a simple table based on, say, Batting Average. That is something which anyone could get using the excellent Cricinfo Statsguru. I will do a composite but not complex analysis of these 70 batsmen.

I have considered three measures for analysis. These are explained below.

1. Batting Average. This is the simplest and most acceptable of all batting measures. Readers can easily identify with this measure and it reflects the batting ability very realistically, notwithstanding the "not outs" conundrum. In this particular analysis even the "not outs" do not matter since most of these batsmen remain not out on quite a few occasions. This measure will carry a weight of 20 points.

2. Dismissed Zeroes. The emphasis here is on both the words. An innings which ends at 0 means that, barring a few exceptional circumstances, very little has been contributed and another batsman, almost always a better one, has been left in the limbo. I have determined the number of dismissed zeros and determined a frequency of innings in which this has occured. The lower this figure is, the worse the batsman is. This measure will carry a weight of 15 points.

3. Average partnership runs added. This is a useful measure since it tests another facet of the tail-end batsman's skills, which is the support he provides to the senior batsmen. Basically I have computed the number of runs added while the tail end batsman was at the crease, mostly at no.10 or no.11, and determined the measure of average partnership runs per innings. This measure will carry a weight of 15 points.

I have considered (and ignored) the batsman's highest score since that does not convey any additional information. I have also not considered the "Balls played" information since that is available only for about a third of Tests. And extrapolating based on team scoring rate will not work since these batsmen are likely to take a lot more balls to score the runs.

Let us take a look at tables, first the support table.

Cty Batsman             Ins  No   Runs Avge  HS Dis  Runs  Avge
                                                0s  Added  Bpa

Zim Mbangwa M            25   8    34  2.00   8   9   171  11.0  
Nzl Martin C.S           65  30    76  2.17  12  25   663  10.9  
Win King R.D             27   8    66  3.47  12   7   275  10.2  
Bng Manjural Islam(Sr)   33  11    81  3.68  21  10   351  10.6  
Ind Chandrasekhar B.S    80  39   167  4.07  22  23   760  10.9  
Ind Maninder Singh       38  12    99  3.81  15  11   396  10.8  
Ind Doshi D.R            38  10   129  4.61  20  14   384  10.9  
Aus Reid B.A             34  14    93  4.65  13   6   262  10.8  
Ind Nehra A              25  11    77  5.50  19  10   221  10.6  
Win Valentine A.L        51  21   141  4.70  14  12   502  10.9  

Now the final table.

Cty Batsman            Batting Avge  Dis 0s Freq    Avge Ptship   Total
                            (20)          (15)           (15)       (50)
Zim Mbangwa M           4.00 (2.00)   2.08 ( 2.78)   5.13 ( 6.84)  11.21
Nzl Martin C.S          4.34 (2.17)   1.95 ( 2.60)   7.65 (10.20)  13.94
Win King R.D            6.95 (3.47)   2.89 ( 3.86)   7.64 (10.19)  17.48
Bng Manjural Islam(Sr)  7.36 (3.68)   2.48 ( 3.30)   7.98 (10.64)  17.82
Ind Chandrasekhar B.S   8.15 (4.07)   2.61 ( 3.48)   7.12 ( 9.50)  17.88
Ind Maninder Singh      7.62 (3.81)   2.59 ( 3.45)   7.82 (10.42)  18.02
Ind Doshi D.R           9.21 (4.61)   2.04 ( 2.71)   7.58 (10.11)  18.83
Aus Reid B.A            9.30 (4.65)   4.25 ( 5.67)   5.78 ( 7.71)  19.33
Ind Nehra A            11.00 (5.50)   1.88 ( 2.50)   6.63 ( 8.84)  19.50
Win Valentine A.L       9.40 (4.70)   3.19 ( 4.25)   7.38 ( 9.84)  19.97

As foreseen, a dark horse has emerged. Who would have thought of a batsman who could come ahead of Chris Martin. (Mpumelelo) Pommy Mbangwa's batting is for the Gods to view. 25 innings, 8 not outs and 34 runs gives him an unbelievable average of 2.00. He has been dismissed at 0 for nearly 40% of his crease visits. He has a highest score of 8, the only one in this elite group not to have crossed 9 runs. He has always batted at no.11. His average partnership is an unbelievably low 6.8. What more do you want. I would have paid money to see Pommy bat. Note his batting sequence: 0, 2, 0, 4, 0*, 0, 0, 0, 0, 2*, 3, 2, 0, 1*, 2, 0*, 0*, 1*, 3, 0, 0, 1*, 8, 0*, 5. One fascinating string of scores.

I can see the New Zealand readers having mixed feelings. They would dearly love to have Chris Martin head this table because they love his batting. I can only suggest that if you increase the number of innings to 30, Chris Martin will be at the top. Let us see Martin's exploits. 65 innings, 30 not outs, 76 runs giving Martin a slightly higher average of 2.17 as compared to Pommy. He has crossed single figures once in his career, an unbeaten 12 against Bangladesh when he outscored O'Brien. He has 25 dismissed zeroes, the most frequent amonst all these batsmen. But his partnership average is a healthy 10+. Only twice has Martin batted at no.10 when Shane Bond and Cummings could not bat. Let me add, I would also pay money to see Chris Martin bat.

Reon King is next. Not as great a fast bowler as some of the other greats such as Walsh or Ambrose, but equally inept a batsman.

Then comes Manjual Islam, followed by three Indian spinners. Reid of Australia separates these three from Ashish Nehra, another rabbit of a batsman. Alf Valentine is last in this table.

Fidel Edwards, who is 11th in the table is the only other batsman wiith a sub-5.00 batting average. However he has recently batted very well, saving West Indies twice at Antigua and Napier.

To view the complete list please click here.

	Ian Botham was at the forefront of that amazing fightback by England at Headingley against Australia in 1981, when the last three wickets added 221 and helped script a remarkable win © Getty Images

During the last few Tests of 2008 I got the feeling that late order batsmen were playing rear-guard innings far more effectively than they normally do. Look back at Clarke with tail in Sydney, Duminy with the tail at the MCG, Nash with the tail in Napier, Haddin with the tail in Perth, Dhoni/Harbhajan at Chepauk, Taylor in Dunedin, McCullum with the tail in Adelaide, Katich with the tail in Brisbane, Dhoni/Harbhajan in Nagpur, Harbhajan/Zaheer in Bangalore et al. All these and other such instances happened during the last three months of 2008.

I felt that this deserved a detailed look. As normally happens, the scope of the article expanded and I have covered the Test tail-enders' batting in depth.

How do we define late order batting? I have decided to be quite conservative and defined a tail-end batting effort as starting from 7 wickets down. While theoretically the late order might start from no.8, I am influenced by the fact that a score of xyz for 6 still represents a reasonable position while xyz for 7 signifies the start of the end. Also, seven down means the two batsmen at the crease are one good batsman with a no.9, or no.8 and no.9 batting together. Thus any batting effort at this juncture is bound to be extremely valuable.

The other criterion I have is that the late order wickets should have added at least 50% of the score at which the seventh wicket fell. Incidentally this also translates to more than 33.33% of the final score. To avoid peculiar situations such as a team, tottering at 20 for 7, having a biff or two or three and trebling the score to 60 all out, I have also excluded the 36 innings which have ended as sub-100 all-out situations.

Let us first do a summary of these situations to determine whether there has been a spurt in late order batting exploits.

Period  Tests  # of instances  Frequency
               > 50% of runs    (Tests)
                 added for 
                 last 3 wkts

All:     1906       641           2.97

2000s:    424       157           2.70

2000:      46        14           3.28
2001:      55        21           2.61
2002:      54         9           6.00
2003:      44        13           3.38
2004:      51        31           1.64
2005:      49        22           2.23
2006:      46        19           2.42
2007:      31         6           5.16
2008-9:    50        17           2.94

Overall the late order batsmen have been successful once in 3 Tests. This figure has improved slightly for the 157 Tests played during the current decade. During 2002 the tail did not wag at all and the 8-9-10-11 batsmen just came in and went. During 2004, it was impossible to dislodge the tail. They stuck like leaches.

During 2007 again the tail has just folded up. However during 2008-09, the frequency has been the same as the all-time Test figure and is in fact slightly higher than the 2000s decade. However I have also found out why we get the feeling of a strongly wagging tail. Out of the 17 instances, 11 have occured during the last 3 months (out of 20 Tests). Hence it is true that during the last three months the bowlers found it difficult to disllodge the late order batsmen.

Let us do one more basic analysis. This is to look at the frequency of such innings by country.

Country       Tests  # of instances  Frequency
                      > 50% of runs   (Tests)
                      added for 
                      last 3 wkts

Australia      705        118           5.97
Bangladesh      59         22           2.68
England        880        122           7.21
India          427         80           5.33
New Zealand    348         76           4.57
Pakistan       335         56           5.98
Soouth Africa  341         66           5.17
Sri Lanka      182         23           7.91
West Indies    451         56           8.05
Zimbabwe        83         22           3.77

First point to remember is that the two frequency values are not comparable, since the number of Tests played by the countries adds to twice the number of Tests played. So the frequency numbers have 50% value.

Bangladesh has the best late order batting record with a very low frequency of 2.68 Tests per such innings. Next comes Zimbabwe, the other weak team with 3.77 Tests. That's probably expected with the poor manner in which these two teams' top orders have batted. New Zealand, South Africa, India, Australia and Pakistan then appear. The other end of the table sees England and Sri Lanka, whose tails have been the poorest of the lot.

Having got a 641-innings database, I have worked on couple of tables, across all 130 odd years of Test cricket.

The first one is a table ordered by the quantum of runs added for the last 3 wickets.

Table of late order batsmen successes: By Runs added

MtNo Year For Final Score                Runs  % of 7 wkt
                                         Added   score

0609 1966 Eng 527 for 10 from 166 for 7   361   217.5%  vs Win
0098 1908 Aus 506 for 10 from 180 for 7   326   181.1%  vs Eng
1336 1996 Pak 553 for 10 from 237 for 7   316   133.3%  vs Zim
1800 2006 Nzl 593 for  8 from 279 for 7   314   112.5%  vs Saf
1902 2008 Saf 459 for 10 from 184 for 7   275   149.5%  vs Aus
0209 1931 Eng 454 for 10 from 190 for 7   264   138.9%  vs Nzl
1139 1990 Nzl 391 for 10 from 131 for 7   260   198.5%  vs Ind
0078 1903 Eng 577 for 10 from 318 for 7   259    81.4%  vs Aus
1573 2001 Nzl 534 for  9 from 281 for 7   253    90.0%  vs Aus
1676 2003 Nzl 563 for 10 from 314 for 7   249    79.3%  vs Pak
0160 1925 Aus 489 for 10 from 253 for 7   236    93.3%  vs Eng
0914 1981 Ind 487 for 10 from 254 for 7   233    91.7%  vs Eng
1380 1997 Pak 456 for 10 from 230 for 7   226    98.3%  vs Saf
0066 1902 Aus 353 for 10 from 128 for 7   225   175.8%  vs Eng
0905 1981 Eng 356 for 10 from 135 for 7   221   163.7%  vs Aus
0136 1921 Aus 499 for 10 from 282 for 7   217    77.0%  vs Eng
1681 2004 Saf 532 for 10 from 315 for 7   217    68.9%  vs Win
0621 1967 Pak 354 for 10 from 139 for 7   215   154.7%  vs Eng
1066 1987 Pak 487 for  9 from 273 for 7   214    78.4%  vs Ind
1397 1998 Saf 517 for 10 from 305 for 7   212    69.5%  vs Aus

The first is an amazing match. After dismissing a strong West Indian side for 268 and against Hall/Griffith/Sobers/Gibbs, England were 166 for 7, there would have been very few takers on England saving the match. Then Graveney, who scored a masterly 165, with support from Murray, who scored 112, took the score to 399 for 9. To add insult to injury, Higgs and Snow, both reaching their 50s, added 128 for the last wicket. England reached 527 and the strong but demoralised West Indies, were all out for 225, losing by an innings.

The 1906 match should not really figure in this list. Australia recovered from 180 for 7 to 506 through Clem Hill's 160. However Hill normally batted at no.3 and by no stretch of imagination a late order batsmen.

Pakistan's recovery from 237 for 7 to 553 was through a massive 257 not out from Wasim Akram and 79 from Saqlain Mushtaq. New Zealand's move from 279 for 7 to 593 for 8 was through Fleming's huge double century and an unlikely 100 from Franklin. South Africa's match and series-winning progression from 184 for 7 to 459 was through Duminy's epic 166 and Steyn's 75.

Botham's once-in-lifetime innings of 149 at Headingley during 1981, which took the post-follow-on score from 135 for 7 to 356 all out also figures late in this table.

The second is a table ordered by the % of runs added.

Table of late order batsmen successes: By % of score at 7 wkt down

MtNo Year For Final Score                Runs  % of 7 wkt
                                         Added   score

0186 1930 Nzl 112 for 10 from  21 for 7    91   433.3%  vs Eng
0623 1967 Pak 255 for 10 from  53 for 7   202   381.1%  vs Eng
0168 1927 Saf 170 for 10 from  38 for 7   132   347.4%  vs Eng
0003 1879 Eng 113 for 10 from  26 for 7    87   334.6%  vs Aus
0111 1910 Saf 174 for 10 from  49 for 7   125   255.1%  vs Aus
0063 1899 Aus 196 for 10 from  57 for 7   139   243.9%  vs Eng
0761 1975 Aus 268 for 10 from  81 for 7   187   230.9%  vs Eng
0609 1966 Eng 527 for 10 from 166 for 7   361   217.5%  vs Win
1459 1999 Aus 188 for 10 from  60 for 7   128   213.3%  vs Slk
1450 1999 Slk 188 for 10 from  61 for 7   127   208.2%  vs Pak
1139 1990 Nzl 391 for 10 from 131 for 7   260   198.5%  vs Ind
0883 1980 Eng 209 for  9 from  73 for 7   136   186.3%  vs Win
1096 1988 Pak 194 for 10 from  68 for 7   126   185.3%  vs Win
0098 1908 Aus 506 for 10 from 180 for 7   326   181.1%  vs Eng
1455 1999 Eng 126 for 10 from  45 for 7    81   180.0%  vs Nzl
0066 1902 Aus 353 for 10 from 128 for 7   225   175.8%  vs Eng
0669 1969 Aus 153 for 10 from  57 for 7    96   168.4%  vs Ind
0327 1950 Eng 122 for 10 from  46 for 7    76   165.2%  vs Aus
0967 1983 Ind 103 for 10 from  39 for 7    64   164.1%  vs Win
0905 1981 Eng 356 for 10 from 135 for 7   221   163.7%  vs Aus

I am aware that a 400% improvement in score could be caused by a sub-25 for 7 situation improving to 100+ all out. However let us give credit to those hapless and less gifted batsmen who have batted bravely. This is their "15 minutes of greatness", at least as far as their batting is concerned.

In the 1930 match New Zealand were 21 for 3 and then lost 4 wickets in one over, including a hat-trick to Maurice Allom, making his debut. They recovered to a score four times bigger, mainly through Blunt. They still lost the match, though.

Pakistan's recovery was amazing. Trailing by 224 against England at The Oval, 53 for 7 and 65 for 8 before Asif Iqbal who scored a thrilling 146, added 190 in partnership with Intikhab Alam who scored 51. They avoided an innings defeat but lost comfortably.

The next three matches are old ones.

During the 1975 Ashes Test, Australia were 81 for 7 against an England total of 315. Follow-on and a huge loss loomed ahead. Then Ross Edwards added 52 with Walker but more importantly 66 with Lillee before he was out. Lillee carried on with Mallet and finished unbeaten on 77. Australia scored 268 and saved the match.

Then we have the England-West Indies Test already described. Then we come to two Tests playing within a month of each other with virtually the same scoring pattern.

First Sri Lanka, playing against Pakistan and trailing by 360+ runs slumps to 61 for 7. Tillakaratne who scored 55, in the company of the last three batsmen, added 127 more runs.

Now, six months later, Australia, batting first, slumps to 60 for 7 before Ponting who scored 96 glorious runs, adds 128 for the last three wickets, mainly with Gillespie. Australia, however, went on to lose the match.

What is the best ever late order recovery? It's impossible to pin-point one innings. However, if there is an imaginary gun pointing at me, I will plump for England against Australia at Headingley during 1981. Note the order of events. Australia scored 401. England scored 174, followed on and slumped to 135 for 7, against Lillee, Lawson and Alderman. 500 to 1 were very generous odds at this point.

At this stage Botham plays his epic 149, is well supported by Dilley (56) and Old (29) and England reach 356. Still Australia needs only 119 to win. Then Willis steps in. His best bowling effort ever, 8 for 43, makes sure Botham's stupendous effort is not wasted. It is my personal opinion that, Calcutta 2001 notwithstanding, that was the greatest recovery in Test cricket. It also happens to be the best in this current analysis. Again my personal view.

	Among batsmen with at least 5000 Test runs, Jack Hobbs has the best consistency index © Getty Images

One thing we admire in our cricketers is consistency. Full marks to the gritty player who scores 50 on a minefield, even though he gets out for 50 when well set on a featherbed. But do we admire so much his team-mate who gets a duck in the first instance, but makes amends by crashing an impressive 100 in the second? They have the same average – but do they provide the same value?

Consistency can measured by calculating the standard deviation, which, in simple terms, seeks to measure the average deviation that each score is from the overall mean. The lower the standard deviation, the lower the variation in the scores.
We can obviously apply this to cricket scores, but a couple of issues need to be resolved: what to do with “not out” scores, and how can we use it to compare the consistency of players with different averages?

To resolve the first, I elected to add any uncompleted innings to the next innings, so that effectively, I was calculating the standard deviation of the runs made between dismissals. If the last innings was a “red ink”, it was ignored.

To allow comparison of consistency between different players, I simply divided the calculated standard deviation by the batting average (ignoring the last innings if it was “not out”).

I performed this exercise three times for Test cricketers; for those who scored at least 1000 runs, for those who scored at least 5000 runs, and for those who scored at least 10000 runs.

The first table lists the most consistent Test batsmen who have scored at least 1000 runs. Australia’s Bruce Laird, who scored with such consistency without scoring a century in his brief late-70s career, heads the list, and is followed by the admirable Sutcliffe, whose consistency is astounding given the extent of his career. Alastair Cook and MS Dhoni are notable current players in this list.

Table 1: Consistency Index: Most Consistent (Minimum 1000 runs)

Batsman	Team	CI	SD	Average	Matches	Innings	Not Out	Runs
Bruce Laird	Australia	0.75	26.48	35.29	21	40	2	1341
Herbert Sutcliffe	England	0.78	47.22	60.73	54	84	9	4555
Douglas Jardine	England	0.79	37.08	46.70	22	33	6	1296
Ashley Giles	England	0.80	16.81	20.90	54	81	13	1421
Alastair Cook	England	0.81	34.24	42.09	36	66	2	2694
Maurice Tate	England	0.82	20.96	25.49	39	52	5	1198
Rusi Surti	India	0.83	23.72	28.70	26	48	4	1263
Jock Cameron	South Africa	0.83	25.05	30.22	26	45	4	1239
George Gunn	England	0.83	33.39	40.00	15	29	1	1120
Chandika Hathurusingha	Sri Lanka	0.84	24.74	29.63	26	44	1	1274
Ian Redpath	Australia	0.84	36.62	43.46	66	120	11	4737
Sid Barnes	Australia	0.85	53.39	63.06	13	19	2	1072
Mark Richardson	New Zealand	0.86	38.33	44.77	38	65	3	2776
Taufeeq Umar	Pakistan	0.87	34.22	39.30	25	46	2	1729
Imran Farhat	Pakistan	0.88	29.02	33.10	27	51	1	1655
Charles Kelleway	Australia	0.88	32.83	37.42	26	42	4	1422
Dwayne Bravo	West Indies	0.88	28.74	32.73	31	57	1	1833
Peter Richardson	England	0.88	33.08	37.47	34	56	1	2061
Chetan Chauhan	India	0.89	28.07	31.58	40	68	2	2084
Colin Bland	South Africa	0.89	43.67	49.09	21	39	5	1669
Trevor Goddard	South Africa	0.89	30.67	34.47	41	78	5	2516
Deryck Murray	West Indies	0.89	20.40	22.91	62	96	9	1993
Mahendra Singh Dhoni	India	0.89	32.20	36.14	35	56	6	1807
David Sheppard	England	0.89	33.70	37.81	22	33	2	1172
Alan Davidson	Australia	0.89	21.97	24.59	44	61	7	1328

At the other end, we also have some current players in the least consistent category, notably Sinclair, Taibu, and until recently, Atapattu, who mixed a dreadful sequence of low scores early in his career with some heavy scoring later on:

Table 2: Consistency Index: Least Consistent (Minimum 1000 runs)

Batsman	Team	CI	SD	Average	Matches	Innings	Not out	Runs
Matthew Sinclair	New Zealand	1.62	52.70	32.55	32	54	5	1595
Vinoo Mankad	India	1.51	47.57	31.48	44	72	5	2109
Jacques Rudolph	South Africa	1.49	53.81	36.21	35	63	7	2028
Guy Whittal	Zimbabwe	1.48	43.65	29.43	46	82	7	2207
Tatenda Taibu	Zimbabwe	1.45	42.94	29.60	24	46	3	1273
Wasim Akram	Pakistan	1.44	32.57	22.63	104	147	19	2898
Mohammad Ashraful	Bangladesh	1.43	34.10	23.88	48	93	4	2125
Javagal Srinath	India	1.43	20.31	14.21	67	92	21	1009
Wasim Jaffer	India	1.42	48.30	34.11	31	58	1	1944
Vic Pollard	New Zealand	1.41	34.35	24.35	32	59	7	1266
Dilip Sardesai	India	1.40	55.10	39.24	30	55	4	2001
Sidath Wettimuny	Sri Lanka	1.39	40.31	29.07	23	43	1	1221
Marvan Atapattu	Sri Lanka	1.39	54.40	39.02	90	156	15	5502
Matthew Elliot	Australia	1.38	46.20	33.49	21	36	1	1172
Madan Lal	India	1.38	31.27	22.65	39	62	16	1042
Ridley Jacobs	West Indies	1.37	38.70	28.32	65	112	21	2577
Tim Robinson	England	1.36	49.34	36.39	29	49	5	1601
Bill Ponsford	Australia	1.35	65.00	48.23	29	48	4	2122
John Bracewell	New Zealand	1.35	27.56	20.43	41	60	11	1001
Jimmy Adams	West Indies	1.35	55.72	41.26	54	90	17	3012

Now for the serious Test batsmen:

Table 3: Consistency Index: Most Consistent (Minimum 5000 runs)

Batsman	Team	CI	SD	Average	Matches	Innings	Not Out	Runs
Jack Hobbs	England	0.92	52.33	56.95	61	102	7	5410
Don Bradman	Australia	0.94	93.49	99.94	52	80	10	6996
Arjuna Ranatunga	Sri Lanka	0.94	33.48	35.50	93	155	12	5105
John Wright	New Zealand	0.97	36.58	37.83	82	148	7	5334
Mark Waugh	Australia	0.97	40.58	41.82	128	209	17	8029
Graham Thorpe	England	0.98	43.25	44.23	100	179	28	6744
Rohan Kanhai	West Indies	0.98	46.58	47.53	79	137	6	6227
Clive Lloyd	West Indies	0.99	46.44	46.68	110	175	14	7515
Denis Compton	England	1.00	49.9	50.06	78	131	15	5807
Sourav Ganguly	India	1.00	42.22	42.18	113	188	17	7212
Bill Lawry	Australia	1.03	48.43	47.15	67	123	12	5234
Ken Barrington	England	1.03	59.9	58.28	82	131	15	6806
Matthew Hayden	Australia	1.04	52.77	50.74	103	184	14	8625
Ricky Ponting	Australia	1.05	59.47	56.88	128	215	26	10750
Michael Slater	Australia	1.05	45.09	42.84	74	131	7	5312
Doug Walters	Australia	1.06	50.86	48.10	74	125	14	5357
Marcus Trescothick	England	1.06	46.34	43.80	76	143	10	5825
Sunil Gavaskar	India	1.06	54.42	51.12	125	214	16	10122
David Gower	England	1.07	47.29	44.25	117	204	18	8231
Vivian Richards	West Indies	1.07	53.69	50.24	121	182	12	8540
Michael Atherton	England	1.07	40.41	37.70	115	212	7	7728
Len Hutton	England	1.07	60.86	56.67	79	138	15	6971

The higher Consistency Indices show that it is much harder to maintain consistency over a longer career. It is interesting to observe that the two most consistent batsmen are two “old-timers”, Hobbs and Bradman – class will out! And who would have thought that the most consistent Australian after Bradman in this category was Mark Waugh!

At the other end of the scale for this category, we find Waugh’s twin brother prominently placed:

Table 4: Consistency Index: Least consistent (Min 5000 runs)

Player	For	CI	SD	Ave	M	I	NO	Runs
Marvan Atapattu	SL	1.39	54.40	39.02	90	156	15	5502
Zaheer Abbas	Pak	1.32	59.29	44.80	78	124	11	5062
Kumar Sangakkara	SL	1.31	71.23	54.38	78	129	9	6525
Virender Sehwag	Ind	1.27	64.81	51.06	66	114	4	5617
Steve Waugh	Aus	1.26	64.16	51.06	168	260	46	10927
Shivnarine Chanderpaul	WI	1.25	62.37	49.72	114	196	31	8203
Brian Lara	WI	1.24	65.33	52.89	131	232	6	11953
Herschelle Gibbs	SA	1.24	51.85	41.95	90	154	7	6167
Ian Botham	Eng	1.24	41.69	33.55	102	161	6	5200
Sanath Jayasuriya	SL	1.23	49.15	40.07	110	188	14	6973
VVS Laxman	Ind	1.22	54.24	44.46	102	169	24	6446
Aravinda de Silva	SL	1.21	52.21	42.98	93	159	11	6361
Mark Taylor	Aus	1.19	51.55	43.50	104	186	13	7525
Wally Hammond	Eng	1.19	69.46	58.46	85	140	16	7249
Jacques Kallis	SA	1.19	64.91	54.58	128	216	33	9988
Mahela Jayawardene	SL	1.18	61.73	52.36	100	164	12	7959
Carl Hooper	WI	1.18	43.09	36.47	102	173	15	5762
Sachin Tendulkar	Ind	1.1	64.28	54.28	156	256	27	12429
Rahul Dravid	Ind	1.17	61.07	52.28	131	227	26	10509
Stephen Fleming	NZ	1.17	47.05	40.07	111	189	10	7172

The case of Chanderpaul is interesting. Ten years ago, he was heading towards being one of the most consistent batsmen ever, with a CI of 0.82. Over the last decade, while he has been one the Windies few shining lights, there has also been much greater variation in his scoring.

This group also contains a few batsmen who play more aggressively than most: Sehwag, Jayasuriya and Botham are notable here. One would expect, naturally, their consistency to suffer as a result of their aggression.

Finally, a table just for the mega-stars, those who have scored 10000 Test runs, plus Kallis, who will surely join them the next time he goes to bat:

Table 5: Consistency Index: Top eight run-scorers

Player	For	CI	SD	Ave	M	I	NO	Runs
Ricky Ponting	Aus	1.05	59.47	56.88	128	215	26	10750
Sunil Gavaskar	Ind	1.06	54.42	51.12	125	214	16	10122
Allan Border	Aus	1.08	54.45	50.37	156	265	44	11174
Rahul Dravid	Ind	1.17	61.07	52.28	131	227	26	10509
Sachin Tendulkar	Ind	1.18	64.28	54.28	156	256	27	12429
Jacques Kallis	SA	1.19	64.91	54.58	128	216	33	9988
Brian Lara	WI	1.24	65.33	52.89	131	232	6	11953
Steve Waugh	Aus	1.26	64.16	51.06	168	260	46	10927

I for one was surprised to find the Aussie captain heading this list, and Tendulkar so far down the table. And perhaps Gavaskar was a better player than he is perhaps given credit for.

I hope the browsers of this site find this a worthwhile exercise. I would value their comments.

	Herbert Sutcliffe: the best of the lot © Getty Images

Mathew Hayden's retirement has drawn the curtains on the career of one of the greatest openers of all time. He, along with Sehwag and Greame Smith, re-defined the art of Test opening. Where do these wonderful opening batsmen stand vis-a-vis other greats like Hobbs, Gavaskar and Sutcliffe? I feel that this is the right time to do such a study.

The study of opening batsmen is a complicated task. Over the years the role of opening batsmen has changed. From defensive, stay-at-wicket-at-all-costs batsmen they have become match-winners who have been primarily responsible for the attacking attitudes which captains employ now. The study has to recognise this evolution and be fair to all types of opening batsmen.

The first task is to fix a minimum limit criteria. I have fixed this as 3000 runs, scored in the opening position (not complete career). This lets in most great openers. The only top-drawer opener left out is Hanif Mohammad (2638 runs). Unfortunately nothing can be done. I apologise to my Pakistani friends for this. I have also given at the end Hanif Mohammad's values. The other great opener left out, Victor Trumper, has scored only 1650 runs in the opening position. I wanted to avoid any longevity-based weighting and the only way is to keep a high entrance bar. The number of qualifying batsmen has also to be kept at a reasonable number, 35 in this case.

In order to cater to the different playing times, tactics, grounds et al, I have used the following 7 criteria. Each is explained in full later.

1. Home Batting Average.
2. Away batting Average.
3. Average Runs scored - weighted by the quality of bowling attack.
4. Scoring Rate.
5. Average opening partnerships participated in.
6. Quality of the top 3 pace bowlers faced.
7. Quality of batting support - Other opener and next 3 batsmen.

The principle I have followed is that the three direct measures, Home average, Away average and Average weighted runs, will carry a total weight of 50%. The other four secondary measures will have equal weight.

1. Home Batting Average (15 points).

This is the most basic of all measures. It is a straight forward computation of the home batting average. Since the minimum number of home runs scored by a batsman in the group of 35 is 1246 (by Michael Vaughan), any average figure will be valid.

The highest home average is that of Herbert Sutcliffe who has an outanding 64.60 average while playing as an opener in England. Mike Atherton of England is at the bottom with an average of 39.14.

2. Away batting Average (20 points).

This is the other basic measure. It is a straight forward computation of the away batting average. It carries a higher weighting than the home batting average for obvious reasons. Since the minimum number of away runs scored by a batsman in the group of 35 is 916 (by John Edrich), any average figure will be reasonably valid.

Away from home, the other great opener Hobbs averages 59.17. Mudassar Nazar travels very poorly with an average of 25.75.

3. Average Runs scored - weighted by the quality of bowling attack (15 points).

The first two were basic measures. However there is need to value the runs scored against better bowling attacks higher. Greame Smith should get much more credit for his knock of 154 against England as compared to his innings of 232 against Bangladesh even though both were match-winning innings and the second is 50% higher. This is done by weighting the runs scored by the bowling strength of the opposing team and averaging the same.

Hobbs' run tally comes down to 90% while Andrew Strauss' tally moves up to 109%.

4. Scoring Rate (12.5 points).

This is a new measure. The openers have changed the way the Tests are played now. First Hayden and then Greame Smith, Sehwag and Gayle et al have scored consistently at well above 3 runs per over and this has resulted in many more decisive games. This factor has to be recognized and has been.

We have accurate balls played information for the past 15 years and this can be used. For the early Tests I have assigned to the opening batsmen the team's strike rate for the innings. This might vary slightly from actual balls played information, which is, unfortunately, available nowhere. However this will even out over a career. It is also true that the olden day openers, barring a very few attacking players, played quite slowly and most of them would in reality be benefited by this methodology. For openers such as Jayasuriya, Greenidge, Haynes et al, wherever available, actual balls faced information is utilised.

The highest scoring rate for an opener has been achieved by Sehwag who has scored at an incredible 4.75 runs per over.

5. Average opening partnerships participated in (12.5 points).

This is a very good measure since it provides an indication of the effectiveness of the opener. Herbert Sutcliffe has averaged opening stands around 73 runs. The lowest figure is for Alec Stewart, around 36 runs.

6. Quality of the top 3 pace bowlers faced (12.5 points).

When the openers walk in at 0 for 0, they have a daunting task. If they reach lunch at xyz for 0, they would have done their job. Everything afterwards is a bonus. During these two hours or so, the opening batsmen are likely to face the three best pace bowlers of the other team. If these three happen to be Marshall, Holding and Garner as a few opening pairs faced during the 80s, as against the openers who faced Madan Lal, Amarnath and Solkar, they have to be given due credit.

The best three pace bowlers' averages are summed and averaged over the number of times the batsman opened.

Alec Stewart has faced the toughest pace bowlers with a low average of 27.75. A number of recent English opening batsmen have somewhat low figures since they have faced strong Australian attacks in frequent Ashes series. At the other end Hobbs, surprisingly, has had the easiest of opening stints at 37.09. Understandable since the non-English bowling between 1908 and 1930 was quite ordinary.

7. Quality of batting support - Other opener and next 3 batsmen (12.5 points).

Imagine Greenidge walking in with Haynes, with Richards, Kallicharan and Lloyd to follow. Or Langer walking in with Hayden with Ponting, Clarke and Hussey to follow. Contrast this with Gavaskar walking with the happy-go-lucky Srikkanth and P Sharma, Viswanath and BP Patil to follow. These are the extremes. This measure takes into account the supporting batsmen. The other opener gets highest weighting, followed by the no.3, no.4 and no.5 batsmen with progressive lower weightings. These proportionate averages are added and averaged. Higher credit is given for lower support averages.

It is clear that a strong bowler in a weak team has the benefit that he can take a greater share of wickets than a strong bowler in a strong team (Hadlee/Muralitharan against McGrath/Warne). Contrast this with batting where good support is always a boost to the batsmen.

As can be expected, Justin Langer has the best supporting batting with a figure of around 50. Don't forget that Langer had Mathew Hayden as the other opener. The one who had the least support is Chris Gayle with 33.63, despite the presence of Lara at no.4.

Table of top opening batsmen of all time

No Cty Batsman                 HmAvg  AwAvg AdjRpt ScRate OpPshp PaceBow BatSup

                       100.00  15.00  20.00  15.00  12.50  12.50  12.50  12.50

 1.Eng Sutcliffe H      72.00  12.92  15.20  11.40   5.43  11.51   7.03   8.51
 2.Ind Sehwag V         71.72  10.41  14.05  11.12   9.89   8.25   8.85   9.15
 3.Aus Simpson R.B      70.71  10.51  15.60  11.36   5.56  10.71   8.05   8.93
 4.Saf Smith G.C        69.46   9.13  15.31  10.13   7.69  10.03   7.60   9.57
 5.Eng Hobbs J.B        68.70  10.46  15.78  10.08   5.98  10.05   6.45   9.91
 6.Ind Gavaskar S.M     67.80   9.57  14.11  10.33   5.84   6.95   9.49  11.50
 7.Eng Hutton L         67.69  11.60  14.54  10.56   5.01   8.52   7.34  10.11
 8.Eng Amiss D.L        66.77  11.18  13.94  11.40   5.29   6.73   7.22  11.02
 9.Aus Hayden M.L       66.26  11.58  11.38  10.33   7.51   8.91   8.53   8.01
10.Eng Boycott G        65.55   9.68  12.77  10.14   5.01   8.40   9.09  10.46
11.Eng Vaughan M.P      65.52  11.33  10.71   9.39   6.77   9.59   7.72  10.02
12.Win Greenidge C.G    65.15   9.84  11.34   9.18   6.78   9.30   9.31   9.40
13.Pak Saeed Anwar      64.61   9.27  12.72   9.44   6.97   5.80   9.14  11.28
14.Aus Langer J.L       64.42  10.15  11.98   9.97   7.24   9.27   8.50   7.32
15.Saf Gibbs H.H        64.40   9.22  12.92   9.66   6.54   8.61   8.82   8.63
16.Eng Trescothick M.E  64.22  10.21   9.63   9.40   6.81   9.52   8.48  10.18
17.Eng Stewart A.J      64.15  10.17  11.03   9.21   6.08   5.64  11.12  10.92
18.Win Haynes D.L       63.21  11.33   8.94   8.50   6.65   8.74   9.36   9.69
19.Aus Lawry W.M        63.21  11.27  10.56   9.67   5.38   9.15   7.92   9.24
20.Eng Gooch G.A        63.10   9.56  10.12   9.16   6.03   6.82  10.39  11.03
21.Win Fredericks R.C   63.06   9.22  10.68   9.18   6.24   9.69   8.58   9.47
22.Eng Edrich J.H       62.16   9.14  11.10   9.40   5.25   8.37   9.05   9.84
23.Slk Jayasuriya S.T   62.15   8.85  10.07   8.00   8.14   8.41   8.92   9.76
24.Eng Strauss A.J      61.92   8.15  11.97   9.19   6.11   7.97   9.03   9.52
25.Aus Slater M.J       61.77  10.53   9.41   8.43   6.66   8.55   9.02   9.18
26.Win Hunte C.C        61.64  10.70  10.32   9.42   5.78   8.12   7.18  10.12
27.Win Gayle C.H        61.60   7.66  11.28   8.36   7.17   7.00   8.54  11.59
28.Aus Taylor M.A       61.25   8.68  11.63   8.65   5.37   7.42   9.82   9.69
29.Slk Atapattu M.S     60.46   8.28  12.05   8.12   5.59   8.48   8.45   9.49
30.Aus Morris A.R       60.25   7.75  14.74   8.91   5.79   6.10   7.97   8.98
31.Saf Kirsten G        59.80   7.90  11.81   8.65   5.20   6.39   9.33  10.52
32.Eng Atherton M.A     59.27   8.28   9.63   8.35   4.86   6.40  10.98  10.76
33.Aus McDonald C.C     57.65   9.53   8.89   8.40   5.01   7.34   8.02  10.46
34.Nzl Wright J.G       57.11   8.40   9.00   7.48   5.08   6.03   8.98  12.14
35.Pak Mudassar Nazar   56.04  10.43   6.87   7.20   6.25   5.81   9.02  10.47

Herbert Sutcliffe's position at the top is a well-earned one. He leads in two of the key measures

	- Home average, 
	- Average opening partnership and
	- Has a very good Away batting average of 57.00

He is only one of two batsmen, the other being Miandad, who has never fallen below 50 in their (reasonably long) career. He clocks in comfortably in the other measures. He however had good support (Hobbs/Hammond) at the other end. The bowling Sutcliffe faced was nothing great.

Sehwag's second position should not surprise any unbiased observer. His credentials are listed below.

	- 50+ averages both home and away, 
	- Almost all his top scores have been against top class bowling,
	- He has an excellent strike rate of 4.75 rpo, 
	- Has faced very good quality pace bowling almost always and 
	- He has scored only around 200 runs in 5 Tests against Bangladesh/Zimbabwe.

In fact he would have been at the top if the Strike Rate measure was, say, 15.00 instead of 12.50. That would have been a worthy position for Sehwag. He has won many matches for India through his uncompromising attacking style.

Bobby Simpson is the surprise package. The main reason is that his overall batting average is only 46.82. However his opening average is 55.52, that too, 52.55 at home and 58.48 away. His opening partnerships, mostly with Lawry, averaged 68 and he faced good quality pace bowling almost always.

Then comes Graeme Smith, who is somewhat similar to Sehwag and Hayden. He has an away average of 57.43. He loses out slightly in view of the runs scored against weaker teams, and also the quality of pace attacks faced.

Then come three great openers of yesteryears. Hobbs, Gavaskar and Hutton. Each of them could have been at the top with no questions asked. All have very good averages. Gavaskar loses in the average opening partnership but gains on the pace bowling quality and a very average middle order.

Hayden has lost out a little because of the indifferent end to his career (His average dropped by 2.5 runs during the last 10 Tests). Otherwise he would have challenged for a place in the top 5.

Readers would note that the top 10 opening batsmen comprise of 3 attacking match-winning openers of today and 7 openers of the previous eras. It is clear that for any opener of today to break into the top-10 they have to be extraordinarily good, as these three have been. One does not necessarily have to score at around 4 rpo, in which case, they have to average well above 50, both home and away and do that consistently against the top sides, not just the minnows. Being part of a good opening pair and consistently putting up above average partnerships would help.

As I had indicated earlier, I have given below Hanif Mohammad's summary figures. What is very relevent is his away batting average, which, standing at 44.05, is 20% better than his Home average. Also the total lack of support batting.

Pak Hanif Mohammad   56.62   7.37  11.75   8.01   4.38   5.44   7.17  12.50

Finally a note to the readers. One factor I keep in my mind always is that each of the measures used in all my articles should be understood by all the readers, without exception. One of the reasons I try to stay away from complex statistical measures and methodologies.

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	Brendon McCullum launched such an assault on Bangladesh that their bowlers didn't know what hit them © Getty Images

This is my second lightweight post in preparation for the serious analysis on Test Captains.

While I was perusing a table I found that there was an innings scoring rate of 15.83. I went back to the scorecard and saw what could be termed as the most devastating win in ODI history. I started thinking about such matches. Until now we have only looked at wins by huge number of runs or by 10 wickets as comprehensive wins. Now there is a different angle in terms of scoring rates.

This also enables us to look across both types of matches, whether teams win batting first or second. In both these matches the RpO differential is a clear indicator of the extent of domination. We should remember that a 10-wkt win need not be that dominating a victory. Imagine a team bats first and scores 200 in 40 overs. The chasing team bats very carefully and wins, say, in 45 overs by 10 wickets. This is certainly not a very comprehensive a win.

There are no qualifying conditions for this analysis. It is a very simple one of finding the RpO differential and ranking by this measure. I have separated the two tables so that we can have a clearer understanding of the win margins.

Let us look at the tables.

Big wins in ODI matches : Batting second

No. MtId Year FBt Score         RpO WonBy Score         RpO   RpO  Result
                                                              Diff

 1. 2660 2007 Bng  93/10 (37.5) 2.46 NZL  95/ 0 ( 6.0) 15.83 13.38 10 wkts
 2. 1776 2001 Zim  38/10 (15.4) 2.43 SLK  40/ 1 ( 4.2)  9.23  6.81  9 wkts
 3. 1940 2003 Eng 117/10 (41.0) 2.85 AUS 118/ 0 (12.2)  9.57  6.71 10 wkts
 4. 1958 2003 Can  36/10 (18.4) 1.93 SLK  37/ 1 ( 4.4)  7.93  6.00  9 wkts
 5. 1961 2003 Bng 108/10 (35.1) 3.07 SAF 109/ 0 (12.0)  9.08  6.01 10 wkts
 6. 1883 2002 Hol 136/10 (50.0) 2.72 PAK 142/ 1 (16.2)  8.69  5.97  9 wkts
 7. 1221 1997 Bng 130/ 8 (43.0) 3.02 IND 132/ 1 (15.0)  8.80  5.78  9 wkts
 8. 2172 2004 Usa  65/10 (24.0) 2.71 AUS  66/ 1 ( 7.5)  8.43  5.72  9 wkts
 9. 2521 2007 Pak 107/10 (45.4) 2.34 SAF 113/ 0 (14.0)  8.07  5.73 10 wkts
10. 1464 1999 Bng 178/ 7 (50.0) 3.56 AUS 181/ 3 (19.5)  9.13  5.57  7 wkts
11. 1758 2001 Ken  90/10 (37.1) 2.42 IND  91/ 0 (11.3)  7.91  5.49 10 wkts
12. 1963 2003 Can 202/10 (42.5) 4.72 WIN 206/ 3 (20.3) 10.05  5.33  7 wkts
13. 2575 2007 Ire  77/10 (27.4) 2.78 SLK  81/ 2 (10.0)  8.10  5.32  8 wkts
14. 2574 2007 Eng 154/10 (48.0) 3.21 SAF 157/ 1 (19.2)  8.12  4.91  9 wkts
15. 1465 1999 Sco  68/10 (31.3) 2.16 WIN  70/ 2 (10.1)  6.89  4.73  8 wkts
16. 2677 2008 Eng 158/10 (35.1) 4.49 NZL 165/ 0 (18.1)  9.08  4.59 10 wkts 
(D/L)
17. 2063 2003 Eng  88/10 (46.1) 1.91 SLK  89/ 0 (13.5)  6.43  4.53 10 wkts
18. 1891 2002 Bng 154/ 9 (50.0) 3.08 SAF 155/ 0 (20.2)  7.62  4.54 10 wkts
19. 1977 2003 Can 196/10 (47.0) 4.17 NZL 197/ 5 (23.0)  8.57  4.40  5 wkts
20. 2026 2003 Pak 185/10 (44.0) 4.20 ENG 189/ 3 (22.0)  8.59  4.39  7 wkts

The first match in this table defies description. Bangladesh is not a weak team such as Hong Kong or Bermuda are. It is not clear what prompted McCullum's assault on the hapless Bangladesh bowlers. Maybe a Bangladeshi remark on beating New Zealand before the match or a personal comment on McCullum. Anyhow here are the details. Bangladesh, batting first, scored 93 in 38 overs and would have expected to pick up a wicket or two in 20 overs during which New Zealand would have cantered towards a comprehensive win.

What happened cannot be forgotten. New Zealand scored these 95 runs in 6 overs at a rate of 15.83, the highest for an innings, by a margin of over 50%, in ODI history. McCullum scored 80 in 28 balls, the second fastest completed 50+ innings in history. The difference in RpO is 13.38. The mind goes blank.

Given below is McCullum's scoring sequence. 6x6s, 9x4s and only 7 dot balls. Makes great viewing on print and should have made greater viewing, in person. Shahid Afridi, being the only batsman with a 100+ strike rate, who I consider the most attacking batsman ever in ODI cricket would have been proud to own this innings.

4 . 4 4b . 4 6 4 6 . . 2 . 4 4 6 4 1 2 1 6 . 6 2 4 6 . 4

Look at the next entry. In terms of RpO difference, it is almost half of the first. Sri Lanka, chasing the third lowest ever ODI total of 38, reached this target in over 4 overs. McCullum might have reached in 2 overs. The blast in this match did not come from batsmen but from Vaas who took 8 for 19.

The third match is interesting. England were dismissed for 117 and then mayhem. Gilchrist and Hayden (the vintage Hayden, not the 2008 imposter) reached this target in 12 overs (including 22 boundaries).

The West Indies innings rate of 10.05, in the 12th match against Canada, is the secong highest innings scoring rate, one of only two exceeding 10.0. This was a great performance since as many as 206 runs were scored in just over 20 overs, during which 36 boundaries were scored.

Note the number of 10-wicket wins. There are 8 such wins in the top 20. Also the number of times England have been at the receiving end of such margins, four in all, sharing the lead with Bangladesh.

It is surprising that 6 of these losses have been inflicted on the top teams, England 4 times and Pakistan 2 times. Sri Lanka and South Africa lead with 4 wins each.

Big wins in ODI matches : Batting first

No. MtId Year WonBy Score       RpO  Vs  Score         RpO  RpO   Result
                                                            Diff  Won by

 1. 2537 2007 SAF 353/ 3 (40.0) 8.82 Hol 132/ 9 (40.0) 3.30 5.53 221 runs
 2. 2542 2007 IND 413/ 5 (50.0) 8.26 Ber 156/10 (43.1) 3.61 4.65 257 runs
 3. 2716 2008 IND 374/ 4 (50.0) 7.48 Hkg 118/10 (36.5) 3.20 4.28 256 runs
 4. 2272 2005 NZL 397/ 5 (44.0) 9.02 Zim 205/10 (43.0) 4.77 4.26 192 runs
 5. 2727 2008 NZL 402/ 2 (50.0) 8.04 Ire 112/10 (28.4) 3.91 4.13 290 runs
 6. 1652 2000 SLK 299/ 5 (50.0) 5.98 Ind  54/10 (26.3) 2.04 3.94 245 runs
 7. 0297 1985 AUS 323/ 2 (50.0) 6.46 Slk  91/10 (35.5) 2.54 3.92 232 runs
 8. 2376 2006 ZIM 338/ 7 (50.0) 6.76 Ber 144/ 7 (50.0) 2.88 3.88 194 runs
 9. 1763 2001 SAF 354/ 3 (50.0) 7.08 Ken 146/10 (45.3) 3.21 3.87 208 runs
10. 1599 2000 PAK 320/ 3 (50.0) 6.40 Bng  87/10 (34.2) 2.53 3.87 233 runs
11. 0531 1988 PAK 284/ 3 (45.0) 6.31 Bng 111/ 6 (45.0) 2.47 3.84 173 runs
12. 0457 1987 WIN 360/ 4 (50.0) 7.20 Slk 169/ 4 (50.0) 3.38 3.82 191 runs
13. 2390 2006 SLK 443/ 9 (50.0) 8.86 Hol 248/10 (48.3) 5.11 3.75 195 runs
14. 0951 1994 SLK 296/ 4 (50.0) 5.92 Zim 105/10 (48.1) 2.18 3.74 191 runs
15. 2169 2004 NZL 347/ 4 (50.0) 6.94 Usa 137/10 (42.4) 3.21 3.73 210 runs
16. 1764 2001 IND 351/ 3 (50.0) 7.02 Ken 165/ 5 (50.0) 3.30 3.72 186 runs
17. 1868 2002 AUS 332/ 5 (50.0) 6.64 Pak 108/10 (36.0) 3.00 3.64 224 runs
18. 0405 1986 WIN 248/ 5 (45.0) 5.51 Slk  55/10 (28.3) 1.93 3.58 193 runs
19. 2420 2006 SAF 418/ 5 (50.0) 8.36 Zim 247/ 4 (50.0) 4.94 3.42 171 runs
20. 2532 2007 AUS 334/ 6 (50.0) 6.68 Sco 131/10 (40.1) 3.26 3.42 203 runs

It is necessary to understand the reason why South Africa's win over Holland (by 221 runs) is placed ahead of India's win over Bermuda (by 257 runs). The first was over 40 overs while the second was over 50 overs. New Zealand's win by 290 runs over Ireland has an RpO differential of only 4.13 since Ireland scored quite freely.

India has two of the most comprehensive wins in the top 5 while New Zealand also has two. But all these 5 matches are against the minnows.

The most comprehensive "relevant" win was Sri Lanka's 245 run win over India. Jayasuriya and Vaas contributed to this demolition job.

Five of the losses have been sustained by the top teams, Sri Lanka sustaining such heavy defeats thrice, all during mid-1980s. Quite a few teams, including Sri Lanka have done this thrice in the top-20 table.

	Mahela Jayawardene and Kumar Sangakkara were involved in a stand that yielded more than 77% of their team's total runs against South Africa in Durban in 2000 © AFP

Since I have started work on a rather heavy and probably contentious analysis of Test captains, I have, inter alia, worked on a couple of interesting single-topic single-table posts, the first of which is this one.

All of us are familiar with the exploits of one batsman in a single innings. This list is led by Charles Bannerman who scored an unbeaten 165 out of 245 in the first ever Test innings played. This value of 67.3% has remained unsurpassed during all these 130 years. Slater came close with 66.8% and Laxman's Sydney masterpiece clocked in at 64.0%. It is not an easy task to score over two-thirds of the team total as proved by the longevity of Bannerman's achievement.

I started thinking about this type of a dominance, but from a partnership point of view. I wondered about single dominating partnerships, and very little else. The possibilities are fascinating. A huge partnership and very little else means that there exist(s) one or more huge batting collapses.

If this partnership was for an early wicket, there had to be an immediate batting collapse afterwards. If this was for one of the middle wickets, there have been batting slumps either side of the partnership. However, if there was a big partnership for a late wicket such as ninth, the batting team was looking at a huge disaster and possibly recovered.

With this background, let us look at the table. The only criteria I have considered is that a team has to be all out. This is the only way to ensure that the stated objective is met correctly. Otherwise India's score of 410 for 1, consisting of an opening partnership of 410 will, incorrectly, qualify. Similarly Amla's and Kallis' partnership of 330 out of a South African score of 422 for 3 will, mistakenly, qualify. Just two examples to illustrate the idea.

The excellent partnership between Strauss and Collingwood at Chennai, although not enough to prevent a great win by India, had a high 68.8% share of the team score. However this could not be considered since Pietersen declared the England innings. On the other hand, the dominating partnership of Gambhir and Dravid at Mohali would have made the cut in the appropriate table with a % of team total figure of 69.3.

Table of high % partnerships

No Year Test I For    Oth Ptshp  (Wicket)       Tot   %

 1.1999 1451 2 WIN vs Aus 344 for Fifth wkt    (431-79.8%)
            (Lara 213* & Adams 94)

 2.2000 1526 2 SLK vs Saf 168 for Third wkt    (216-77.8%)
            (Sangakkara 74 & Jayawardene 98)

 3.1882 0007 2 AUS vs Eng 199 for Fourth wkt   (260-76.5%)
            (ACBannerman 70 & McDonnell 147)

 4.1968 0642 2 AUS vs Win 217 for Second wkt   (284-76.4%)
            (Lawry 105 & IM Chappell 117)

 5.1952 0351 1 IND vs Eng 222 for Fourth wkt   (293-75.8%)
            (Hazare 89 & Manjrekar 133)

 6.1985 1022 1 ENG vs Aus 351 for Second wkt   (464-75.6%)
            (Gooch 196 & Gower 157)

 7.1999 1477 1 WIN vs Nzl 276 for First wkt    (365-75.6%)
            (Griffith 114 & Campbell 170)

 8.2001 1547 2 ENG vs Pak 267 for Third wkt    (357-74.8%)
            (Vaughn 120 & Thorpe 138)

 9.1967 0623 3 PAK vs Eng 190 for Ninth wkt    (255-74.5%)
            (Asif Iqbal 146 & Intekhab 51)

10.1985 1016 3 NZL vs Win 210 for Second wkt   (283-74.2%)
            (Howart 84 & JJ Crowe 112)

The highest share of a single partnership is at a very high level of 79.8%. West Indies slumped to 34 for 4 when Lara and Adams got together and added 334 for the fifth wicket. Then West Indies slumped 378 for 5 to 431 all out. This follows the scenarios of two mini-collapses.

Sri Lanka lost the first 2 wickets for 2 runs. Then Sangakkara and Jayawardene added 168 and took them to 170 for 2. From this position they lost 8 wickets for 46 runs.

Similar story in the third entry. England slips to 15 for 3, then 199 gets added and then 7 wickets for 45 runs. All these three follow the same pattern.

Let us look at the seventh entry. Griffith and Campbell added 276 for the first wicket. Then all 10 wickets were lost for 89 runs. But the story does not end there.

From 276 for no loss West Indies lost their next 40 wickets for 599 runs and lost the series 0-2. Lara gave up the captaincy.

The ninth entry is interesting. Pakistan, 234 behind, collapsed to 65 for 8. Then Asif Iqbal and Intikhab Alam added a record 190 runs for the ninth wicket and avoided an innings defeat. Asif Iqbal's 146 was a wondeful essay of defiance.

The other partnerships which exceed 70% of the team total are shown below.

11.1927 0068 2 ENG vs Saf 230 for Second  wkt  (313-73.5%)
12.1946 0277 2 IND vs Eng 124 for First   wkt  (170-72.9%)
13.1999 1472 2 AUS vs Pak 327 for Fifth   wkt  (451-72.5%)
14.1993 1240 4 ZIM vs Pak 135 for Second  wkt  (187-72.2%)
15.1933 0230 3 IND vs Eng 186 for Third   wkt  (258-72.1%)
16.2001 1551 3 ZIM vs Win 164 for First   wkt  (228-71.9%)
17.1997 1391 2 PAK vs Win 298 for First   wkt  (417-71.5%)
18.2000 1494 1 PAK vs Win 206 for Sixth   wkt  (288-71.5%)
19.1980 0875 1 WIN vs Nzl 162 for Fourth  wkt  (228-71.1%)
20.1912 0129 4 AUS vs Eng  46 for Second  wkt  ( 65-70.8%)
21.2005 1774 3 ENG vs Pak 175 for Third   wkt  (248-70.6%)
22.1960 0497 1 PAK vs Ind 246 for Second  wkt  (350-70.3%)
23.1907 0093 2 SAF vs Eng  98 for Fourth  wkt  (140-70.0%)

A footnote to the previous article on Australia:

South Africa let go many opportunities during the Perth Test. However they took advantage of the last one offered in a decisive manner and this wonderful win by South Africa, against all odds, has clearly proved that Australia have genuinely lost their edge. This is not just a passing phase. Not that they would drop down like West Indies in the 90s. They would still be one of the 3/4 teams which compete for the top spot.

India's tactics on the fourth and fifth days at Mohali were disappointing. Unfortunately individual records again took priority over team requirements. A very aggressive captain would have declared at the start of play on the fifth day. A positive captain would have declared at 175 for 4. Unfortunately, at least during this test, Dhoni has shown to be neither.

Before anyone pounces on me, please read further. The way India played in this Test is perfect for a team aspiring for the second position but not sufficient if India is aiming to unseat Australia from the top position. All efforts should have been made for a 2-0 result, even accepting a 5% possibility of a 1-1 result.

Please peruse this excellent Cricinfo article by S Aga, if you have not already done so.

Holders of the record for most Test runs

From Match Number	Player	Tests Record Held	Final Runs	Starting	Days Record Held
1	C Bannerman	4	239	19/03/1877	1752
5	G Ulyett	11	676	04/01/1882	952
16	WL Murdoch	8	860	13/08/1884	731
24	A Shrewsbury	43	1277	14/08/1886	5641
67	J Darling	1	1293	23/01/1902	26
68	SE Gregory	3	1366	18/02/1902	116
71	AC MacLaren	3	1531	14/06/1902	42
74	C Hill	84	3412	26/07/1902	8374
158	JB Hobbs	102	5410	27/12/1924	4567
260	WR Hammond	414	7249	29/06/1937	12209
674	MC Cowdrey	21	7459	02/12/1970	482
695	GStA Sobers	219	8032	28/03/1972	3562
914	G Boycott	53	8114	28/12/1981	688
967	SM Gavaskar	248	10122	16/11/1983	3392
1215	AR Border	558	11174	28/02/1993	4657
1773	Brian Lara	116	11953	29/11/2005	1057
1889	SR Tendulkar	1	12037	21/10/2008	-

This offering is less an analysis than a useful table to ensure you dominate at quiz nights. Alternatively, you may be able to impress your workmates at a tea break with your far-reaching knowledge. Questions you will now be able to answer include:

• Who has held the record for the longest time? (Wally Hammond)
• Who has held the record for the most number of Tests? (Allan Border)
• Which player held the record for just one Test? (Joe Darling)
• How many players have held the record? (seventeen)
• How many players held the record in the 1902 calendar year? (five)
• Who was the only player to hold the record posthumously? (Hammond)
• How many currenly-living players have held the record? (six)
• Which country has provided the most players to hold the record? (England, seven)

Note: The dates used are the dates of the last day of the Test in which the record was achieved, rather than the actual date on which it was achieved.

I was keen to observe whether or not Bangladesh has made material progress since it won full ODI status ten years ago. To do this, I took the 17 bilateral one-day series of three matches against Test-playing opposition (and excluding Zimbabwe) that it has participated in over that time, and extracted the batting average of Bangladesh and its opponents in those series:

Comparing Bangladesh's batting average with opposition's in ODIs

Season	Versus	Opp. batting ave	Bangla batting ave	Batting ratio
2001-02	Pakistan	41.41	23.28	0.56
2002	Sri Lanka	43.31	17.93	0.41
2002-03	South Africa	55.27	15.10	0.27
	West Indies	51.38	20.30	0.40
2003	Australia	50.90	13.13	0.26
	Pakistan	45.03	23.23	0.52
2003-04	England	51.78	15.83	0.31
	West Indies	20.42	15.78	0.77
2004-05	New Zealand	25.92	14.78	0.57
	India	35.09	27.69	0.79
2005-06	Sri Lanka	29.09	22.48	0.77
	Australia	47.75	16.73	0.35
2007	Sri Lanka	27.19	15.27	0.56
2007-08	New Zealand	70.33	18.27	0.26
	South Africa	72.29	16.47	0.23
	Pakistan	47.54	22.84	0.48
2008	Australia	38.00	10.90	0.29

The ratio in the last column is obtained by dividing Bangladesh’s batting average by the average of the opposition. It will be noted that all these values are less than 1, indicating that on no occasion has Bangladesh been able to match it with the opposition.

	Click here for a bigger image © Ric Finlay

Bangladesh had some poor results early, particularly against South Africa and Australia, but there was a perceptible improvement from 2004, giving hope that it would soon match it with allcomers. However, they have let the standard lapse significantly in the last year or so, and three of its worst five performances have occurred in the last twelve months.

Using an Excel chart, I plotted these results on a graph, and asked the software to superimpose a trend line. As can be seen in the graphic, the trendline has a negative slope, indicating that Bangladesh’s performances are in fact deteriorating. It appears that much work needs to be done with the cricketers in that country yet. With so many big names moving over to the ICL, the task becomes even more difficult for Bangladesh.

It is with great interest that I read Ananth Narayanan’s analysis of one-day players. Independently, our database provides a ranking of batsmen, which first of all adjusts each innings played according to batting conditions and the quality of the opposition bowling, then takes these adjusted scores and combines them with the scoring rate and also longevity in the game to provide a career batting quality measure. The results are given here below:

The best ODI batsmen

Rank	Player	Bat Quality	M	Runs	Ave	100s	R/100b
1	Sachin Tendulkar	94.69	417	15481	41.95	34	80.83
2	Vivian Richards	87.92	187	6692	46.80	10	89.83
3	Michael Bevan	87.08	232	6695	51.90	3	72.00
4	Ricky Ponting	83.05	301	10422	40.55	15	75.33
5	Michael Hussey	82.35	93	2252	52.37	1	78.83
6	Brian Lara	80.59	299	9952	38.72	12	75.83
7	Jacques Kallis	80.02	279	9107	42.36	11	67.50
8	Adam Gilchrist	79.09	287	9031	33.70	12	91.00
9	Sanath Jayasuriya	79.01	421	11977	30.63	20	85.33
10	Inzamam-ul-Haq	78.90	378	11054	37.22	8	69.83
11	Kevin Pietersen	78.12	82	2699	45.75	5	83.67
12	Sourav Ganguly	77.95	311	10476	37.82	16	68.00
13	Mahendra Singh Dhoni	77.31	120	3484	43.55	3	83.83
14	Mohammad Yousuf	77.19	269	8522	39.82	7	69.50
15	Dean Jones	77.03	164	5921	43.54	7	70.83
16	Rahul Dravid	76.91	333	10064	37.55	7	67.67
17	Mark Waugh	76.00	244	8162	37.79	12	73.83
18	Saeed Anwar	75.68	247	8263	36.72	11	75.50
19	Zaheer Abbas	75.47	62	2425	44.91	4	80.00
20	Desmond Haynes	75.08	238	8447	40.42	17	61.67
21	Andrew Symonds	75.02	193	4709	37.98	4	87.50
22	Aravinda de Silva	74.83	308	8977	33.75	11	78.33
23	Javed Miandad	74.69	233	7226	40.82	6	65.50
24	Mohammed Azharuddin	74.60	334	9058	35.66	4	71.50
25	Lance Klusener	74.48	171	3458	39.75	1	86.83
26	Matthew Hayden	74.19	161	5663	40.45	8	72.83
27	Gary Kirsten	73.58	185	6557	39.50	10	69.50
28	Gordon Greenidge	72.72	128	4963	43.54	6	62.67
29	Shivnarine Chanderpaul	72.17	235	7128	38.12	3	66.50
30	Hansie Cronje	71.84	188	5447	37.83	5	74.83

The top two players are, as with Ananth’s scheme, Tendulkar and Richards, with the former enjoying a significant lead over the latter. Seven of Ananth’s top ten are in our top ten. But whereas Ananth has Haynes, Javed Miandad and Symonds, we have Hussey, Lara and Kallis. Two notable absentees in Ananth’s top 30 who rank quite highly in ours are Pietersen and Dhoni, 11th and 13th respectively.

Given that limited-overs cricket is all about scoring runs, and scoring them quickly,a much simpler algorithm to arrive at the best ODI batsmen is to multiply the batting average by the scoring rate, and divide the product by 1000 to reduce the magnitude of the result. This requires a minimum qualification of (in this case) 50 matches, otherwise the well known Canadian, Rizwan Cheema, heads the list after only three ODIs! This method will favour modern players because of increased scoring rates in modern times, but we find that Zaheer Abbas and Viv Richards still make the top eleven:

Combining batting average and scoring rate

Rank	Player	Index	M	Runs	Ave
1	Michael Hussey	4.91	93	2457	57.14
2	Mahendra Singh Dhoni	4.33	120	3793	47.41
3	Vivian Richards	4.24	187	6721	47.00
4	Kevin Pietersen	4.19	82	2822	47.83
5	Zaheer Abbas	4.04	62	2572	47.63
6	Michael Bevan	3.99	232	6912	53.58
7	Sachin Tendulkar	3.79	417	16361	44.34
8	Andrew Symonds	3.76	193	5006	40.37
9	Lance Klusener	3.69	171	3576	41.10
10	Adam Gilchrist	3.48	287	9619	35.89
11	Ricky Ponting	3.48	301	11113	43.24

The largely-forgotten Klusener rates well, but apart from him, they all are prominent in the both Ananth’s table, and mine above.

	Viv Richards takes the top spot among ODI batsmen again © Getty Images

The large number of comments received and the very valid points mentioned in these have made me come out with a follow-up to my article on the best ODI batsman. In the article itself I had mentioned the following points as worthy of consideration for possible tweaks. I see no additions to these now.

1. Avoidance of double weighting for "Wins".
2. Possible cap on runs scored weightage.
3. Adjust for the paucity of matches played during the early 10 years.
4. Giving weight to key tournament wins such as World Cup and Champion's Trophy.
5. The subjective nature of MOMs, already mentioned by me in the main post did not go well with readers.
6. Quite a few readers have, while accepting Tendulkar's position at no.1, have questioned the wide gap between Tendulkar and Richards. It worries some readers that this gap will keep on widening. Let me deal with these one by one. The last point is automatically taken care of by the tweaks.

1. Wins weightage and avoiding double weightage:

Ultimately winning has to carry some weightage in any analysis. Why do we respect and admire the 1980s West Indian teams. Not just because they had great players but because they won more than a fair share of the matches played. The recent Australian team might not be as admired as the earlier West Indian teams. However they are certainly respected, by peer players and viewers alike. I have looked at this carefully and have decided not to do any changes. The Win% does not seem to have any problems. The actual Wins had some comments but that carries only 5% weightage.

2. Possible cap on runs scored weightage and adjusting for the paucity of matches played during the early 10 years.

I have combined these two points. First I considered putting a cap on the runs scored weightage. The problem is that whatever figure I choose as the cap, it will only affect the very few players above that cap. For instance if I fix the cap at 10.0 points, only the 7 batsmen who have scored above 10,000 runs will be affected. That seems too arbitrary and discriminatory to me. The purpose would only be to put down a few players which is wrong.

The better alternative would be to leave the runs scored weightage as it is and adjust the early players' runs scored points upwards by an acceptable factor. This also means that we would increase certain players' rating points, for a valid reason, and not penalise a few.

After a few trials and errors, I have come out with the following formula which, I feel, would be acceptable to most readers and critics. This is a linear and simple formula.

No. of years played by the batsman: YEARS

Total number of matches played during these years: MATCHES
                     
                     YEARS x 75
Multiplying Factor = ----------
                      MATCHES

Runs scored Index points = Runs scored Index points x Multiplying Factor.

Note: 75 is the average number of matches played per year during the period 1971-2008. Taking the average over all the 38 years will be less beneficial to the earlier era batsmen than taking the average, say, over the recent 10 years, working to 140. I am ready to accept this since the last 10 years have seen the ridiculuous peak of 191 matches during 2007 and so on. We have to allow for the natural growth patterns being maintained.

Example of Richards' adjustment
-------------------------------
Career span: 16 years (1975 to 1991)
Matches during career: 657 (22:first to 678:last)
Adjusting Factor: (16 x 75) / 657 = 1.8264
Richards' Runs scored index value = 6721/1000 = 6.721
Adjusted Runs scored index value = 6.721 x 1.8264 = 12.28

This looks eminently fair and equitable. What this tweak says is that if there had been more matches played during Richards' career of 16 years, he would have played in 341 matches and scored 12,280 runs. The only assumption is that the batsmen would have maintained their average. This is a very fair assumption.

I have taken all the matches played as the basis instead of the matches played by the batsman's country since this is a better method over a long period of time. Also the matches skipped do not play any point.

There is no doubt that the readers will come out with simple and complex alternatives to this segment. No denying that these may also be better. However I have gone on a simple, easy-to-understand-and-implement algorithm. The objective of redressing the balance between today's batsmen and earlier batsmen has been achieved.

Care is taken that if the Multiplying Factor is < 1.0, the adjustment does not take place. In other words no current player is penalised.

3. Giving weight to World Cup and Champion's Trophy wins & avoiding the subjective weighting for MOMs:

Readers will note that the MOM issue was raised by me in the original article itself. I myself am concerned with the subjective nature of MOMs and the fact that for many years batsmen got the preference while assigning MOMs. I cannot also deny the validity of statements asking for weight to be given for World Cup successes. These are once-in-four-years grand events and doing well in these is very essential for all top batsmen. I have also considered the 5 ICC/Champion's Trophys, this being second only to the 9 World Cups. No other tournament has been considered. With one stroke I have taken care of these two points.

What I have done is to completely remove the MOM weightings. Indtead the 5 points are allocated for Major Cup wins in the following manner.

World Cup wins: 1.0 point.
World Cup finalists: 0.5 point.
ICC/Champions' Trophy wins: 0.5 point.

Both Sri Lanka and India which shared the 2002 ICC Trophy get 0.5 point each. Again there may be arguments. However let me say this. One can argue till the cows come home, go out and then come home again, there is no single perfect answer. With 5 points available for allocation, this seems to be very fair. The top point scorers are given below.

Ponting: 4.0 points (3 WC wins + 1 WC finalist + 1 ICT win).
Gilchrist: 3.50 points (3 WC wins + 1 ICT win).
Richards: 2.50 points (2 WC wins + 1 WC finalist)
...
Tendulkar: 1.00 points (1 WC finalist + 1 ICT win)

It can be seen that Richards and Tendulkar, each with a WC finalist tag, are not too far apart. Also Tendulkar could add to his silverware.

Let us now look at the revised table.

ODI : The best batsmen ever - upto match no 2759 (31 Aug 2008)

No Cty Batsman          Total  Runs  Avge  R/I  S/R  BwQty Wins Win% % TS WC/Icc

                        100.0  20.0  15.0  5.0  25.0  15.0  5.0  5.0  5.0  5.0

 1.Win Richards I.V.A   77.37 12.28 11.75 4.02 24.60 12.20 2.64 3.53 3.85 2.50
 2.Ind Tendulkar S.R    75.96 16.36 11.08 4.02 21.16 12.13 4.12 2.47 3.61 1.00
 3.Aus Ponting R.T      73.09 11.11 10.81 3.81 19.63 12.63 4.32 3.59 3.19 4.00
 4.Aus Gilchrist A.C    71.73  9.62  8.97 3.45 23.59 12.12 4.04 3.52 2.93 3.50
 5.Slk Jayasuriya S.T   70.61 12.80  8.18 3.13 22.52 12.01 4.44 2.64 2.89 2.00
 6.Aus Bevan M.G        67.96  6.91 13.40 3.53 18.31 13.88 3.10 3.34 3.00 2.50
 7.Win Haynes D.L       66.93 12.38 10.34 3.65 16.74 12.16 3.18 3.34 3.63 1.50
 8.Pak Inzamam-ul-Haq   66.74 11.74  9.88 3.35 18.31 11.81 4.28 2.83 3.04 1.50
 9.Pak Javed Miandad    65.21 11.04 10.43 3.39 17.98 13.04 2.38 2.55 3.40 1.00
10.Aus Symonds A        65.20  5.01 10.09 3.19 22.41 12.58 2.98 3.86 2.58 2.50
11.Win Lara B.C         65.19 10.40 10.12 3.60 19.64 12.38 2.78 2.33 3.43 0.50
12.Saf Kallis J.H       65.15  9.61 11.17 3.64 17.33 12.98 3.50 3.15 3.26 0.50
13.Win Greenidge C.G    64.65  9.45 11.26 4.04 17.70 10.49 1.80 3.52 3.88 2.50
14.Aus Waugh M.E        64.49  8.50  9.84 3.60 19.39 12.29 3.04 3.11 3.22 1.50
15.Aus Hayden M.L       64.08  6.13 10.95 3.96 19.36 12.26 2.38 3.70 3.34 2.00
16.Ind Dravid R         64.00 10.59  9.87 3.44 17.36 13.25 3.14 2.36 3.00 1.00
17.Ind Ganguly S.C      63.84 11.36 10.26 3.79 18.14 10.64 2.98 2.40 3.27 1.00
18.Slk de Silva P.A     63.47  9.28  8.73 3.14 20.61 12.52 2.56 2.08 3.06 1.50
19.Aus Waugh S.R        63.24  7.57  8.23 2.63 19.26 13.75 3.92 3.02 2.38 2.50
20.Pak Saeed Anwar      62.98  8.82  9.80 3.62 20.20 10.95 2.82 2.85 3.42 0.50
21.Win Lloyd C.H        62.88  5.74  9.77 2.83 22.05 12.17 1.32 3.79 2.71 2.50
22.Aus Chappell G.S     62.82 10.70 10.05 3.24 21.60 10.27 0.70 2.36 3.39 0.50
23.Aus Jones D.M        62.26  6.99 11.15 3.77 18.86 11.99 1.96 2.99 3.55 1.00
24.Pak Mohammad Yousuf  61.81  9.24 10.80 3.64 18.19 10.81 3.12 2.90 3.12 0.00
25.Saf Rhodes J.N       61.75  5.93  8.78 2.70 20.11 15.00 3.10 3.16 2.46 0.50
26.Aus Hussey M.E.K     61.61  2.39 13.91 3.47 20.54 12.26 1.30 3.57 2.68 1.50
27.Ind Sehwag V         61.36  5.81  8.11 3.12 23.82 12.41 1.90 2.49 2.70 1.00
28.Saf Gibbs H.H        61.31  7.59  9.12 3.39 20.24 11.95 2.88 3.12 3.03 0.00
29.Pak Zaheer Abbas     61.23  6.53 11.91 4.29 22.42  8.82 0.60 2.42 4.25 0.00
30.Ind Azharuddin M     61.21  9.38  9.23 3.04 18.97 12.09 3.20 2.40 2.90 0.00

Richards has gained on two indices, the run scored index and Cup wins index. These are sufficient to move him just ahead of Tendulkar. Tendulkar could catch up with Richards by scoring additional runs while maintaining his average and run-rate figures. He could also win the World Cup and/or Champions' Trophy.

Ponting, Gilchrist and Jayasuriya exchange places. Bevan, Haynes, Miandad and Symonds move up. Lara, Kallis and Ganguly move out of the Top 10.

What is important is that in the earlier top-10 group there was only one player from an earlier era, Richards. Now we have three players, all great ones worthy of this placing. These are Richards, Haynes and Javed Miandad.

To view the complete list, click here

A final note to the readers.

Richards was the uncrowned king of his era between 1975 and 1990. Tendulkar similarly was the greatest batsman of his era, between 1990 and now. These are the two greatest batsmen of all time. The top placement of either of these batsmen does not demean the other. To recognise Richards' greatness it is not necessary to put Tendulkar down. Similarly Tendulkar need not be deified by villifying Richards. You would honour your own favourite batsmen if you recognise the greatness of the other great batsmen. Neither of them needs nor deserves blind hero worship. Simply accept that they are the two greatest ODI batsmen ever.

Did Richards cause the loss of 1983 WC for West Indies. Did Tendulkar cause the loss of the 2003 WC for India. No way. It was the collective inability of the respective losing teams to rise to the occasion which lost them the matches. To be fair, it was the totally committed way India played in 1983 and Australia played in 2003 which made them deserved winners. Any other interpretation takes credit away from the winning teams' performances.

A similar situation exists with the 1992 and 1996 World Cups. Imran Khan, Inzamam, Miandad, Wasim Akram, Aaqib and Mushtaq all contributed to a great Pakistani win. Four years later, Aravinda D'Silva, Gurusinha and Ranatunga fashioned a wonderful victory. I suggest you savour these great moments instead of arguing about odd failures.

Let me also mention that I would not have gone ahead with these tweaks if I had not been convinced of the validity of such changes. It is difficult for me to acknowledge specific readers since there were many who sent in invaluable comments. My thanks to all these discerning readers.

There will be no follow-up to this follow-up article. Comments will be published only if they respect the writers, other readers and more importantly players, all of them great ones. And, please, positively none of these "XYZ IS THE GREATEST." type of messages.

	Sachin Tendulkar pips Viv Richards to the top of the list © AFP

I started this. So I have to finish it...

It is amusing. A few days back whole lot of people were lambasting me for not having Tendulkar on top. Now another set of people are screaming that Tendulkar is on top. Hey guys, this is only an analysis. I am one insignificant analyst who works with a computer and a Cricket database. The greats remain greats, whatever I (or for that matter you all) say.

Just one more thing. Unlike what some have suggested, I have not gone out of the way to put Tendulkar on top. He is one of the greatest but NOT my favourite batsman.

As done before I have incorporated a summary response to readers' comments at the end.

In my previous article I had taken two important ODI batting measures and attempted to analyse batsmen skills using those. It elicited the usual comments on the additional parameters for consideration. Hence instead of doing a straightforward follow-up to that analysis, I have gone the whole hog and after considering all relevant parameters, come out with what I feel should be a very fair ODI batsmen ranking based on what they have achieved over their careers.

The following 8 facors are considered.

1. Total runs scored (TRS)
2. Batting Average (AVGE)
3. Runs per Innings (RPI)
4. Strike Rate (STRT)
5. Quality of bowlers faced (BOWQTY)
6. % of Team runs (TRPER)
7. Wins achieved 
   - Absolute number of wins (WINS)
   - Win % of matches played (WINSPER)
8. MOM awards received/frequency (MOM).

A brief description of each factor and the weights given to each parameter is outlined below. The total points add up to a nice round sum of 100.

1. Total runs scored (20 points)

This is a recognition of the longevity of the player. There is no doubt that the runs scored has to be given decent weightage. At the same time care has been taken to see that the olden era players such as Richards, Greenidge et al do not suffer unduly. My belief is that it is very unlikely for any batsman, including Tendulkar, to exceed 20000 runs. Hence the limit seems correct. The formula used is

• TRS = Total runs scored / 1000.

2. Batting Average (15 points)

This is a straightforward calculation. We need not worry about not-outs since there is a separate factor for that. Since the batting average is unlikely ever to exceed 60.0, we are within the maximum level. The formula used is

• AVGE = Batting average / 4.0.

Note: David Barry is doing some simulation work with a view to establish a correlation between Average and Strike Rates. It is too early to incorporate these first level findings. Hence at this stage I have taken the simple, easily understandable method of separating the Average and Strike Rate measures with individual weightages. Similarly Jeff Grimshaw's ideas about treating balls played as a resource and giving credit for the same is quite good. However I do not want too many overlapping parameters. Already I have Average and RPI.

3. Runs per Innings (5 points)

This is to mitigate the factor of a high number of not-outs, especially for middle-order batsmen. Again a straightforward calculation. Since the Batting average is unlikely ever to exceed 50.0, we are within the maximum level. The formula used is

• RPI = Runs per innings / 10.0.

Note: I briefly toyed with Abhihjeet Dongre's excellent suggestion of excluding from the total number of innings the innings in which the batsman has finished not out at a score below his batting average. This redresses the balance towards middle order batsmen slightly. However I have finally rejected this tweak since I feel that they have already got the full benefit of not outs while calculating the Batting Average. The purpose of separation of these two factors will be lost if I do not use the full complement of innings played.

4. Strike Rate (25 points)

I consider this factor as the most important measure and that is reflected in the weightage. However much we talk about the importance of scoring runs, it is essential that these are scored at a reasonable pace. It does not mean that every century should be a run-a-ball one. However, it is true that many a match has been lost because the batsmen have not moved up the scoring rate at the right time.

However a major tweak has been done. The actual strike rates have been adjusted up or down based on the decade scoring rates pro-rata. In other words, if Viv Richards played between 1975 and 1991, his actual scoring rate has been adjusted pro-rata for the three decades, viz., 1970s, 1980s and 1990s. In general this will mean that the older players will get a slight benefit since the scoring rates were lower, as indicated in the table below.

                          AllMats   1970s   1980s   1990s   2000s

Matches played               2759      82     516     933    1228
Batsmen innings             47947    1418    8838   16266   21425
Runs scored               1142018   30292  202884  386508  522334
Balls bowled              1473233   46208  277516  505727  643782
Runs per ball               0.775   0.656   0.731   0.764   0.811
% of all-matches avge      100.0%   84.6%   94.3%   98.6%  104.7%

The actual and adjusted strike rates for a few top players is given below. All these adjustments seem very reasonable. The only clear cases are for batsmen such as Pietersen and Dhoni who have played all their matches in the current decade and hence have the same adjustment of -4.4%. The others are pro-rata. For instance, Tendulkar's and Lara's strike rates have been adjusted much less since they have played during 1980s, 1990s and 2000s. Zaheer Abbas gains the maximum since his career spanned 1975-1985, the low-scoring years.

Batsman         Prev SR   Adj SR   % chg

Richards I.V.A    90.2     98.4    +9.1%
Haynes D.L        63.1     66.9    +6.0%
Jones D.M         72.6     75.4    +3.9%
Greenidge C.G     64.9     70.8    +9.1%
Zaheer Abbas      80.0     89.7   +12.1%

Tendulkar S.R     85.5     84.6    -1.1%
Jayasuriya S.T    91.0     90.1    -1.1%
Gilchrist A.C     96.9     94.4    -2.7%
Lara B.C          79.5     78.6    -1.3%
Sehwag V          99.1     95.3    -3.8%
Shahid Afridi    111.2    108.2    -2.7%
Klusener L        89.9     88.2    -1.9%
Dhoni M.S         91.3     87.2    -4.4%
Pietersen K.P     87.5     83.6    -4.4%

Since the only Strike Rate to exceed 1.00 is that of Shahid Afridi, I have accepted the fact that only he will exceed the maximum level. The formula used is

• STRT = (Adjusted) Strike Rate x 25.0.

5. Quality of bowling faced (15 points)

This is a double weighted adjustment. The objective is to make sure that the runs acored against stronger teams such as Australia are given much higher weighting than the runs scored against weaker countries such as Zimbabwe. Care also has to be taken that the weaker Australian teams such as those during the mid-1980s are treated accordingly. The complex process is explained below.

First a bowling quality index is found for each innings. This is done by the following formula (somewhat similar to the one used by David Barry). I had thought of this earlier, but dismissed it as too complex. Now I think it is necessary.

              Sum of (Balls bowled by each bowler x Bowler's bowling avge)
Innings BQI = -----------------------------------------------------
                          Sum of (Balls bowled by each bowler)

In one of my earlier articles on Team Strength analysis I used a simple average of the top 5 Bowling averages. That was when I was trying to find the strength of team as it walked on to the field. However here I am trying to find how valuable the batsman's innings was. Hence the actual deployment of the bowling resources is necessary. Wasim Akram will make the Pakistani team that much strong, on paper, however, if he did not bowl a single ball, to that extent the bowling lacks sting.

Now comes the second weighting. For this the actual scores of batsman and the Innings BQI are used. The formula is explained below.

                     Sum of (Batsman innings score x Innings BQI)
Batsman career BQI = --------------------------------------------
                           Sum of (Batsman innings score)

There is some convergence of values as batsmen score many runs. Note the BOWQTY value for the top 5 batsmen. Hence special care has to be taken to assign points. Amongst batsmen who have scored greater than 2000 runs, Craig McMillan is the best with a BQI of 34.48 and Habibul Bashar the worst with a BQI of 43.47. If we lower the limit to 1000 runs, Nicky Boje is the best with a BQI of 31.3 and Glenn Turner the worst with a BQI of 47.63. No batsman has a career BQI below 30.00 and no batsman has a career BQI above 50.0. The Batsman career BQI is used to derive the index value based on the following formula.

• BOWQTY = 50.0 - Batsman career BQI.

6. % of Team runs (5 points).

The value of a batsman to the team is also determined by the share of the batting load he takes. In other words the % of team runs he scores. This is a secondary parameters and has a weighting only of 5 points. With a criteria of 2500 runs and above, the highest share of team runs scored is by Zaheer Abbas with 21.6%, followed by Greenidge with 19.2%, then by Richards with 19.2% and finally by Tendulkar with 18.1%. The formula used is

• TSPER = % of Team share * 20.0.

Upto this point, the full weight will be given only if the batsman has scored above 2000 runs. Else the points secured will be proportionately downsized.

7. Wins achieved (5 points)

Winning is something special, if not everything (as the Americans profess). No one wants to lose. Hence we should give value to this important aspect of the game without going overboard. This is done in two parts. The first is to derive an index value solely based on the number of wins achieved. This will benefit players who have played more games and have been part of successful teams. The highest number of wins achieved is 220 by Jayasuriya, followed by Ponting with 216, Inzamam with 214, Gilchrist with 214 and Tendulkar with 206. The formula used is

• WINS = No of wins /50.0.

8. Win % achieved (5 points)

What about Richards who achieved 132 wins in 187 matches (a 70.6 win %), which is much higher than that of Tendulkar, 206 wins in 417 matches (49.4%) or Steve Waugh, 196 in 325 (60.3%). His win % suffers only in comparison to the current Australian team, some of whom having over 75%.

This factor addresses this problem. Credit is given to the % of wins achieved, subject to minimum number of matches being reached. The formula used is

• WINSPER = % of wins x 5.0.

9. MOM awards received (5 points).

The last parameter is on the MOM awards achieved. This is the only subjective measure, as pointed to by Shankar Krishnan of Riyadh. However since this is the only individual evaluation measure available I have to consider it. Whatever be the idiosyncracies of the adjudicators there is no doubt that the MOM awards are a pointer to the contribution to the wins achieved by the team.

I have tried to remove the subjective factor, to a certain extent, by considering the frequency of awards also in addition to the absolute number of awards. This is also fair to the older players. Consider this. Richards has got 31 awards in 187 matches. He lags far behind Jayasuriya who has got 45 awards in 415 matches. However when we consider the frequency, Richards has a frequency of one in 6 matches, while Jayasuriya, one in 9.2 matches. Incidentally Tendulkar leads the absolute number of awards with 55. The frequency ranges from 6.0 to 20.0 (limiting value). The formula used is

• MOM = (MOM Awards/30.0) + (3.0 * (20.0 - MOM Frequency)/15.0).

For the last two points, the full weight will be given only if the batsman has played above 50 matches. Else the points secured will be proportionately downsized.

Now the table of top 30 ODI batsmen of all time. The table is current upto match 2759, the facile English win over the hapless South Africans, giving them a 4-0 lead.

The top ODI batsmen of all time - as on 28 August 2008.

No.Cty Batsman         Total  Runs  Avge  R/I  S/R  BwQty Wins Win% % TS MOMs

                       100.0  20.0  15.0  5.0  25.0  15.0  5.0  5.0  5.0  5.0

 1.Ind Tendulkar S.R   79.27 16.36 11.08 4.02 21.16 12.13 4.12 2.47 3.61 4.32 
 2.Win Richards I.V.A  73.14  6.72 11.75 4.02 24.60 12.20 2.64 3.53 3.85 3.83 
 3.Slk Jayasuriya S.T  72.24 12.80  8.18 3.13 22.52 12.01 4.44 2.64 2.89 3.63 
 4.Aus Ponting R.T     71.87 11.11 10.81 3.81 19.63 12.63 4.32 3.59 3.19 2.78 
 5.Aus Gilchrist A.C   71.12  9.62  8.97 3.45 23.59 12.12 4.04 3.52 2.93 2.88 
 6.Win Lara B.C        67.70 10.40 10.12 3.60 19.64 12.38 2.78 2.33 3.43 3.01 
 7.Saf Kallis J.H      67.70  9.61 11.17 3.64 17.33 12.98 3.50 3.15 3.26 3.05 
 8.Pak Inzamam-ul-Haq  66.72 11.74  9.88 3.35 18.31 11.81 4.28 2.83 3.04 1.48 
 9.Aus Bevan M.G       66.00  6.91 13.40 3.53 18.31 13.88 3.10 3.34 3.00 0.53 
10.Ind Ganguly S.C     65.87 11.36 10.26 3.79 18.14 10.64 2.98 2.40 3.27 3.03 
11.Pak Saeed Anwar     65.55  8.82  9.80 3.62 20.20 10.95 2.82 2.85 3.42 3.07 
12.Aus Waugh M.E       65.50  8.50  9.84 3.60 19.39 12.29 3.04 3.11 3.22 2.52 
13.Aus Symonds A       65.43  5.01 10.09 3.19 22.41 12.58 2.98 3.86 2.58 2.74 
14.Slk de Silva P.A    65.02  9.28  8.73 3.14 20.61 12.52 2.56 2.08 3.06 3.05 
15.Win Haynes D.L      64.62  8.65 10.34 3.65 16.74 12.16 3.18 3.34 3.63 2.93 
16.Saf Gibbs H.H       63.66  7.59  9.12 3.39 20.24 11.95 2.88 3.12 3.03 2.36 
17.Ind Dravid R        63.47 10.59  9.87 3.44 17.36 13.25 3.14 2.36 3.00 0.47 
18.Pak Mohammad Yousuf 63.22  9.24 10.80 3.64 18.19 10.81 3.12 2.90 3.12 1.40 
19.Saf Kirsten G       63.06  6.80 10.24 3.67 17.88 13.45 2.40 3.24 3.35 2.03 
20.Saf Klusener L      62.90  3.58 10.28 2.61 22.05 13.92 2.18 3.19 2.27 2.83 
21.Aus Jones D.M       62.82  6.07 11.15 3.77 18.86 11.99 1.96 2.99 3.55 2.48 
22.Aus Hayden M.L      62.80  6.13 10.95 3.96 19.36 12.26 2.38 3.70 3.34 0.72 
23.Pak Javed Miandad   62.74  7.38 10.43 3.39 17.98 13.04 2.38 2.55 3.40 2.18 
24.Saf Rhodes J.N      62.73  5.93  8.78 2.70 20.11 15.00 3.10 3.16 2.46 1.47 
25.Eng Pietersen K.P   62.46  2.82 11.96 3.87 20.90 14.46 0.68 2.10 3.44 2.24 
26.Ind Sehwag V        62.31  5.81  8.11 3.12 23.82 12.41 1.90 2.49 2.70 1.95 
27.Ind Dhoni M.S       62.26  3.79 11.85 3.54 21.80 12.73 1.30 2.71 2.90 1.63 
28.Ind Azharuddin M    62.10  9.38  9.23 3.04 18.97 12.09 3.20 2.40 2.90 0.89 
29.Aus Waugh S.R       61.95  7.57  8.23 2.63 19.26 13.75 3.92 3.02 2.38 1.21 
30.Saf Cronje W.J      61.91  5.57  9.66 3.18 19.26 13.51 2.34 3.11 2.92 2.35

Tendulkar is on top, and deservedly so. He has not only scored lots of runs but scored these at a good pace, scored these against good bowlers and contributed more than his share to the Indian cause.

Richards is in second place, again deservedly so. He has scored only 6721 runs, but made up for the huge shortfall in index points with his outstanding average, strike rate, win % and MOM frequency. He may very well move a little bit down in the list in the years to come. But will not lose any of the aura.

Jayasuriya is next, having made up for his low Average and RPI with a mountain of runs scored at a scorching pace. The Lankan readers will be happy that the contributions of the entertainer non-pareil have been recognized. He has managed to retain the third position depsite a poor run of ODI matches against India.

Ponting and Gilchrist, two great Australian batsman, follow in the next two positions, through different combination of high points. Ponting with high average and good strike rate while Gilchrist with lower average and excellent strike rate. Both have great win related numbers.

Lara, Kallis Inzamam, Bevan and Ganguly complete the top 10. This elite placing of these quality batsmen cannot be debated. In fact Lara and Kallis exchanged places after the last match.

There is no doubt that players such as Pietersen (25th currently), Sehwag (26th), Dhoni (27th) and Hussey (39th) will move up the list as they score more runs. However this may be partly compensated by the possible decrease in their averages. Dhoni is surely on the way to becoming an excellent finisher in the Bevan/Hussey mode and as such is unlikely to drop his average. Pietersen's average could drop a little bit. Hussey's could drop significantly unless otherwise he does what Bevan did over a long career.

It should be noted that if we change the weightings, the batsmen will move up or down the list. For instance, Strike Rate could be reduced to 20 points. In that case, Jayasuriya and Ponting will exchange places. But these are minor movements only. It is my firm belief that the top 2, Tendulkar and Richards will remain where they are, whatever be the weightings.

Batsmen such as Kluesener, Dhoni and Pietersen, who have not even scored 4000 ODI runs have managed to reach the top 30 positions in the all-time best batsmen table. This indicates that the weightings for non-longevity measures have been given due importance.

Finally, one important point to be noted. No analyst starts with an idea to prove that one batsman is superior to another or push their favourite batsmen on top. Such shallow analyses will be found out in no time at all. The idea is to come out with a vehicle for healthy discussion and exchange of views. Hence please avoid rude and vicious comments. They have no chance of being read by any one. Pl make your point in a courteous and acceptable manner. The readers have their right to be heard but also their responsibilities to be constructive and courteous.

To view the complete list, click here

This list consists of batsmen who have scored a minimum of 1000 ODI runs. Please remember that many of the calculated points are downsized for batsmen in the 1000-2000 range. They are included only to show where some of the batsmen from the lesser countries stand.

Summary response to readers' comments (Possible tweaks)

1. Avoidance of double weighting for "Wins".

2. Possible cap on Runs scored weighting.

3. Adjust for the paucity of matches played during the early 10 years.

4. Giving weight to key tournament wins such as World Cup and Champion's Trophy.

5. The subjective nature of MOMs, already mentioned by me in the main post does not go well with readers.

6. Quite a few readers have, while accepting Tendulkar's position at no.1, have questioned the wide gap between Tendulkar and Richards. It worries some readers that this gap will keep on widening.

	99.94 perhaps will remain as the most recalled figure in cricket © Getty Images

1. Best ever batting performance in a test

During 2001, Wisden came out with a list of the 100 best Test innings of all time. Don Bradman's 270 played in Melbourne in 1937 was adjudged the best ever test innings. This was closely followed by Brian Lara's match-winning 153* and Graham Gooch's 154*.

Playing on a gluepot, Bradman declared at 200 for 9 and Gubby Allen countered by declaring at 76 for 9. The wicket was still very difficult and Bradman sent his tailenders in. Soon they were 97 for 5. Then Bradman and Jack Fingleton added 346 for the sixth wicket, . Bradman continued on and was ninth out at 270. England fought gamely but lost by a big margin. A tactical battle was won by Bradman, the captain and he led from the front. A potted summary of the match is given below.

Test # 257. Australia vs England.
Played on 1,2,4,5,6,7 January 1937 
at Melbourne Cricket Ground.
Australia won by 365 runs.
Australia: 200 for 9 wkt(s)
England: 76 for 9 wkt(s)
Australia: 564 all out (Bradman 270, Fingleton 136)
England: 323 all out

2. The best 10-innings stretch

Bradman's best 10-innings stretch was during 1937-46, when he scored 1236 runs at an average of 154.50

The scores were 212, 169, 51, 144*, 18, 102*, 103, 16, 187 and 234.

Also relevant here is "Alex"'s comment, reproduced below.

Also, regarding the 'best 10-innings stretch'. Bradman scored 1370 runs in 10 innings during 1930 and 1931: 131, 254, 1, 334, 14, 232, 4, 25, 223, 152. There were no not-outs during this period however, so his average was 'only' 137.0.

3. The worst 10-innings stretch

Bradman's worst 10-innings stretch started during the second Bodyline test during 1932-33 and continued until 1934 when he scored 426 runs (in 11 innings) at an average of 38.72. He finished this streak with his monumental 304 at Headingley during 1934.

The scores were 8, 66, 76, 24, 48, 71, 29, 25, 36, 13 and 30.

4. Highest average reached (after 10 innings)

Bradman reached his highest career average of 112.29 after the Adelaide Test against South Africa, in which he scored 299*.

5. Lowest average reached (after 10 innings)

Bradman reached his lowest career average, after passing the initial period of 10 Tests, of 89.56 after the Old Trafford Test against England during 1934. Not surprisingly this was the end of his worst streak, referred to elsewhere in this article.

6. When the average of 100.00 was reached

Surprisingly Bradman did not have a great start to his career. He reached an average of 100.00 (agreed very few have ever touched this milestone) only after 15 innings.

7. Quality of opposition bowling

Surprisingly the bowling Bradman faced in his career was slightly below the all-time average, 29.62 against 29.50. However it must be noted that he faced this level of bowling almost all the time. The all-time average arrived consists of 40s and 20s scattered across the 1800-odd Test matches.

8. Runs scored in each batting position

Batting Position      3      4      5       6      7
Runs scored         5078    485    427     681    325
Batting Average    103.63  53.89  142.33  97.29  162.50

The No. 7 total is bolstered by that amazing innings of 270 referred to earlier in this article.

9. Analysis by batting position

Bradman's Batting Position Average is 3.65, indicating that he batted at No. 3 most of the time. For the record he batted at No. 3 a total of 56 times (70%).

10. Analysis of 100s

This is the one measure where he has yielded to a contemporary batsman. The average of the 29 hundreds Bradman has scored in Test cricket is a very high 185.97. Till a few weeks back, he was the No.1 batsman in this regard. Sehwag overtook this figure with his 319 in Chennai. However, Bradman's 100s frequency of 1.8 Tests per hundred is way ahead of any one else.

11. Home/Away runs scored

Not so surprisingly, considering his success in England, Bradman's away performance is superior to his Australian performances. He has scored 2674 runs away at an average of 102.85 while in Australia, he has scored 4322 runs at an average of 98.22.

12. How far ahead of the next

Just to show how far ahead Bradman is of the other batsmen, a relative scale table is shown below.

Measure          Bradman     %    Next Best    %     Difference

Batting Avge      99.96    100.0    68.38    68.47     31.53    (Hussey)
Runs per test    134.53    100.0    99.54    74.00     26.00    (Headley)
Tests per 100      1.79    100.0     2.20    81.00     19.00    (Headley) 
Inns per 100       2.76    100.0     4.00    69.00     31.00    (Headley)

13. Man of the Match awards

Hey what is this, no Man of the Match awards were given when Bradman played. True. So I have gone through the scorecards and using the Innings Rating points, determined which player could have got the MOM award, if these were given. Bradman would have got no less than 16 MOM awards in the 52 Tests he played, a frequency of 3.25 tests per award. Compare this with the current leaders. The best is a frequency of 6.00.

Kallis         123     20    6.15
Muralitharan   123     19    6.47
Wasim Akram    104     17    6.12
Shane Warne    145     17    8.52
Ambrose         84     14    6.00

14. Movement of averages

Finally a footnote. I am not sure whether I would jump with joy if someone, as reported recently, conclusively proved that Bradman scored those elusive four runs, by mistake credited to Jack Ryder, during 1929. The figure of 99.94 is etched into the memory of people and sounds far better than 100.00. It also confirms a nice human element to one perceived to be a super-human.

	Adjusting for the strength of bowlers he faced, Sachin Tendulkar's batting average drops to 47.4 © AFP

Some of you may recall the quotient of BQI to bowling average discussed in this post. Roughly speaking, the idea is to reward bowlers who take the wickets of better batsmen. In this post, I'll flip the idea round, and reward batsmen who score against better bowling attacks.
***
Firstly, a digression on Ananth's post. The quotient was defined by summing up the batting averages of the batsmen dismissed by a particular bowler, and then dividing by the bowler's regular average. This is, to my mind, a very useful stat, perhaps the best of its kind for its simplicity (you can of course make it better by making it more complicated in appropriate ways). The only problem is that the numbers you get don't correspond to numbers we're used to in following cricket. How good is a 1.2 bowler? A 0.9 bowler?

Happily, there's an interpretation of this stat that puts the numbers on a scale we're familiar with. It's equivalent to the usual average (runs conceded divided by number of wickets taken), with each wicket weighted by the average of the batsman dismissed. You can set a 'benchmark' average (its value is arbitrary), and I'll set it at 31.5. Dismissing a batsman who averages 31.5 is worth 1 wicket. Dimissing a batsman who averages 47.25 is worth 1.5 wickets. A quotient Q is then equivalent to an average of 31.5 / Q. So, a bowler with a quotient of 1.2 has an 'adjusted average' of 31.5 / 1.2 = 26.25. This is the sort of number we're used to thinking about with bowlers' averages.

I don't know who first came up with the idea of weighting wickets in this way – it was first suggested to me by a friend of mine. Probably various people over the years have thought of it.

Working in the reverse direction (adjusting batsmen's averages) is more difficult, since apart from the last few years, we don't know which bowlers each batsman faced. But we can make a first attempt, by taking the average of the bowlers' averages for each innings, weighting each by the number of overs that they bowled.

To take an example, suppose that in one innings, four bowlers were used:

Bowler A, career average 28, bowls 30 overs.
Bowler B, career average 30, bowls 30 overs.
Bowler C, career average 35, bowls 25 overs.
Bowler D, career average 40, bowls 20 overs.

The "average average" is then (28*30 + 30*30 + 35*25 + 40*20) / (30 + 30 + 25 + 20) = 32.52.

Each batsman's runs for this innings would be multiplied by 31.5 / 32.52 – they'll all be slightly decreased, because the attack is slightly weaker than our benchmark average of 31.5.

(Note: if a bowler never took a wicket, or has an average above 100, then I set that bowler's average at 100. This seems reasonable to me.)

We do this for all innings, and we get adjusted averages for all batsmen.

One useful feature of this method (for both batsmen and bowlers) is that it adjusts across changes in the relative strength of bat and ball (as well as rewarding players who do well against strong opposition). In an era where averages are high (such as today), bowlers are rewarded more for wickets and batsmen less for runs. For players in the low-scoring years before 1900, the reverse is true. Of course, it's possible that in a given era, runs are low because there happen to be a lot of good bowlers and not many good batsmen, and in this case the bowlers are unfairly punished (and batsmen unfairly rewarded). But to my mind the results are better than raw averages.

So onto the results. Qualification: 20 Test innings. Here's the top 20.

name            inns  no  runs  avg   adj avg
DG Bradman      80    10  6996  99.9  90.4
GA Headley      40    4   2190  60.8  62.8
MEK Hussey      42    8   2325  68.4  59.4
CL Walcott      74    7   3798  56.7  58.3
ED Weekes       81    5   4455  58.6  55.9
FS Jackson      33    4   1415  48.8  55.4
JB Hobbs        102   7   5410  56.9  55.0
GS Sobers       160   21  8032  57.8  54.6
L Hutton        138   15  6971  56.7  53.8
H Sutcliffe     84    9   4555  60.7  53.6
AD Nourse       62    7   2960  53.8  53.4
KF Barrington   131   15  6806  58.7  52.6
GS Chappell     151   19  7110  53.9  52.3
GE Tyldesley    20    2   990   55.0  52.2
RG Pollock      41    4   2256  61.0  52.0
KS Ranjitsinhji 26    4   989   45.0  50.8
BC Lara         230   6   11912 53.2  50.4
J Ryder         32    5   1394  51.6  50.4
RT Ponting      197   26  9999  58.5  50.3
FMM Worrell     87    9   3860  49.5  49.5
AG Steel        20    3   600   35.3  49.0

The modern-day greats are surprisingly low down. That their averages should be heavily reduced is not surprising, since the bat has been very dominant over the ball in the past few years. But they're still further down that I had expected. Perhaps there is some bias in the method, or perhaps we should pay more attention to Neil Harvey when he compares modern players to those of his day.

(There's another possibility worth thinking about, and that is a gradual increase in competitiveness of the sport, so that today there are fewer players on the high and low extremes and more players towards the middle. I don't know how big an effect this would be.)

Here is a list of players from recent years:

name            inns  no  runs  avg   adj avg
MEK Hussey      42    8   2325  68.4  59.4
BC Lara         230   6   11912 53.2  50.4
RT Ponting      197   26  9999  58.5  50.3
KP Pietersen    80    3   3890  50.5  48.8
JH Kallis       207   32  9678  55.3  48.3
V Sehwag        100   4   5074  52.9  48.0
Moh'd Yousuf    134   12  6770  55.5  47.8
SR Tendulkar    244   25  11877 54.2  47.4
RS Dravid       214   26  10223 54.4  47.3
A Flower        112   19  4794  51.5  46.5
KC Sangakkara   125   9   6356  54.8  46.5

Tendulkar's low position is a bit of a surprise. It's an anomaly that jars with most people's impressions. But remember that averages are not perfect indicators of a batsman's 'true talent' – there's some inherent uncertainty with them.

A full list of batsmen (with an adjusted average of at least 25), click here.

Some further comments:

- Opening batsmen face the opening bowlers disproportionately often, and this isn't taken into account.

- The conditions or characteristics of the batsmen on a given day can change the effectiveness of the bowlers, and the captain would use his bowlers accordingly. So the simple weighting by career average is not a perfect reflection of the overall skill of the attack. But in the long run the above method should be pretty close.

- There's no allowance for ground or pitch conditions, etc.

- I've ignored not-outs. This is worthy of a post of its own, but not-outs don't affect averages much in Test cricket.

- I've used career averages of the bowlers, mainly because it's easy to do. Career-to-date averages can be unstable. It would be reasonable to add a correction factor for the experience of each bowler. But while I've done a small amount of work in this area, I don't have enough results for it to be usable.

In view of the huge number of comments I have to resort to providing a generic response to the comments. This has been shown at the end of the article.

Martin Crowe, who needs no introduction, had sent in a very valuable comment and Kartik had requested whether Martin could comment on the changes in ODI game over the years. Martin kindly responded to this request and his perceptive comments are shown below. Martin, thanks a ton.

The basic fundamental of the change has been change itself - in the rules. The skill level over all generations has always been constant and consistent. But the framework of each era is determined by the rules of the day. E.g in general there were no 15 over restrictions or powerplays in the 80s, and rules for boundary length was determined by size of ground (inside fence) - but now its a standard 65m. A few examples - We started the exploitation of rules with Greatbatch as pinch hitter opening the batting, Patel opening the bowling Sri Lanka took it a step further in 96'. Personally, I used to practice chipping the ball 45-50m over the inner ring and way short of the boundary rider standing at 80-90m, to score 2 runs. I only ever used to attempt hitting a six over a fielder if there was a short boundary like at Eden Pk, 50-60m square of the wicket otherwise I never tried to clear a fielder 80-90m away. i.e. hitting 6's is so much easier now with standard length boundaries of 65m in place. In this aspect alone, there is a major difference between scoring 250 and 300. And yes the bats are bigger and lighter, but not in my opinion necessarily better for Tests. In the 80's I used a bat weighing 2'4"-2'6" to combat the 4 prong pace attack of the Windies. With each change or addition to the rules brings an evolution of playing strategy, mainly in batting but also captaincy. T20 will only further encourage the evolution. In 5 years ODIs will be 4 x 20 overs each. In summary the rules will continue to evolve to excite the fan. As it should be. Test cricket on the other hand will rightly be left alone.

Martin Crowe

The ODI bowling average is a fantastic measure since it incorporates the two key components needed to measure a bowler's performance, viz, strike-rate and economy-rate, as shown in the following equation. If either of the economy-rate or strike-rate goes up the bowling average goes up and vice versa.

                  Runs scored off
Bowling Average = ----------------       & can be rewritten as
                  Wickets captured

                   Runs scored off        Balls bowled
Bowling Average =  ---------------   x   ---------------
                    Balls bowled         Wickets captured
Hence

Bowling Average = Economy Rate (R/B) x Bowling Strike Rate (B/W)

Unfortunately the batting average is a single-dimensional measure incorporating only one part of the total measure needed to measure a batsman, viz, runs scored. The batting strike-rate (runs per ball) is another independent measure and the two have to be considered together to determine the quality of a batsman. This article attempts to locate a single measure, somewhat equivalent to the bowling average.

Note the following players' figures.

                            M    Runs  Balls   St Rt  BatAvge
Turner G.M           Nzl   41    1598   2291   69.75   47.00
Greenidge C.G        Win  128    5134   7748   66.26   45.04
Javed Miandad        Pak  233    7381  10979   67.23   41.70
Haynes D.L           Win  238    8648  13566   63.75   41.38
Broad B.C            Eng   34    1361   2425   56.12   40.03

These are a set of high-average, low-strike rate batsmen who once ruled the roost in ODIs. There was a time when an ODI opener had to fall into this mould of a patient 150-ball-century person. Scores of 250-plus were eminently defendable and these batsmen fitted into the scheme of things.

                            M    Runs  Balls   St Rt  BatAvge
Ganguly S            Ind  300   11363  15416   73.71   41.02
Chanderpaul S        Win  230    7407  10473   70.72   40.26

Today the situation has changed. It is uncommon to see such a figure among current players who are playing ODIs. Even the opening batsmen have to have a higher strike-rate. If, in the bargain, their batting average drops, it is acceptable. The current batsmen who fit into the above group are, say, Ganguly and Chanderpaul. Both have reasonably high batting averages and not-too-high strike rates.

Now note the figures for the following batsmen.

                      M    Runs  Balls  St Rt  BatAvge
Shahid Afridi        248   5469   4911 111.36   23.47
Sehwag V             186   5867   5884  99.71   32.78
Powell R.L           100   2085   2157  96.66   24.82
Kapil Dev N          198   3783   4146  91.24   23.79
Jayasuriya S.T       404  12688  13931  91.08   32.87
McCullum B.B         111   2602   2874  90.54   29.24

These batsmen have very high-strike rates, above 90, but sub-35 batting averages. These are acceptable today, whether for opening batsmen or middle-order finishers. While everyone would like a Shahid Afridi or Sehwag to have higher batting averages, their very method of playing, attacking from the first ball, prevents them from having higher batting averages. Their role in today's ODI matches, however, cannot be denied.

However there is a need to look at things in perspective. Batsmen such as Chanderpaul and Ganguly, with averages of 40+ and strike rates of 70+ are still valuable in ODIs. How do they compare with, say, Andrew Flintoff, who only averages 31+ but has a strike rate of 87+. Similarly how do two middle-order batsmen of contrasting styles such as Yuvraj Singh and Mohammad Yousuf compare.

To compare ODI batsmen, I have thought of a simple index, hereinafter called ODI Batting Index (OBI). Since there are two measures both of which have the characteristic of, the higher the better, we multiply the batting average by the strike-rate and arrive at the OBI. Because it is a product, both values have equal weightage. This OBI Index is used to compare the ODI batsmen.

Now let us look at a table of the top 20 ODI batsmen ever based on the OBI. The minimum criteria is 2000 ODI runs which represents between 50 and 60 ODI matches, a fair measure of a settled batsman. A total of 143 batsmen qualify under this criteria. The analysis is correct until match # 2739, Ireland vs Scotland, one of the many inconsequential matches.

SNo LH Batsman             Ctry Inns  NO   Runs    Avge   StRt   Idx1

  1 ~ Hussey M.E.K         Aus   68   26   2307   54.93   85.6  47.04
  2   Dhoni M.S            Ind  101   27   3536   47.78   91.9  43.93
  3   Richards I.V.A       Win  167   24   6721   47.00   88.7  41.67
  4   Pietersen K.P        Eng   70   13   2687   47.14   86.6  40.85
  5 ~ Bevan M.G            Aus  196   67   6914   53.60   74.4  39.85
  6   Tendulkar S.R        Ind  407   38  16361   44.34   85.5  37.90
  7   Symonds A            Aus  157   33   5006   40.37   92.8  37.46
  8   Zaheer Abbas         Pak   60    6   2572   47.63   78.6  37.44
  9 ~ Klusener L           Saf  137   50   3576   41.10   89.9  36.95
 10   Clarke M.J           Aus  121   28   4037   43.41   80.5  34.93
 11 ~ Gilchrist A.C        Aus  279   11   9619   35.89   96.9  34.79
 12   Ponting R.T          Aus  292   35  11112   43.24   80.3  34.72
 13 ~ Hayden M.L           Aus  155   15   6132   43.80   78.9  34.58
 14 ~ Gambhir G            Ind   56    7   2018   41.18   82.7  34.06
 15 ~ Smith G.C            Saf  131    9   5016   41.11   81.8  33.63
 16   Sarwan R.R           Win  123   25   4251   43.38   76.5  33.17
 17   Sehwag V             Ind  186    7   5867   32.78   99.7  32.68
 18   Jones D.M            Aus  161   25   6068   44.62   73.2  32.65
 19   Mohammad Yousuf      Pak  254   40   9243   43.19   75.4  32.55
 20 ~ Lara B.C             Win  289   32  10406   40.49   79.7  32.27

To view the full list, please click here.

This is a true measure of the greatness of an ODI batsman. The batsmen with very high batting averages such as Michael Hussey, Mahendra Singh Dhoni, Viv Richards and Kevin Pietersen are at the top because they also possess very good strike-rates, in excess of 85. Bevan drops off a little, because he does not have a very high strike-rate. Then come Sachin Tendulkar and Andrew Symonds, both with very good averages and eminently acceptable strike-rates. Zaheer Abbas has a very high batting average and an acceptable strike-rate. Lance Klusener is a surprise presence in the Top 10, mainly because people tend to think only of his explosive striking ability, forgetting that he has a batting average better than Adam Gilchrist or Brian Lara. There is no doubt his spat with Graeme Smith has deprived South Africa of an outstanding player. No one can deny Michael Clarke a place in the Top 10.

The batsman with the lowest batting average to make it the list of Top 20 is Sehwag and he has made to the Top 20 because of his near-100 strike-rate. Gilchrist is in with similar credentials. Similarly the batsman with the lowest strike-rate in this Top 20 is Dean Jones, again another deserving candidate with a very high average. It's a similar case with Mohammad Yousuf.

One can conclude that an OBI value of above 30 signifies a very good ODI batsman.

Alternative 1

Some people might question that the product is not a true measure to define the combined value of two diverse factors because of skews. A 10% increase in either of the measures, will increase the Index value by 10%. A 10% increase in both the measures will increase the Index value by 21%. This may not be acceptable and readers may be justified in suggesting that a sum, rather than a product, should be done. It can easily be achieved with the following, slightly more complex, method.

OBIdx2 = Batting Average + (50.0 * Strike-Rate).

This is an excellent way of measuring the batting qualities since a batting Average of 50.0 is almost the pinnacle and a strike-rate is 1.00 is almost the same lofty level. I personally prefer this index as the better balanced of the two.

SNo LH Batsman             Ctry Inns  NO   Runs    Avge   StRt   Idx2

  1 ~ Hussey M.E.K         Aus   68   26   2307   54.93   85.6  97.75
  2   Dhoni M.S            Ind  101   27   3536   47.78   91.9  93.75
  3   Richards I.V.A       Win  167   24   6721   47.00   88.7  91.33
  4 ~ Bevan M.G            Aus  196   67   6914   53.60   74.4  90.77
  5   Pietersen K.P        Eng   70   13   2687   47.14   86.6  90.47
  6   Tendulkar S.R        Ind  407   38  16361   44.34   85.5  87.08
  7   Zaheer Abbas         Pak   60    6   2572   47.63   78.6  86.93
  8   Symonds A            Aus  157   33   5006   40.37   92.8  86.77
  9 ~ Klusener L           Saf  137   50   3576   41.10   89.9  86.05
 10 ~ Gilchrist A.C        Aus  279   11   9619   35.89   96.9  84.36
 11   Clarke M.J           Aus  121   28   4037   43.41   80.5  83.64
 12   Ponting R.T          Aus  292   35  11112   43.24   80.3  83.39
 13 ~ Hayden M.L           Aus  155   15   6132   43.80   78.9  83.27
 14   Sehwag V             Ind  186    7   5867   32.78   99.7  82.63
 15 ~ Gambhir G            Ind   56    7   2018   41.18   82.7  82.54
 16 ~ Smith G.C            Saf  131    9   5016   41.11   81.8  82.01
 17   Sarwan R.R           Win  123   25   4251   43.38   76.5  81.61
 18   Jones D.M            Aus  161   25   6068   44.62   73.2  81.21
 19   Kallis J.H           Saf  260   49   9542   45.22   71.4  80.90
 20   Mohammad Yousuf      Pak  254   40   9243   43.19   75.4  80.87

To view the full list, please click here .

The reconstituted table is almost the same, barring minor moves indicating either of the measures can be used. An index value of or around 100.0 is the indication of a truly great ODI batsman.

Michael Bevan and Pietersen swap places, Clarke and Gilchrist also swap places. Gilchrist moves into the Top 10 at the expense of Clarke. The batsman who has benefited most is Sehwag, who moves up three places. Jacques Kallis comes into the Top 20 at the expense of Lara. This computation method, in general, will benefit the low average - high strike-rate batsmen since the multiplication method will not help them greatly.

Alternative 2

There is no denying that the impact of not-outs is too pronounced in the first two cases. While not denying Hussey's place in the top echelons of ODI batsmen, he is placed too high with a batting average of 54.93. He has 28 not-outs out of 68, a very high 41%. Similar cases exist with Dhoni, Bevan, Klusener et al.

Hence a third alternative is tried out. This time I have computed the OB Idx as follows.

OBIdx2 = (Runs/Innings) + (40.0 * Strike Rate).

The multiplying factor is 40.0 (as against 50.0) since the highest runs per innings value is 42.87 and only four batsmen exceed a RPI value of 40.0. Similarly only one batsman exceeds a Strike Rate of 100.0.

This takes care of all anomalies. Only the middle-order batsmen might complain. But it is now fair across the board. Now let us look at the table.

SNo LH Batsman             Ctry Mat Inns   Runs    Avge   StRt   Idx3

  1   Richards I.V.A       Win  187  167   6721   40.25   88.7  75.71
  2   Tendulkar S.R        Ind  417  407  16361   40.20   85.5  74.39
  3   Zaheer Abbas         Pak   62   60   2572   42.87   78.6  74.31
  4 ~ Gilchrist A.C        Aus  287  279   9619   34.48   96.9  73.25
  5   Pietersen K.P        Eng   76   70   2687   38.39   86.6  73.05
  6   Dhoni M.S            Ind  115  101   3536   35.01   91.9  71.79
  7   Sehwag V             Ind  191  186   5867   31.54   99.7  71.43
  8 ~ Hayden M.L           Aus  161  155   6132   39.56   78.9  71.14
  9 ~ Smith G.C            Saf  133  131   5016   38.29   81.8  71.00
 10   Ponting R.T          Aus  301  292  11112   38.05   80.3  70.18
 11 ~ Trescothick M.E      Eng  123  122   4335   35.53   85.2  69.63
 12 ~ Gambhir G            Ind   56   56   2018   36.04   82.7  69.12
 13   Symonds A            Aus  193  157   5006   31.89   92.8  69.00
 14 ~ Saeed Anwar          Pak  247  244   8823   36.16   80.7  68.45
 15 ~ Gayle C.H            Win  183  179   6488   36.25   80.3  68.35
 16 ~ Hussey M.E.K         Aus   90   68   2307   33.93   85.6  68.18
 17 ~ Lara B.C             Win  298  289  10406   36.01   79.7  67.89
 18 ~ Jayasuriya S.T       Slk  415  404  12688   31.41   91.1  67.84
 19   de Villiers A.B      Saf   67   64   2147   33.55   85.3  67.65
 20 ~ Ganguly S.C          Ind  311  300  11363   37.88   73.7  67.36

Ah, now we see the real quality. Richards at the top, followed by Tendulkar, two ODI masters nonpareil. The only surprise in the top 10 is Zaheer Abbas in third position. The other nine will be in anybody's list of top ODI batsmen of all time. Richards, Tendulkar and Gilchrist gain at the expense of Dhoni, Hussey and Bevan, the later two move way down the field. Now about Zaheer Abbas. One of only four batsmen to average over 40 runs per innings (Richards, Tendulkar and Greenidge the other three) and a strike-rate of nearly 80. His RPI value is 42+, two above Richards and Tendulkar. He was and is one of the most under-rated players of all time.

An Idx3 value of 80 is the pinnacle, 70+ signifies greatness, 60+ signifies an outstanding batsman and 55+, a very good batsman. Shahid Afridi, despite his low average, gets an excellent value of 66.60 and is at no. 26.

To view the full list, please click here

I can anticipate a common reader observation. "How did you determine the career balls played for older players such as Richards, Greenidge, Zaheer Abbas et al". The following method is used.

1. Even for some early matches the balls played is available straight off in the Cricinfo archive scorecards.
2. Non-Cricinfo archives have been searched for some important innings.
3. Bill Frindall's excellent ODI scorecards book contains the balls played for a number of key innings.
4. Where nothing is available, the individual batsman strike-rate is extrapolated from the team rate. This method is not complete but gives us a fair idea of the balls faced. It might also be unfair to the more attacking players such as Richards, Kapil Dev et al and would benefit players such as Desmond Haynes, Sunil Gavaskar et al. I can assure readers that this method has only been resorted to when all other avenues have been investigated.

The most acceptable index value is the third one (Idx3) since it negates the impact of not-outs very effectively.

This method treats batsman Nos 1-5 in a fair manner and is possibly slightly unfair to positions 6-7, which is quite acceptable. The addition method is also devoid of statistical imperfections. Hence the third index method is the one I would recommend for consideration.

Based on this index, Viv Richards is at the top, closely followed by Tendulkar and Zaheer Abbas.

Unlike the Extended Batting Average [for Test batsmen], which was a substitute for batting average, this is a new measure which encompasses two of the existing measures. It would be a very useful tool for ranking batsmen and determining the strength of the team. I will be using this measure in the ODI Team Strength Analysis, which will be done sometime in the future.

This concept was first used and explained by me during the Wisden 20-20 Television shows broadcast on Doordarshan during 2001-02. These ideas have since been refined considerably.

Response to user comments

1. This is not an overall "Who is the greatest ODI Batsman" analysis. That has been done by me for Wisden a couple of years back and I will do it again in this column later. In that analysis I will take ino account factors such as Runs scored, Wins, % of Team runs, MOM awards, Quality of opposition et al.

This is a list of top ODI batsmen using only the two relevant factors, viz., Runs scored (Avge or RPI) and Scoring Rate. This should only be compared to "Listing the best ODI bowler by Bowling Average".

2. David Barry has correctly mentioned the Cricinfo Statsguru figures. However let me mention that my need is not an overall "Richards scored xxx runs in yyy balls" information. That will only help a Career analysis. I need information by match and I have resorted to the method shown. May not be perfect. But in this particular case, nothing will be perfect. My Database methodology does not permit (correctly) a career sum, different to the sum of individual innings values.

3. Unlike what some people have implied, I have no intention or desire to push one batsman or other up or down. I do the analysis and leave the readers to judge for themselves. If in the bargain the readers' favourite batsman is not shown where he should be (in their perception), my apologies. Only thing is, don't be rude to me or other readers (your comment will go the trash then, even if it is a good one) nor ascribe the variation to deliberate intention. After all these are only analyses.

4. If the limit of 2000 runs is too low, one could increase it to, say 2500. Maybe then Gambhir would not get in. Then people should accept that Hussey, Botham, Greg Chappell et al would also not get in.

5. David (Barry) has since pointed out that the revised Cricinfo scorecards have complete balls faced data. It is possible that I have used the older version with incomplete scorecards and had to resort to extrapolation. It will take me some time to convert to the newer version since it involves downloading, parsing and updating the database. I will immediately start work on this. Many thanks to David.

6. There has been an excellent suggestion to do some equalizing of Strike Rates between the early years and recent years. Let me look into that. That will at least enable olden greats such as Greenidge, who certainly is not a career strike rate of 66.3 into something more acceptable, say 75.0. In this case a case should be made for equalizing averages or RPI also.

7. Abhijeet Dongre has made a good suggestion. To consider the not out innings as not an innings if the runs scored falls below the average is a novel idea and is worth considering. Let me work on it.

8. Jayasuriya's somewhat low position seems to have offended quite a few people, especially from the lovely little emarald isle. My own take on this is that he would certainly in the Top 10 when I do a comprehensive analysis of ODI Batsmen considering all facts mentioned in point 1 above. Until then my Sri Lankan brethren, please bear with me. At least you don't abuse me. You even make your protests in a gentle manner.

9. Jeff Grimshaw's Balls per dismissal suggestion has a very authentic and solid feel about it and I am seriously looking at incorporating the same. Same as with Abhijeet's suggestion.

	Difficult to dislodge: Shivnarine Chanderpaul © Getty Images

Although he is not the most dynamic batsman going around, Shivnarine Chanderpaul has been carving himself a most unusual statistical place in recent years. His career has been studded with extraordinary spells where he becomes near-impossible to dismiss. Since overcoming a foot problem and undergoing surgery in 2000, he has made a habit of stringing unbeaten innings together, so much so that he has batted for more than 1000 minutes between dismissals on four separate occasions, twice in the past year. His last four Test innings, in the series against Australia, spanned 1115 minutes before until at last he fell lbw to Stuart Clark.

For comparison, consider that only five other batsmen have ever gone unbeaten for over 1000 minutes, none of them more than once.

Longest batting between dismissals

Player	Minutes	Balls	Runs	Scores
S Chanderpaul (2001/02)	1513	1051	362	67*, 101*, 136*, 58
JH Kallis (2001/02)	1241	908	456	157*, 42*, 189*, 68
SR Tendulkar (2003/04)	1224	879	497	241*, 60*, 194*, 2
R Dravid (2000/01)	1145	791	473	41*, 200*, 70*, 162
S Chanderpaul (2007/08)	1115	689	313	107*, 77*, 79*, 50
S Chanderpaul (2007)	1074	677	322	116*, 136*, 70
S Chanderpaul (2004)	1031	698	371	101*, 128*, 97*, 45
N Hussain (1999/2000)	1023	744	231	70*, 146*, 15
Shoaib Mohammad (1990/91)	1007	634	308	203*, 105

These are all relatively recent events, thanks partly to the fact that over-rates are much slower than in olden days. But if we turn to balls faced, Chanderpaul still leads. He is the only batsman to ever face 1000 balls without getting out.

Most balls faced between dismissals

Player	Balls	Minutes	Runs	Scores
S Chanderpaul (2001/02)	1051	1513	362	67*, 101*, 136*, 58
WR Hammond (1928/29)	980	703	296	119*, 177
Hanif Mohammad* (1957/58)	930	973	337	337
JH Kallis (2001/02)	908	1241	456	157*, 42*, 189*, 68
SR Tendulkar (2003/04)	879	1224	497	241*, 60*, 194*, 2
L Hutton (1938)	847	797	364	364
GS Sobers (1957/58)	800	876	490	365*, 125
R Dravid (2000/01)	791	1145	473	41*, 200*, 70*, 162
KF Barrington (1964/65)	780	913	323	54*, 148*, 121

*Balls faced for Hanif is an estimate.

A striking feature is Chanderpaul’s highest score in these purple patches is only 136 not out. It is a sign of the general weakness of his team’s batting, as well as his defensive nature, that he so often is left unbeaten without making huge scores. It could certainly be argued West Indies are losing out on potential runs because of this; perhaps he should bat higher in the order.

Curiously, the 362 runs he scored in that 1000-ball sequence is not even in the Top 20 for most runs between dismissals, which is led by Tendulkar (497) and Sobers (490) in the tables above. Chanderpaul is in the Top 20 thanks to his 371 runs in 2004/05, but well down the list.

One reason for his success is that Chanderpaul has become the nearest thing to an unbowlable batsman seen in Test cricket. This has developed in recent years as his technique has changed. Even though he has been out bowled in 11% of his dismissals, not an especially low figure, many of these dismissals came earlier in his career. From 2004 to 2007, Chanderpaul played a sequence of 57 innings without being out bowled. He scored 2629 runs, faced 5693 balls, and batted over 138 hours without anyone hitting his wicket! Javed Miandad (2055) is the only other batsman to score over 2000 runs without being bowled, although Kumar Sangakkara is now right in the hunt for this record, having scored 1983 runs since he last heard the death rattle. Adam Parore of New Zealand batted 77 times before he was out bowled for the first time in a Test match, scoring 1937 runs.

One other curiosity: Chanderpaul is known for his caution, yet has made one of the fastest Test centuries of all time. His normal scoring rate is just over 43 runs/100 balls: among current batsmen, only Rahul Dravid has scored more runs at a slower rate. Yet Chanderpaul has to his credit the fastest century ever scored against Australia, and the fourth-fastest in all Tests, 69 balls in Georgetown (his home ground) in 2003. Has anyone ever batted quite so “out of character”? Perhaps not. The next fastest century by Chanderpaul, 140 balls (in the same series) is less than half as fast as his best, and the average of his other centuries is 212 balls. No other major batsman has a fastest century so unlike all his others.

	Brian Lara had a remarkably consistent Test career, with hardly any peaks or troughs © AFP

Brian Lara finished his career with a batting average of more than 50. It is certain that during his illustrious career he would have gone through a few peaks and troughs. Not necessarily a sine-wave pattern but certainly up and down. It is also certain that a few of these would have been way outside his career average of 52.89. This article looks at such peaks and troughs occurring in the careers of Test batsmen.

This analysis will be in two parts. The first looks at the batsman's career in fixed segments. The second is to look at batting sequences, both outstanding and abysmal.

As usual, we have to set some criteria and parameters. As also is normally done, these are common-sense based and will meet expectations of most discerning readers. 1. The number of innings played should be 50 or more. This is a fair requirement since otherwise we will not have sufficient data to analyse. The limit of 50 innings means that an average of 30 Tests would have been played by the batsman. Also the batting average should be greater than 25.0. We are certainly not interested in analysing the batting exploits of Curtly Ambrose, Shane Warne, Harbhajan Singh et al who have played well over 50 innings. I know this will exclude players such as JM Parker (NZl), Nick Knight (Eng), Asif Mujtaba (Pak), Mohammad Ashraful (Bng) et al, all with sub-25.0 averages. In order to complete the analysis properly I have included batsmen whose batting average is less than 25.0 but whose BPA (Batting Position Average) is less than 6.0. Twelve batsmen, including all four mentioned above, have now been included. With this criteria, a total of 299 batsmen get selected for analysis.

2. I will consider a unit of 10 innings [or more], hereinafter called a stretch, as a unit for measuring the average and variation from average. This represents between five and eight Tests, normally spanning across two or more series and is a good measure. We will consider the batting average during this period as that is the most accepted unit of batting measure. Runs per inns and Run aggregate both suffer from significant shortcomings.

3. In the first part, each batsman's peak and trough will be measured against his own career batting average. The need for this method of measuring is best proved by considering the batting averages of two opening batsmen of different eras, of totally diverse temperament, skills and application levels. Herbert Sutcliffe had an average of 60.73 and Kris Srikkanth weighed in with 29.88. If Sutcliffe had a stretch average of 20, he would consider it as a very low period while Srikkanth would find it quite acceptable. Sutcliffe would have to have a stretch average of 75+ to think that he had a very good run, while Srikkanth would be over the moon with a stretch average of 45.0.

4. What is a peak? What is a trough? I have defined a peak or a trough to be 50% on either side of the career batting average. In other words, if a batsman has got a batting average which is above 150% of his batting average, it is considered a peak. If a batsman has got a batting average which is below 50% of his batting average, it is considered a trough. Looks subjective, but has been done based on lot of research.

5. The analysis will be done in two distinct parts. The first is an easier and more understandable method where the batsman's career is split into as many fixed stretches as required (1-10, 11-20, 21-30 et al until career-end) and then the peaks and troughs are determined. The last stretch, if below 10 innings, will be ignored. Because of the fixed interval, it is possible that a run such as Mohinder Amarnath's sequence of 4, 7, 0, 0, 1, 0, 0, 0 might be split into two different stretches. It so happens that Amarnath bookended this horrible run with scores of 91, 81, 54, 116 and 36, 101*, 37, 49 on either side. This is a simple exercise.

6. This is a simple (okay, not so simple) analysis of a player's career performance. No allowance has been made for the quality of opposition, bowling quality, home or away Tests, match results et al. The purpose is not to determine the quality of innings but just to determine deviations away from the mean values. I also personally think that failures against stronger teams cannot be justified nor can successes against weaker teams be derided.

Now let us take a look at the tables for Part 1. The analysis is current upto and including the Colombo match in which the vaunted Indian batsmen were found wanting.

1. Table of Peaks, by % of Batting Average

No  Cty Batsman          Stretch Ins No Runs Avge CarAvge  %
                          St End
 1. Slk Tillakaratne H.P  91 100 10  6  641 160.25 42.88 373.74
 2. Saf Kallis J.H        81  90 10  6  711 177.75 56.28 315.80
 3. Slk Sangakkara K.C   101 110 10  4 1036 172.67 54.81 315.01
 4. Ind Vengsarkar D.B   141 150 10  4  788 131.33 42.13 311.70
 5. Saf Pollock S.M       91 100 10  6  398  99.50 32.32 307.89
 6. Slk de Silva P.A     101 110 10  2  961 120.12 42.98 279.49
 7. Eng Gatting M.W       61  70 10  4  568  94.67 35.56 266.24
 8. Saf Pollock S.M       71  80 10  5  421  84.20 32.32 260.55
 9. Aus Trumper V.T       71  80 10  2  774  96.75 39.05 247.76
10. Pak Mudassar Nazar    51  60 10  2  716  89.50 38.09 234.95

There is no doubt that the high averages for most of the stretches in the top 10 have been because of the high number of not-outs. That is a parameter we have laid down and there is nothing fundamentally wrong with that. One has to admire Hashan Tillakaratne for his stretch of 55*, 11, 10, 16, 136*, 10*, 105*, 87, 7* and 204* and Kumar Sangakkara for his stretch of 287, 14, 39, 4, 100*, 156*, 8, 6, 200* and 222*.especially for their determination in scoring big centuries and remaining unbeaten. Also Sangakkara exceeded 1000 runs. Jacques Kallis, the unsung South African batsman, has a few impressive runs such as this stretch consisting of 51, 157*, 42*, 189*, 68, 21*, 24, 89*, 5 and 65*.

To view the complete list, please click here

2. Runs scored by batsman in a stretch

Mohammad Yousuf (1070), Sangakkara (1037) and Viv Richards (1036) are the only batsmen to exceed 1000 runs during any stretch. The year 2006 was a golden year for both Mohammad Yousuf and Sangakkara as was 1976 for the great Richards. As with Lara, Richards has few not-outs, as showed in this sequence. Surprisingly, Mohammad Yousuf also had no not-outs, probably explaining why they dropped down in the previous tables.

At the other end Ian Healy (59), AC Bannerman (72) and Marvan Atapattu (73) have scored the least number of runs during a stretch.

To view the complete list, please click here

3. Table of Troughs, by % of Batting Average

No  Cty Batsman          Stretch Ins No Runs Avge CarAvge  %
                          St End
 1. Aus Ponting R.T       61  70 10  1   74   8.22 58.35 14.09
 2. Slk Atapattu M.S       1  10 10  0   73   7.30 39.02 18.71
 3. Aus Healy I.A        171 180 10  0   59   5.90 27.40 21.54
 4. Eng Edrich W.J         1  10 10  0   87   8.70 40.00 21.75
 5. Eng Compton D.C.S     61  70 10  1  108  12.00 50.06 23.97
 6. Eng Flintoff A        11  20 10  0   86   8.60 32.42 26.53
 7. Ind Jaisimha M.L      61  70 10  1   75   8.33 30.69 27.16
 8. Aus Waugh S.R          1  10 10  1  125  13.89 51.06 27.20
 9. Zim Flower G.W        71  80 10  0   84   8.40 29.55 28.43
10. Nzl Rutherford K.R     1  10 10  0   77   7.70 27.09 28.43

During the subject stretch Ponting averaged only 14.09% of his high career average. His miserable run consisting of 14*, 0, 6, 0, 0, 11, 11, 14, 4 and 14 was caused by the Indian spinners in India during 2001 and Darren Gough in England during the unforgettable Ashes tour. Atapattu's "bit pattern" run of 0, 0, 0, 1, 0, 0, 25, 22, 0 and 25 was at the start of his career. Who would have imagined that he would finish with a career average of nearly 40 and score six double-hundreds. Ian Healy's run of 0, 6, 10, 0, 3, 6, 16, 11, 3 and 4 was at the end of his career and hastened his departure. He needed to make this average ten-fold to keep Gilchrist out.

4. Summary of selected players' peaks and troughs

Cty Batsman             Mats Ins    Stretches
                                 Tot  P  T  A  B
Aus Border A.R           156 265  26  2  0 11 13
Aus Waugh S.R            168 260  26  5  3  8 10
Ind Tendulkar S.R        148 240  24  2  2 10 10
Win Lara B.C             131 232  23  1  0 10 12
Ind Gavaskar S.M         125 214  21  2  2  8  9
Eng Atherton M.A         115 212  21  1  1 11  8
Saf Kallis J.H           121 205  20  4  3  7  6
Pak Inzamam-ul-Haq       120 200  20  0  3 11  6
Nzl Fleming S.P          111 189  19  1  0  7 10
Win Richards I.V.A       121 182  18  2  1  5 10
Slk Jayawardene D.P.M.D   96 156  15  0  0  8  7
Aus Bradman D.G           52  80   8  0  0  4  4

Legend: P-Peaks (above 150%), T-Troughs(below 50%), 
A-Above Batting avg (100-150%), B-Below Batting avg (50-100%).

Border was consistency personified with two peaks and no troughs. Steve Waugh was just the opposite. Quite a few peaks and troughs. Sachin Tendulkar was somewhat more predictable than Steve Waugh. The surprise is Lara - only one peak and no trough. It shows a facet of his batting which has not been appreciated. Surprisingly Gavaskar's and Tendulkar's distributions are identical. Michael Atherton is somewhat like Lara, with no great variations.

Kallis is similar to Steve Waugh, lots of variations. Surprisingly Inzamam is prone to more losses of form. However this is made up by a very high number of stretches which are above average. Richards has twice as many below-average stretches as above average. Possibly a reflection of the carefree batting he practised.

Finally note Mahela Jayawardene's distribution. He has no peak and no trough. He and Don Bradman are the only batsmen in this list with such consistent batting records.

To view the complete list, please click here

Part 2: Analysis of high stretch averages and low stretch averages

This analysis is totally different to the first one. The methodology is briefly explained below.

1. The batsmen are selected on the same basis. This time also 299 batsmen are selected.

2. Each innings played by the qualifying batsman is taken as the base and the rest of the career analysed. For each of these innings, the best stretch average is determined. With a minimum of ten innings as a valid stretch, the running averages are computed and the selection is done. Averages above 100.00 and below 10.00 are tabulated.

3. These tables are studied and because of overlapping stretches, appropriate non-overlapping stretches selected and sequenced.

5. Table of high average run scoring stretches

 1.Sangakkara K.C  105 114 10 4 1185 197.50
{100*,156*,8,6, 200*,222*,57,192,92,152}

 2.Sobers G.St.A    29  38 10 4 1115 185.83 
{365*,125,109*,14, 27,25,142*,4,198,106*}

 3.Tillakaratne H.P 95 105 11 7  721 180.25 
{136*,10*,105*,87, 7*,204*,96,37,3,19*,17*}

 4.Kallis J.H       81  90 10 6  711 177.75 
{51,157*,42*,189*, 68,21*,24,89*,5,65*}

 5.Bradman D.G      50  59 10 2 1236 154.50 
{212,169,51,144*, 18,102*,103,16,187,234}

 6.Kallis J.H      118 127 10 3 1065 152.14 
{158,44,177,73, 130*,130*,92,150*,40,71}

 7.Hammond W.R      88  97 10 4  889 148.17
{87*,29,63*,65, 167,217,5*,0,25,231*}

 8.Bradman D.G      18  28 11 2 1327 147.44 
{223,152,43,0, 226,112,2,167,299*,0,103*}

 9.Vengsarkar D.B  133 142 10 6  584 146.00 
{1*,37*,126*,33,61, 102*,38,0,22*,164*}

10.Bradman D.G      63  72 10 3  984 140.57 
{56*,12,63,185, 13,132,127*,201,57*,138}

Sangakkara's phenomenal run is the best ever and is of recent vintage. Sobers blossomed once he scored his first Test century, which turned to be the world-record breaking one. Tillakaratne had the benefit of quite a few not-outs. But his run was wonderful for a journeyman batsman. Bradman has three distinct stretches. With a career average of 99.96 it is not surprising to see him exceeding 140 three times in his career. There are many overlapping stretches during which Bradman has exceeded averages of 120. Kallis is the only other batsman who has had two separate 140-plus stretch averages. Dilip Vengsarkar is the only Indian batsman in this elite list.

6. The career-best best stretch averages for a few other famous batsmen is given below.

Lara B.C       164 173 10 1  851  94.56 
{68,60,209,10, 80*,29,1,191,1,202}

Tendulkar S.R  105 114 10 3  736 105.14 
{124*,18,126*,15, 44*,217,15,61,0,116}

Ponting R.T     10 119 10 2  928 116.00 
{169,53*,54,50, 242,0,257,31*,25,47}

Dravid R        65  74 10 3  835 119.29 
{28,41*,200*,70*, 162,9,39,25,180,81}

Gavaskar S.M     1  10 10 3  831 118.71 
{65,67*,116,64*, 1,117*,124,220,4,53}

Richards I.V.A  27  36 10 0 1093 109.30 
{177,23,64,232, 63,4,135,66,38,291}

Javed Miandad   23  32 10 5  654 130.80
 {154*,6*,35,100, 62*,81,160*,26,30,0*}

Gilchrist A.C   35  45 11 5  715 119.17 
{83*,7,22,30*, 34,204*,138*,24,91,16,66*}

Flower A        82  94 13 4 1243 138.11 
{183*,70,55,232*, 79,73,23,51,83,45,8*,142,199*}

Lara is the only one who has not exceeded 100. Primarily because he remains not out very few times. Gavaskar's is his debut stretch. Andy Flower has a 13-innings stretch in which he averages 138+. Playing in a weak team, this is a remarkable achievement. Richards has exceeded 100 even though he was dismissed in all 10 of the innings.

7. Table of low average run scoring stretches

 1.Reid J.R          8  17 10 0   36   3.60 
{0,3,6,1,9,7,6,0,3,1}

 2.Bannerman A.C    27  39 13 1   57   4.75 
{8,5,2,15*,4,2,2,0,0,13,5,1,0}

 3.Wishart C.B       6  15 10 0   52   5.20
 {3,2,25,0,10,0,7,3,0,2}

 4.Healy I.A       167 176 10 0   56   5.60 
{0,14,5,12,0,6,10,0,3,6}

 5.Vettori D.L      13  23 11 1   57   5.70 
{0,14*,1,3,16,0,20,0,0,0,3}

 6.Kapil Dev N      38  47 10 0   60   6.00 
{19,2,7,5,0,0,9,0,4,14}

 7.Fletcher K.W.R   19  29 11 1   64   6.40 
{4,2,1,28*,1,0,5,2,0,16,5}

 8.Knott A.P.E      69  78 10 1   65   7.22
 {2,0,0,21,4*,5,0,21,5,7}

 9.Atapattu M.S      1  10 10 0   73   7.30 
{0,0,0,1,0,0,25,22,0,25}

10.Nadkarni R.G     52  62 11 1   73   7.30 
{0,7,14*,9,0,3,15,17,2,0,6}

John Reid's stretch is the worst by any batsman in Test history. Ten consecutive single-digit scores is something, a record no recognised batsman has achieved. Ian Healy's poor scoring stretch is towards the end of his career. He has averaged 8.12 in a 17-innings stretch. Atapattu's stretch is on his debut. Fletcher, with an average of 6.40 early in his career, is one of the three recognised Test batsman to have had very low stretches.

I have implemented Daniel Cotton's suggestion of 10 dismissals instead of 10 innings and the results are tabulated below.

Table of Peaks, based on 10 consecutive dismissals, by % of Batting Average

Batsman          Stretch Ins No Runs StrAvge
                  St End

Based on running average
Sobers G.St.A      29  42 14  4 1774 177.40
{365*,125,109*,14,27,25,142*,4,198,106*,29,9,44,0}

Flower A           85  99 15  5 1561 156.10
{232*,79,73,23,51,83,45,8*,142,199*,67,14*,28,114*,42}

Bradman D.G        18  29 12  2 1523 152.30 
{223,152,43,0,226,112,2,167,299*,0,103*,8}

Kallis J.H         81  96 16  6 1481 148.10
{51,157*,42*,189*,68,21*,24,89*,5,65*,38,99,4,34,3,8}

Sangakkara K.C    109 120 12  2 1433 143.30 
{200*,222*,57,192,92,152,1,46,50,21,10,14}

Based on innings played
Tillakaratne H.P   95 113 19  9 1186 118.60
{136*,10*,105*,87,7*,204*,96,37,3,19*,17*,20,
39,20,32*,18,5*,24,27}

Chanderpaul S     176 193 18  8 1044 104.40
{116*,136*,70,104,8,65*,70*,0,23,3,18,86*,118,
11,107*,77*,79*,50}

Kallis J.H         79  95 17  7 1259 125.90
{30*,17,51,157*,42*,189*,68,21*,24,89*,5,
65*,38,99,4,34,3}

Javed Miandad      23  39 17  7 1204 120.40
{154*,6*,35,100,62*,81,160*,26,30,0*,19,16,
129*,19,76,30*,34}

Chappell G.S       59  74 16  6 1031 103.10
{4*,123,109*,13,43,52,182*,6*,4,48*,68,54*,
52,70,121,67}

In response to the requests of the readers to do an analysis, not limiting to 10 innings and having a stretch anywhere, not just at 1, 11, 21 etc., I have given below the top 10 entries in this table.

Table of Peaks, with stretches > 10 innings, by % of Batting Average

Cty Batsman              Stretch Ins No Runs Avge CarAvge  %
                          St End

 1. Pak Mudassar Nazar    42  54 13  4  959 106.56 38.09 279.73
 2. Ind Vengsarkar D.B   136 145 10  3  796 113.71 42.13 269.88
 3. Slk Tillakaratne H.P  89 100 12  6  665 110.83 42.88 258.49
 4. Nzl Greatbatch M.J     1  13 13  4  693  77.00 30.62 251.46
 5. Ind Nadkarni R.G      35  45 11  5  378  63.00 25.71 245.05
 6. Win Adams J.C         11  21 11  3  781  97.62 41.23 236.76
 7. Eng Boycott G         71  82 12  4  890 111.25 47.73 233.08
 8. Ind Gavaskar S.M       1  10 10  3  831 118.71 51.12 232.22
 9. Aus Taylor M.A       164 173 10  3  701 100.14 43.50 230.23
10. Eng Hick G.A          56  67 12  3  642  71.33 31.32 227.73

To view the complete list, please click here

Response to comments

1. Apologise for mixing up Kallis and Sangakkara sequences. Has been corrected.

2. Very good suggestion on taking 10 consecutive dismissals rather than 10 consecutive innings. Will take it up.

3. A few people have questioned the need for fixed 10-innings stretches (1-10, 11-20, ...) and have suggested variable duration stretches. Let me say that I did all the work in completing the analysis for variable lenth of stretches and my first cut of the article was with 6 tables with these two variations. Then I found that there was not much variation between the two, the article was too long and I was missing an analysis completely excluding the Batting average. Hence I re-did the second part as it stands today. The tables are displayed in the main part of the article.

4. David (Barry) has raised a valid comment on the fact that the number of Peaks outnumber number of Troughs by 2 to 1. My response is set out below.

a. This is not an analysis either side of a a single mean measure (Batting Average), It is based on 10-innings stretches and hence the normal statistical conclusions may not be applicable.

b. Only the Peaks outnumber the Troughs (330 vs 171). However the number of Above-average stretches actually trail the Below-average stretches (1043 to 1334).

c. So the conclusion is that the 50% on either side is probably not equitable. It is possible that a more correct cut-off pair might be 140% and 40%.

5. Every article of mine gets converted into a Lara vs Tendulkar one so much that I will probably do an article analyzing Lara and Tendulkar WITHOUT COMING TO ANY SPECIFIC CONCLUSION. Let readers draw their own conclusions.

6. A valid question has been raised on the methodology in determining the variable stretches. One method is to keep on going until the cumulative average falls below the limit of 150%. In this case the emphasis is on the length of the stretch. The other method is to keep on going until the highest % value is reached. In other words, close the stretch once the % figure drops off. In this case the emphasis is on the % value rather than length.

Both tables were craeted. However what has been presented is the value based one, in other wirds, the highest %. 7. Shishir and Peter have made valid points on the 'point' nature of the stretches. I accept this comment. However it must be remembered that this was only the starting point of the exercise. Please look at the other analytical tables. This problem will disappear since there is no artificial limit of 10 innings in these analysis.

	Sanath Jayasuriya's 340 was the cornerstone of Sri Lanka's 952 for 6 declared, the highest total in Test cricket © Getty Images

When comparing the biggest team scores in Tests, the results can be a bit messy. This is because cricket often does not allow teams to carry their innings to completion, and big innings are often truncated by declaration or lack of time. We know for sure that the highest innings in a Test match is Sri Lanka’s 952 for 6 in 1997, but an interesting side question would ask if this is also the most ‘extraordinary’ score in Tests. For example, we know that the West Indies once made a score of 790 for 3. Where might such an innings have gone if it had continued? Can we compare it to Sri Lanka’s record?

While we can never know for sure, it is possible to make a statistical estimate. The approach is to look at the way that innings naturally progress over a wide range of scores. Of course, there is plenty of variation between innings [part of cricket’s appeal], but there are statistical patterns. A team that is, say, five wickets down, will on average add a certain number of runs if the innings is played to completion.

This average number of runs added also depends on the starting point. A team on, say, 50 for 5, can be expected to add fewer runs than a team on 500 for 5 before being bowled out. But there is a surprising result to be found here. Contrary to expectation, the number of runs at the starting point is not very important, with only a limited effect on the future progress of the innings. This is shown in the following table, calculated from the outcomes of all relevant Test innings, which gives the average number of runs added by teams with five wickets down, at different starting points.

Average runs added when five down

Starting score	Runs added (average)	Projected all-out score
50 for 5	85	135
100 for 5	91	191
200 for 5	99	299
300 for 5	114	414
400 for 5	116	516
500 for 5	114	614
600 for 5	110	710

What we see here is that above a certain level, in this case about 300 runs, there is very little change in the potential scoring of a team. This is surprising, but it probably comes down to the fact that a batsman coming in at a score of 600 for 5 is likely to bat in a riskier manner, or with less intensity, than one who comes in at 300 for 5. This would appear to balance out any advantage from tired bowling or benign conditions. This pattern is also seen at 6, 7, 8 or 9 wickets down.

It should be stressed that these runs added will often be theoretical in practice. For example, the projected all-out score for teams that reach 600 for 5 is 710, but in practice most such innings will not reach 700, often because of declarations. What the projected all-out score gives us is an estimate of where the innings was headed if the limits of time and tactics had been removed – its trajectory if you will.

With modern computer power, the result of this process is an “Innings Projector” that can give a projected estimate for any score. (In practice, it only works for innings with two or more wickets down.) Estimates for extreme innings must remain provisional because of the rarity of the situations, but the fact that trends are so stable, as illustrated by the first table, adds confidence to the results.

So what are the most extreme projected scores? Here is a list of the results:

Most extreme projected scores

Team	Opponent	Venue, year	Score	Projected score
Sri Lanka	India	Colombo (RPS) 1997	952-6	1028
West Indies	Pakistan	Kingston, Jamaica 1958	790-3	996
England	Australia	The Oval 1938	903-7	951
Sri Lanka	Zimbabwe	Bulawayo 2004	713-3	919
Sri Lanka	South Africa	Colombo (SSC) 2006	756-5	866
West Indies	England	St John’s, Antigua 2004	751-4	861
England	West Indies	Kingston, Jamaica 1930	849-10	849
New Zealand	Sri Lanka	Wellington 1991	671-4	821
India	Bangladesh	Dhaka (Mirpur) 2007	610-3	816
Australia	Zimbabwe	Perth (WACA) 2003	735-6	810
Pakistan	India	Lahore 1989	699-5	809
South Africa	Zimbabwe	Harare 2001	600-3	806
Australia	England	Lord’s 1930	729-6	804
England	India	Lord’s 1990	653-4	803
Australia	England	Leeds (Headingley) 1993	653-4	803
Australia	England	The Oval 2001	641-4	791
Australia	West Indies	Kingston, Jamaica 1955	758-8	788
Pakistan	India	Hyderabad (Pak) 1983	581-3	787
India	Pakistan	Multan 2004	675-5	785
Australia	England	Lord’s 1993	632-4	782
England	South Africa	Lord’s 1924	531-2	779
West Indies	New Zealand	Wellington 1995	660-5	770
England	South Africa	Durban 1939	654-5	764
Pakistan	Sri Lanka	Faisalabad 1985	555-3	761
South Africa	England	Lord’s 2003	682-6	757
Pakistan	Bangladesh	Multan 2001	546-3	752
India	Australia	Sydney 2004	705-7	752
India	Australia	Sydney 1986	600-4	750

So Sri Lanka retains the No. 1 position under this calculation. However, the West Indies 790 for 3 moves up to second place, while England’s 849 all out in the Timeless Test of 1930 moves down to seventh.

Another aspect to these scores is that the distribution of the scores around these projections can be calculated, which means that the probability of a specific score can also be calculated. For example, the probability of a score of 790 for 3 actually exceeding the 1028 assigned to Sri Lanka’s record is about 24%.

One other possible calculation here is a re-appraisal of the most one-sided innings victories in Tests. Using the projected score, the margin of victory can be re-calculated and compared more evenly. The most one-sided Tests in this analysis are:

Most one-sided Tests

Venue, year	Team	Opponent	Score	Projected score	Original margin	Projected margin
The Oval 1938	England	Australia	903-7	951	Inng and 579	Inng and 627
Multan 2001	Pakistan	Bangladesh	546-3	752	Inng and 264	Inng and 470
Bulawayo 2004	Sri Lanka	Zimbabwe	713-3	919	Inng and 254	Inng and 460
Kolkata 1958	West Indies	India	614-5	724	Inng and 336	Inng and 446
Dhaka (Mirpur) 2007	India	Bangladesh	610-3	816	Inng and 239	Inng and 445
Wellington 1995	West Indies	New Zealand	660-5	770	Inng and 322	Inng and 432
Johannesburg (New Wanderers) 2002	Australia	South Africa	652-7	699	Inng and 360	Inng and 407

(Please, no comments that the ‘highest’ does not mean the ‘greatest’. No one is claiming that it does. We are just looking at extremes here.)

[Technical note: the trajectory at large scores must be calculated with care, because teams that continue with great success from a high starting point rarely complete their innings. This must be allowed for in the calculation. The way to do this is through an iterative process, where big innings that are declared closed are themselves calculated through to completion, firstly for innings that are nine wickets down, then eight, seven, and so forth, and these results are then fed back into the calculation for end points starting from fewer wickets down.

For example, take a score of 500 for 3. This has occurred 37 times in Test matches. The projected score in this case is 705 all out. However, only three of the 37 teams have actually reached or exceeded a score of 705, while nine have been bowled out for less than 700. The reason that the projected score is above 700 is that many teams continue to do well but declare before reaching 700. Careful iterative analysis of these declared scores produces the average estimate of 205 runs added, or 705 all out for a projected score.]

	Matthew Hoggard has played some vital night-watchman innings © Getty Images

In the first part I looked at a methodology for determining night-watchman situations and looked at individual performances. In this concluding part, I have done a team analysis and come to a conclusion whether the night-watchman experiment is a success or not. I have also looked at readers' comments.

Note: David Barry has sent me an invaluable file containing the day-end batsmen data for all the tests. I myself had gone to my own Text archive and found that this information is available for most matches. However parsing those files would have required lot more effort than parsing the CSV file David has sent.

I will complete the work and come out with a revised article incorporating the actual player data. I will also do a comparison of the actual results and my own derived results. However this will be after some time after looking at a few other interesting ideas already in the pipeline.

I owe David one for this.

There was a suggestion to use the day-end player data which is available in text scorecards. While accepting that this is available in most scorecards, I have to express the inability to do so at the current stage because I have to download quite a few scorecards, do a text-based data mining to extract this data, do some complex parsing work and link this data to the player and fall-of-wicket data already available. This is certainly possible. However, this will take too much time and resources and it is not possible to do this at this instance. Possibly at a later date.

The question of setting up 25.0 as the cut-off batting average has already been raised in two forms. One, questioning the arbitrary nature of this cut-off value, and two, the applicability of lowering this for the pre-WW1 Tests in which the batting averages were consistently lower.

It is impossible for me to work out an algorithm to do a more objective determination of this cut-off value. Whatever I do is likely to be questioned and be subjected to unacceptable variations. I have done this summary of batting averages, over 1879 tests, to substantiate the 25.0 cut-off.

Total Bat Runs: 1719071
Innings:          66117
Not Outs:          8622
Bat Average:      29.90

This is the overall average. This is about 10% below the mid point of the highest average (68.8, excluding Bradman's freakish figure) and lowest average (0.0). As such a figure which is 25% below the mid point figure seems to be the ideal cut-off point for determining night-watchmen. This works out to 25.8, which is just above the current cut-off. Hence the cut-off of 25.0 is retained.

However there is a justification to have this cut-off at a lower figure of 20.0 for all Tests played before 1914. This has excluded some night-watchman instances. The number has now decreased from 563 to 552 since 11 instances which were earlier determined to be night-watchman instances are now outside the

scope.

There was a suggestion that a situation where a No.7 batsman such as Vettori is substituted by a no.11 batsman such as Martin should be considered as a night-watchman instance. In this particular case, the average differential, 26+ against 2+, makes it a correct and valid suggestion. However, this cannot be generalised. If Kumble's place is taken by Sreesanth, the situation is murky. Kumble has an average of 18.25 and Sreesanth has an average of 15.50. By no stretch of imagination can we deem this to be a night-watchman situation. For that matter these numbers could even be reversed. Hence, while readily acknowledging the validity of the readers' suggestion, I have to, with reluctance, stick to my decision that only nos. 3-6 will be considered as night-watchman positions.

Then we come to the requirement that we have to consider the batting average of the batsman being replaced. This is something I am very loath to do because of the many inherent weaknesses. Until now I have determined a night-watchman situation solely by the measures of the specific batsman, what was his career-to-date batting average, what was his BPA and which position did he bat in. When I am not even sure who would have been the next batsman, such a move is fraught with problems.

Country summary (1879 tests)

Cty   NWI  Tests  Tests/NWI    # 3-6 inns  Inns/NWI

Aus:   96    696     7.25         4688       48.8

Bng:    5     53    10.60          417       83.4

Eng:  124    873     7.04         5880       47.4

Ind:   56    418     7.46         2797       49.9

Nzl:   50    342     6.84         2403       48.0

Pak:   62    335     5.40         2220       35.8

Saf:   55    332     6.03         2318       42.1

Slk:   22    177     8.04         1181       53.7

Win:   69    448     6.49         3023       43.8

Zim:   13     83     6.49          607       46.7

Icc:    0      1     0.00            8        0

      552   3758     6.80 (3.40)

Pakistan has used night-watchmen most often and Bangladesh the least. Sri Lanka have been quite reluctant to use the night-watchman option but South Africa haven't been averse to doing so. However, Bangladesh figures may not be accurate since only three of their batsmen have averages higher than 25.0 and a few night-watchman innings would have been lost. I did not want to lower the cut-off for them only to 20.0, which might have been the correct thing to do. It wasn't worth the effort since it might only add couple more instances.

The last column is a measure of night-watchman occurence based on the number of qualifying innings (nos. 3-6) for the concerned country. Here again Pakistan leads with one instance every 36 innings, followed by South Africa, once every 44 innings. Bangladesh, possibly for reasons already discussed, emplys this once every 83 innings. Just for information, Bangladesh have played 106 Test innings. Out of these, they have lost fewer than four wickets only three times - once the innings didn't start, once they lost three wickets and once they lost just two.

Overall the night-watchman instance occurs once in about three-and-a-half Tests.

Conclusion

Now for the difficlut task of determining whether the night-watchman experiment has been a success or not.

There was a very good suggestion to consider factors other than the night-watchman innings itself, such as how the innings progressed, how much the next batsman scored et al to determine whether a night-watchman stint was a success. I am not very comfortable with the idea of linking the actual performance of the night-watchman to what happened in the game itself. If Gillespie came in as night-watchman and lasted 100 balls, it was an uqualified success. Whether Michael Clarke, who Gillespie replaced, scored 0 or 100 the next day doesn't really matter. Whether Australia won or lost beacuse of this decision again does not matter. We are only looking at whether the night-watchman did his job or not. If he scored 1 in 50 balls he had succeeded. If he scored 9 in 15 balls, got out and the next batsman had to bat the same day, his stint was a failure.

Assuming that no captain would be dumb enough to send a night-watchman an hour before close of play, we are looking at a possible maximum of around 8-10 overs to be played during the evening. We must also assume that the night-watchman should last for some time the next day. A valid conclusion is that if a night-watchman bats for 30 balls, he has more than done his job, since he has probably been in the middle for around 45 minutes.

The balls faced will either be the actual number (available in most of the matches) or the one derived from the team scoring rate, as explained in Part 1. While accepting that there could be very good scores by night-watchman of 0s, 1s, 2s ..., there is no way to actually cull out this data. The only concession I will make is that any night-watchman who scores 15 or more has done his job. Outside edges and wild swings (unlikely) could get him around 10 runs but not 15. It is very likely that he has faced a fair number of deliveries, possibly 30+, to score 15 or more. This criteria can now be applied irrespective of the method of arriving at the "balls played" information. 221 out of the 552 night-watchmen innings fall under this either-or criteria (at least 30 balls faced or 15 runs scored).

Out of the total population of 552, it can be deduced that 221 have succeeded in their task, making the success rate of the night-watchmen exercise around 40%. This figure is certainly much more than what I expected. The success stories are very significant, as were the cases with Gillespie, Hoggard, Tudor and Larwood. One great factor in these night-watchmen decisions is that they are sent in with the expectation that he might fail more often than not, especially if his name does not start with 'G'. If they succeed, that is a bonus, and if not, other than the loss of one late-order wicket, no serious damage has occurred. Hence a success rate of 40% seems beyond all expectation.

We have to conclude that, over time, the night-watchman experiment has been a great success. Having said that, there is a lot to be said for top-order batsmen taking up the responsibility of batting in difficult conditions, a task for which they are eminently trained, both in skill and temparament.

I must acknowledge the contributions of Dr.Ashwin Mahesh, my co-founder at Thirdslip.Com who, long time back, mooted the idea of using the difference between the BPA and actual batting position to identify a night-watchman situation.

Click here to see the complete list of night-watchman instances

Click here to see the list of successful night-watchman instances

Click here to see the list of unsuccessful night-watchman instances

	Jason Gillespie averages 116 balls per stint as night-watchman © AFP

After a light-weight ODI related post last time around (The "Unfulfilled team innings in ODIs"), I am now reverting to Test matches and a considerably more complex analysis.

The night-watchman concept in Test cricket is a paradox. A batsman of far lesser ability is sent to bat in place of a far more accomplished batsman, in possibly inferior batting conditions. The better batsman is preserved to bat when conditions are better. But this is as much part of Test cricket as white clothing, follow-on, new ball after 80 overs et al and deserves an in-depth look.

This time I have taken a conscious decision to do this post in two parts. The first part will deal with the individual batsmen performances while the second one will analyse the whole night-watchman canvas by team and by period. In addition, I will take a view on whether the night-watchman concept has been successful. I will also incorporate relevant readers' suggestions.

This analysis is based on the earlier study I have made on the Test batting positions. In that analysis, we looked at batting positions as a measure. To summarize that analysis, I had looked at the career Batting Position Average (BPA) of Test batsmen, keeping the two opening positions as 1. That index is used to have an analytical look at the night-watchmen.

Using night-watchmen as a tactic has existed down the ages. The night-watchmen regularly padded up an hour before close, and would walk in at the fall of a wicket. If he survived, great. Else, send another one hoping that at least he would survive. I have seen matches in which two such night-watchmen had failed and the regularly scheduled player was forced to bat, this time with his team having lost two more wickets. However, there have been many cases where the night-watchman survived that day and for quite some time the next day.

The Australians, led by Steve Waugh, changed things. A top-order batsman was expected to bat whatever be the time of the day, be it 10.47am or 16.53pm. There is no denying that this worked. Overall this seems to me to be the correct approach. Most other teams, for that matter even the Australians now, take the nigt-watchmen approach.

Our interest here is analytical. Let us first define a night-watchman. This is very difficult especially as there is very little data available on things like the time of the day when a batsman came to the wicket. So we can only take an algorithmic approach using the BPA and the batting position the batsman batted in. We may get it right 95% of the time, but that is enough.

A simple starting definition may be that a night-watchman is one who bats (somewhat) higher than his intended position. But we have to take care of situations such as an accomplished batsman like Gilchrist opening for Australia or Wasim Akram/Dhoni coming in earlier to speed up the scoring. Gilchrist's Batting Position Index in Tests is 6.68, indicating that he is a batsman who has batted at No.7 most of his career. Wasim Akram, scorer of three Test
centuries and a BPA of 8.1, batting at number 3 or 4, would have to be taken care of. In order to do a correct job of selecting true night-watchmen for our analysis, it is necessary to define a number of related parameters other than batting position alone.

1. First our knowledge, research and intuition lets us decide who is not a night-watchman. Any batsman whose career-to-date batting average is higher than 25.00 cannot be classified as a night-watchman. No captain is going to risk a batsman of the calibre of Vettori (ave 26.65) to protect Styris (36.05). His wicket is too valuable to risk losing. In this regard, we also have to take care of genuine batsmen like Wasim Akram (22.64), Benaud (24.46) etc who have batting averages between 20 and 25. A slight tweak takes care of such batsmen.

• Career-to-date average rather than career average is taken since by now I have realised the importance of taking this value as against career figure in certain situations. I have also realised the readers' preferences and have anticipated their inputs. It is also true that I have developed the Career-to-date figures and incorporated in my data base because of suggestions relating to earier postings making my task that much easier.
  
• In this case there is perfect justification. A player's cumulative measures keep on changing. A captain who decides to use a player as a night-watchman at a certain point in his career may not do so at another point depending on changes. For instance, in match 1486 against India, Nicky Boje was used as a night-watchman when the first wicket fell late in the day. His career-to-date batting average at that time was only 14.00. Hence we have treated this correctly as a night-watchman innings even though his end-career average was 25.23. If the career figure was used, this match-winning innings of 85 would have been missed out. This is just an example.

2. We should also ignore players whose BPA is less than 7.00. If a player normally bats in positions 1-6, and he moves up, he cannot be treated as a night-watchman. For instance a batsman with a batting average of 24 and BPA of 5.2 opens the batting, this is not an example of a night-watchman.

3. We have to look at it the other way as well: only innings in which tailenders have batted at positions 1-6 will qualify as night-watchmen innings. A no.10 batsman batting at no.8 is certainly not a night-watchman instance.

4. Finally, the key criterion. An innings will be considered as a night-watchmen innings if the difference between the batsman's BPA (rounded to nearest integer) and the one he actually bats in is greater than or equal to 3. Examples, a no.8 batsman batting at 5 or above, a no.10 batsman opening, a no.9 batsman sent at the fall of first wicket and so on.

• A note on the need to round off BPA. A BPA value of 7.86 indicates a batsman who has batted at no.8 or below more often than at no.7 or above. Similarly a BPA value of 5.18 indicates a batsman who has batted at no.5 or above more often than at no.6 or below. It is necessary to round up 7.86 to 8.00 and round down 5.18 to 5.00. This is how the rounding off is effected.


• The difference criteria of 3 was arrived at after many trials. If the difference was set up at 4, many a true night-watchman innings, such as a batsman with BPA of 9 batting at no.6, would be lost. A change to 2 would mean inclusion of many normal innings, such as a batsman with BPA of 7 batting at no.5.

5. There are situations when a batsmen such as Irfan Pathan or Derek Murray might genuinely have been asked to open a few times for strategic purposes. These are clearly non-night-watchman situations. However there is no way I can separate out these since their rounded BPA might be 7.0 and they have batted at no.1. The only way out seems to take a courageous decision that if a lower level batsman bats at the opening position, it is not a night-watchman situation. It is reasonable to expect that no captain would send his no.9 batsman to open, solely to protect his opening batsman, however late in the day the innings starts. This will also take out quite a few pre-WW1 batsmen such as Blackham who have opened at will. A total of 127 opening batsman innings have been handled by low order batsmen with BPA greater than or equal to 7.

It is true that many of the above criteria may seem arbitrary. However, before readers rush to comment after a 10-minute perusal of the article, I would like to remind them that I have been studying this fascinating aspect for over 2 years and have run programs with varying parameters many times before settling on the methodology. However, I am certain that by the time all readers' comments are received, the analysis would be improved considerably based on their feedback.

A. Analysis results

A total of 563 innings qualify under these criteria. It is possible that we might have missed a few genuine night-watchman innings and included a few non-night-watchman innings. I have aimed for 95% accuracy and am confident that I have achieved that. This works to slightly less than one in three tests. A perusal of the recent Test scorecards will indicate that this is a fairly accurate proportion.

These 563 innings are analysed in different ways below.

B. Runs scored


The top 10 individual scores are listed below.

Year MtNo Batsman            For Vs  Bat BPA Runs(BallsFaced) Batting Avge

                                                  Act  Calc   CTD*   Career

2006 1799 Gillespie J.N      Aus Bng  3  9.0 201*(425) (425) 15.69 [18.78]

1977 0811 Mann A.L           Aus Ind  3  7.0 105 (n/a) (214) 18.33 [23.62]

1999 1455 Tudor A.J          Eng Nzl  3  8.0  99*(119) (119) 22.33 [19.08]

1933 0224 Larwood H          Eng Aus  4  9.0  98 (n/a) (221) 16.12 [19.40]

1983 0944 Hemmings E.E       Eng Aus  3  9.0  95 (n/a) (174) 12.88 [22.53]

1978 0832 Wasim Bari         Pak Ind  3  9.0  85 (n/a) (125) 15.33 [15.88]

2000 1486 Boje N             Saf Ind  3  8.0  85 (198) (198) 14.00 [25.23]

1885 0018 Jarvis A.H         Aus Eng  5  8.0  82 (n/a) (322) 16.83 [16.83]

1948 0302 Bedser A.V         Eng Aus  4  9.0  79 (n/a) (183) 15.06 [12.75]

1959 0478 Nadkarni R.G       Ind Eng  4  7.0  76 (n/a) (223) 21.78 [25.71]

* Career-to-date average

• The top innings has been the double-century scored by Gillespie. Coming in at 67 for 1, he lasted nearly 10 hours and remained unbeaten on 201 while 514 runs were scored, including a stand of 320 with Michael Clarke. This must be the leading contender for the most amazing innings in Test cricket history.

  But what about a few centuries which are being discussed as "Night-watchmen centuries". Let us look at all these.
  

• Eknath Solkar scored his only century batting at no.3 against West Indies in 1975. However this innings gets ruled out since Solkar has scored over 1000 runs at an average of 25.43. It would be unfair to call him a night-watchman.
  
• What about Nasim-ul-Ghani's 101. It is true that Nasim-ul-Ghani has come in as night-watchman in a few matches. However in the specific match against England he batted at No.6 and scored 101. His rounded BPA is 8. So this innings does not fall into the basket of night-watchman innings.
  
• Consider the unbeaten 99 by A J Tudor playing for England against New Zealand. England, needing 210 to win, sent Tudor in as a night-watchman. He responded by remaining unbeaten on 99, just missing out on a unique achievement. A similarly stunning performance is that of Larwood, who, after going in at No.4 instead of his more customary No.9, scored 98 against Australia in the Bodyline series.
  
• Kirmani scored a hundred batting at no.5. However, with a career batting average of 27.05 he surely does not qualify as a night-watchman by any standards. His career-todate batting average when he played the hundred was 26.44.
  

C. Balls faced


The top 10 innings, in terms of balls faced, are listed below.

Year MtNo Batsman            For Vs  Bat BPA Runs(BallsFaced) Batting Avge

                                                  Act  Calc   CTD   Career

2006 1799 Gillespie J.N      Aus Bng  3  9.0 201*(425) (425) 15.69 [18.78]

1885 0018 Jarvis A.H         Aus Eng  5  8.0  82 (n/a) (322) 16.83 [16.83]

1959 0478 Nadkarni R.G       Ind Eng  4  7.0  76 (n/a) (223) 21.78 [25.71]

1933 0224 Larwood H          Eng Aus  4  9.0  98 (n/a) (221) 16.12 [19.40]

1977 0811 Mann A.L           Aus Ind  3  7.0 105 (n/a) (214) 18.33 [23.62]

2000 1486 Boje N             Saf Ind  3  8.0  85 (198) (198) 14.00 [25.23]

2002 1597 Harris C.Z         Nzl Eng  4  7.0  71 (185) (185) 19.40 [20.45]

1948 0302 Bedser A.V         Eng Aus  4  9.0  79 (n/a) (183) 15.06 [12.75]

1983 0944 Hemmings E.E       Eng Aus  3  9.0  95 (n/a) (174) 12.88 [22.53]

1994 1246 de Villiers P.S    Saf Aus  5 10.0  30 (170) (170)  8.00 [18.89]

• The "balls played" information is available only for 173 of the 563 innings. In order to a complete "balls played" analysis, I have done a pro-rata allocation of the "team balls" value to the 390 night-watchman who do not have the "balls played" information, based on batsman runs and team runs. It must be remembered that this calculation has been done for a limited purpose and I am ready to accept the possible variations. The zeros have a token 1 ball allocated. However this article is not to determine the best night-watchman zero, so I can live with that.
  
• The maximum number of balls faced by a night-watchman, with no doubts whatsoever, is the 425 balls faced by Gillespie while scoring 201, against Bangladesh. It is safe to say that when the year 2100 dawns, Lara's record might have been broken, but not this record. It was a once-in-hundred-years innings.
  
• The 201 by Gillespie is an extraordinary innings. Notwithstanding this innings, the most significant and arguably the best ever innings played by a night watchman in Test matches must be Gillespie's 4-hour vigil at Chennai last year when he played 165 balls while scoring 26. This was a vicious spinning track and the Indian bowlers included Harbhajan and Kumble. Gillespie played the way Gavaskar batted in his farewell innings against Pakistan at Bangalore during 1987, dropping the ball dead beyond the reach of the close cordon of fielders. The importance of the series, the significance of the result and what happened on the fifth day must surely make this the greatest night-watchman innings ever. I would go to the extent of placing this innings among the best 5 innings ever played on Indian soil. It was ironical that it is by an Australian batsman, and was also possible only because Gilchrist was the captain. A Steve Waugh might have sent Michael Clark or Lehmann the previous day.
  

D. The batsmen who have been the night-watchmen most often (Min 7 attempts):

Player           Inns    Runs     Balls       BpI


Saqlain     (Pak) 11      98       384       34.9

Hoggard     (Eng) 11      39       249       22.6

Gillespie   (Aus)  9     327      1040      116.0

Warne       (Aus)  7      34        92       12.9 

Headley     (Ind)  7      30       177       25.3

Prasanna    (Ind)  7      61

Morrison    (Nzl)  7       7

Venkat      (Ind)  7       4

Saqlain Mushtaq (very effectively) and Hoggard (less effectively) lead the field, followed by Gillespie, the night-watchman par excellence. However Gillespie is way ahead of the others in the key indicator, Balls per innings. Warne just makes to the list, having batted in positions 3,4 and 5 few times. He is, surprisingly, a failure as a night-watchman, scoring zero in three of his seven inngs. Maybe he resented being sent as a night-watchman. Venkataraghavan is still worse, scoring only 4 runs in his 7 innings, including 5 zeros. Maybe he also felt offended.

Morrison was the biggest failure, scoring 7 runs in one innings and not opening his account in the six other innings. It is a miracle why the captains continued to use Morrison as the night-watchman. One possibility is that he lasted quite a few balls without opening his account. I wait to be enlightened. Prasanna was better, scoring 61 runs in 7 attempts. Headley was also quite good, scoring 30 runs and lasting 177 balls.

E. Conclusion

Who has been the best night-watchman in history. Easy to guess. Jason Gillespie, in 9 innings has scored a total of 327 runs at an average (no doubt aided by the unbeaten 201) of 40.87. More relevantly, he has faced a total of 1040 balls in these 9 innings, an average of 116 balls per innings. His two great innings total 590 balls. However, note his sequence, in terms of balls played: 425, 165, 145, 79, 73, 71, 43, 35 and 5. Only one failure. He sold his wicket dearly. He wins the title hands down.

What has been the best night-watchman innings played. No need to look beyond Gillespie's two classics, his match-saving effort at Chennai and the mammoth 201 against Bangladesh. As far as I am (and most people are) concerned, the Chennai innings is the best, by a mile. It was a watershed innings and changed the course of one of the most important series of recent times. If India had won on that fourth day, they might very well be sitting at the top of the ICC Test Rankings now.

The second part will follow in a week's time.

	Ramiz Raja scored an unbeaten 102 off 158 balls as Pakistan limped to 220 for 2 and lost to West Indies by ten wickets in 1992 © Getty Images

Continuing the ODI analysis work, here is another aspect. What do I mean by "unfulfilled" innings? An example, from an imaginary match will suffice.

England: 250 for 2 in 50.0 overs lost to Australia: 251 for 7 in 49.3 overs

A single line summary of a match. It conveys a lot. We do not need any further match or player information to sense that there was something wrong as far as the England innings was concerned. What were the England batsmen thinking? Whoever be the Australian bowlers, should they not have gone on to score, say, 270 for 6 or for that matter, 290 for 9. Especially as the Australian bowlers seemed to have taken very few wickets, indicating a batsmen-friendly pitch and/or lack of penetration. Let us ignore the current favourite broadcasters' jargon, "no bounce", "two-paced", "not coming on to bat", "ball stopping" et al. The bottom line, especially in view of the Australian reply, was that English batsmen messed up, and messed up big time.

If England were 150 for 0/1/2 at the end of 40 overs, one cannot blame the batsmen who played the last 10 overs. The initial 40 overs were played too slowly. If England were 180 for 0/1/2 at the end of 40 overs, one cannot blame the early batsmen since there was a good platform. The blame rests squarely on the last 10 overs' strategy. In any case, there was a huge strategy mis-fire.

It is a tricky bit of data mining work to unearth such matches. The criteria, gathered after a lot of hits and misses, are outlined below. We cannot afford to have too many matches to study, nor, for that matter, too few.

1. First batting team to lose the match. I have couple of matches relating to a chasing situation at the end of the article.
2. Losing team to have quite a number of wickets at their disposal at the innings end, say no less than 6.
3. Winning team not to have too much of the team resources (as nicely defined by Duckworth and Lewis) at their disposal. In other words, not too many wickets left nor too many deliveries. If the chasing team won with 7/8 wickets in hand and over 5 overs at their disposal, anything more the first batting team did would probably have been insufficient.
4. No D/L coming into play. D/L throws everything out of gear. In the 2003 WC Final, after Australia scored 359, if the match had been abandoned after 20 overs, India could have won with scores of 90/0, 102/1 or 118/3 or lost with scores of 88/0, 100/1 or 116/3. Most sane analyses go out of the window in these matches.

It does not matter at all in these innings which batsmen were still available to bat at the end. Once it has been concluded that there were no less than 7 batsmen available, it does not matter a wee bit, whether this lot of seven or more contained Shahid Afridi or Chris Martin.

It must be remembered that the chasing team has the major advantage that they know their target and they could afford to lose the wickets, even in a heap, in order to reach the target. The first batting team does not have such luxuries. However there is no getting away from the fact, in such matches, that all the resources at their disposal were not put to 100% use. It is also possible that, especially in matches where teams have scored high and lost, the bowlers could be blamed. However that is outside the scope of this analysis.

The idea is to clearly separate matches in which the first batting team messed up in a big way. The reasons why they did so is not important. It is enough to isolate such matches. I have identified a total of 14 matches. An additional interesting data I have shown is the unbeaten partnership at the end of the innings. This will let us get a slightly better idea of the innings.

Team batting first

Odi# 717. Pakistan vs West Indies
Played on 23 February 1992 at Melbourne Cricket Ground.
West Indies won by 10 wickets.
Pakistan: 220 for 2 wkt(s) in 50.0 overs. Unbeaten 3rd wkt ptshp: 123

• Rameez Raja 102*(158), Javed Miandad 57*(61)

West Indies: 221 for 0 wkt(s) in 46.5 overs

• Haynes D.L 93*(144), Lara B.C 88r(101)

This match does not fall into the data mining criteria already given and is provided only to show the type of matches left out. There is no doubt that Pakistan under-achieved to the tune of about 30 runs. Note how self-centred Ramiz Raja's innings was, taking 158 balls to score 102 runs. However West Indies' response indicated that they had the resources, both wickets and balls to score these 30 runs and more.

Only one match in which the losing team lost just 2 wickets.

1. ODI # 2096. South Africa vs West Indies.
Played on 4 February 2004 at New Wanderers Stadium, Johannesburg.
South Africa won by 4 wickets.
West Indies: 304 for 2 wkt(s) in 50.0 overs. Unbeaten 3rd wkt ptshp: 92

• Gayle C.H 152*(153), Chanderpaul S 85 (114), Powell R.L 49*(24)

South Africa: 310 for 6 wkt(s) in 49.4 overs

• Smith G.C 58 (60), Kallis J.H 139 (142)

The first match selected is painful for me because I watched this match and was furious at the way West Indies messed up their innings. In this case the blame must rest on their early batsman since the last 10 overs added over 100 runs. Look at the South African innings. They had very little to spare, especially balls. They had almost reached their limits. If West Indies had scored 20 more runs, which was there for the taking, they would have won the match. A classic example of a team which shoots itself in the foot.

Now for the teams which lost 3 wickets.

2. ODI # 1391. England vs Sri Lanka.
Played on 23 January 1999 at Adelaide Oval.
Sri Lanka won by 1 wicket.
England: 302 for 3 wkt(s) in 50.0 overs. Unbeaten 4th wkt ptshp: 154

• Hick G.A 126*(118) Fairbrother N.H 78*(71)

Sri Lanka: 303 for 9 wkt(s) in 49.4 overs

• Jayasuriya S.T 51 (36), Jayawardene D.P.M.D 120 (111)

This is as perfect as we are likely to get to this particular type of match. England with 7 wickets in hand probably fell 30 runs short. Sri Lanka just about managed it. Only one wicket and two balls at their disposal. 5 runs would have been their limit. It is probably unfair to throw the blame on the English batsmen when they finished with a 300+ score. However there is no denying the fact that they fell a few runs short. Either Hick or Fairbrother should have pressed the pedal.

3. ODI # 538. India vs New Zealand.
Played on 17 December 1988 at Moti Bagh Stadium, Baroda.
India won by 2 wickets.
New Zealand: 278 for 3 wkt(s) in 50.0 overs. Unbeaten 4th wkt ptshp: 67

• Wright J.G 70 (96), Jones A.H 57 (85), Greatbatch M.J 84*(67)

India: 282 for 8 wkt(s) in 47.1 overs

• Manjrekar S.V 52 (69), Azharuddin M 108*(65), Sharma A.K 50 (36)

Somewhat similar to the previous match. New Zealand should have come closer to the 300 mark, considering the fact that India were well placed at the end so far as balls were concerned, but not in terms of wickets. Note Azharuddin's innings which has remained the fastest century by an Indian batsman for nearly 20 years.

4. ODI # 1572. India vs South Africa.
Played on 9 March 2000 at Nehru Stadium, Kochi.
India won by 3 wickets.
South Africa: 301 for 3 wkt(s) in 50.0 overs. Unbeaten 4th wkt ptshp: 52

• Kirsten G 115 (123), Gibbs H.H 111 (127)

India: 302 for 7 wkt(s) in 49.4 overs

• Jadeja A 92 (109)

A peculiar match. Two good centuries from the losing team. Here the last 10 overs were the problem since South Africa were 238 for 1 in 40 and added only 63 in the last 10 overs. Kallis and Cronje just could not speed up enough. Like Sri Lanka against England, reported earlier, India had very little in the tank at the end.

5. ODI # 1824. South Africa vs Australia.
Played on 6 April 2002 at St George's Park, Port Elizabeth.
Australia won by 3 wickets.
South Africa: 326 for 3 wkt(s) in 50.0 overs. Unbeaten 4th wkt ptshp: 132

• Smith G.C 84 (103), Kallis J.H 80*( 59), Rhodes J.N 71*( 50)

Australia: 330 for 7 wkt(s) in 49.1 overs

• Gilchrist A.C 52 (34), Ponting R.T 92 (107), Lehmann D.S 91 (94)

A very high score by South Africa chased with nonchalance by Australia. Difficult to blame a team which scored 326 runs and lost. The finish of the innings by Kallis and Rhodes was spectacular. This also brings us to the interesting point whether nothing more could be done beyond a certain stage. Maybe the accelarator pedal was already at the floor.

6. ODI # 301. Australia vs West Indies.
Played on 10 February 1985 at Melbourne Cricket Ground.
West Indies won by 4 wickets.
Australia: 271 for 3 wkt(s) in 50.0 overs. Unbeaten 4th wkt ptshp: 68

• Smith S.B 54 (90), Wood G.M 81 (119), Phillips W.B 56*(37)

West Indies: 273 for 6 wkt(s) in 49.2 overs

• Richardson R.B 50 (90), Logie A.L 60 (56)

Smith and Wood were probably too slow at the beginning; so was Richardson for West Indies. However they were clear about their target and just reached the same.

7. ODI # 794. India vs England.
Played on 18 January 1993 at Sawai Mansingh Stadium, Jaipur.
England won by 4 wickets.
India: 223 for 3 wkt(s) in 48.0 overs. Unbeaten 4th wkt ptshp: 164

• Kambli V.G 100*(149), Tendulkar S.R 82*( 81)

England: 224 for 6 wkt(s) in 48.0 overs

• Stewart A.J 91 (126)

A low scoring match lost by India. Somewhat similar to Ramiz Raja's century mentioned earlier, Kambli's was probably quite slow. That India had slipped to 59 for 3 does not absolve the Mumbai pair of the tardiness of the partnership. It must be mentioned that Azharuddin, who essayed a 65-ball 108 in 1988, played a match-losing 6 in 28 balls here.

8. ODI # 615. West Indies vs England.
Played on 3 April 1990 at Kensington Oval, Bridgetown, Barbados.
West Indies won by 4 wickets.
England: 214 for 3 wkt(s) in 38.0 overs. Unbeaten 4th wkt ptshp: 53

• Smith R.A 69 (84) Lamb A.J 55*(39)

West Indies: 217 for 6 wkt(s) in 37.3 overs

• Richardson R.B 80 (84), Best C.A 51 (43)

Somewhat similar to the previous match. David Smith of England took 31 balls for his score of 5 and Wayne Larkins, 73 balls for his 34. Together they had a strike rate of 2.4 runs per over.

The matches in which the first batting team lost 4 wickets and the second batting team lost 7 wickets or more are shown in a summary form.

 9.2349 2006 Aus 434/4 in 50.0 Saf 438/9 in 49.5 won by 1 wicket
10.2499 2007 Ire 284/4 in 50.0 Ken 286/9 in 49.0 won by 1 wicket
11.1035 1996 Aus 242/4 in 50.0 Slk 246/7 in 49.4 won by 3 wickets
12.0716 1992 Zim 312/4 in 50.0 Slk 313/7 in 49.2 won by 3 wickets
13.2439 2006 Win 272/4 in 50.0 Eng 276/7 in 48.3 won by 3 wickets
14.2184 2004 Zim 252/4 in 50.0 Pak 258/7 in 48.1 won by 3 wickets

The first match needs a mention. I hope a reader does not come back and blast me for implying that Australia should have scored a few more runs. It was South Africa's relentless aggression and continuous attacking play that finally won them the match. Having said this I must mention that Lee could score only a single off the last two balls bowled by Telemachus. A four or two would have helped.

In the second match, K.J.O'Brien scored 142 in 123 for Ireland. Kenya were 231 for 9 and a great Irish victory seemed certaiin. Then Odoyo, with a blistering 61 in 36 added 55 for the tenth wicket in 5 overs and won. A few more runsfor Ireland and who knows what might have happened.

No particlular team has messed up their first innings, in this regard, more often than the others, although, for the record, Australia have been the culprit three times. Sri Lanka does not appear in this list even once.

Team batting second

Now for the team batting second. Here I have ignored all matches decided through D/L or equivalent methods. The reason has already been explained. In other matches, only reasonably close matches, where the margin of loss was less than 30 runs, are considered. That leaves us with only 3 competitive matches.

1. ODI # 56. Pakistan vs India.
Played on 3 November 1978 at Zafar Ali Stadium, Sahiwal.
Pakistan won (conceded by India).
Pakistan: 205 for 7 wkt(s) in 40.0 overs

• Asif Iqbal 62 (76)

India: 183 for 2 wkt(s) in 37.4 overs

• Gaekwad A.D 78*(103), Amarnath S 62 (86)

This was the match conceded by India after Sarfraz bowled a series of bouncers in the 38th over. I do not want to get into an argument with anyone. It is clear that the short pitched balls were over-used. It is also clear that the rules were very vague and Pakistan were justified in using the rules to their advantage. Mushtaq Mohammad cannot be blamed for that. If Bedi was the fielding captain, surely he would also have done the same thing, although he could not very well have asked Ghavri and Mohinder Amarnath to bowl bouncers at 120 kmph. Anyhow why should a captain concede a match when so close to the target. Bedi should take responsibility for that.

2. ODI # 160. Pakistan vs Australia.
Played on 8 October 1982 at Gaddafi Stadium, Lahore.
Pakistan won by 28 runs.
Pakistan: 234 for 3 wkt(s) in 40.0 overs

• Zaheer Abbas 109 (117), Javed Miandad 61*(65)

Australia: 206 for 4 wkt(s) in 40.0 overs

• Laird B.M 91*(114), Hughes K.J 64 (80)

Possibly defensive fields and defensive bowling prevented Australia from speeding towards the end. Alternately the lack of experience in handling chases could have been the reason. It must be conceded that a scoring rate of nearly 6 was quite difficult to achieve those days.

3. ODI # 333. Sri Lanka vs India.
Played on 21 September 1985 at P.Saravanamuttu Stadium, Colombo.
Sri Lanka won by 14 runs.
Sri Lanka: 171 for 5 wkt(s) in 28.0 overs

• Madugalle R.S 50*(39)

India: 157 for 4 wkt(s) in 28.0 overs

• Vengsarkar D.B 50 (46)

The asking rate was quite high (6.10) and India, despite having Srikkanth and Kapil could not do much against the accurate Sri Lankan bowling, led by John.

Finally I cannot close this without referring to this particular classic (mis)match.

ODI # 19. England vs India.
Played on 7 June 1975 at Lord's, London.
England won by 202 runs.
England: 334 for 4 wkt(s) in 60.0 overs

• Amiss D.L 137 (147), Fletcher K.W.R 68 (107), Old C.M 51*(30)

India: 132 for 3 wkt(s) in 60.0 overs

• Gavaskar S.M 36 (174), Viswanath G.R 37 (59)

This was the infamous Gavaskar crawl. Even though this was India's third ever ODI match, it is beyond anyone's, including his own, comprehension what Gavaskar was thinking. However, enough has been written on the subject.

At least for this post let me hope that readers do not respond with messages such as "why was abc not considered", "xyz is superior to pqr", "efg was the best" et al. Consider these as the only matches to be looked into.

Comments such as "This is a useless analysis" will not be published since there is no insight provided. On the other hand, a comment such as "The analysis is flawed since only the wickets lost are taken into account. The balls remaining should also be taken into consideration" will be published since that is a genuine comment on the article and adds value.

	Lower-order batsmen like Daniel Vettori get more recognition for their batting skills in this methodology © Getty Images

The original article received nearly 200 responses. Unfortunately not all could be posted, mainly because quite a few responses contained readers' own selection of their all-time best ODI teams. This was outside the theme of the article and I can assure the readers that they will have a chance later to come out with their views on this topic as well. Some posts were also rejected because they contained offensive language and/or referred to other responders in negative terms.

I must thank the readers for the interest they have shown. I must confess that I keep learning new things because of the interaction. There are new perspectives which had escaped me the first time around.

I have gone through all the responses. I have adopted the following three significant improvements. There were a few other valid suggestions which have not been implemented. These are summarised at the end, with my reasons for not implementing them.

1. The most important and often-repeated comment was that the game has changed considerably over the years and the analysis should make allowances for such changes. Most of these readers' observations are subjective in nature (Difficult to score runs in the 80s; Scoring rates nowadays are higher; Easier to chase targets nowadays; et al). However since these have been made with a deep understanding of the game, there is no way I can refuse to accept these, especially as I myself share these observations. It is my responsibility, as a computer analyst to translate such subjective inferences into objective, verifiable and acceptable algorithms. I have done this adjustment in my Test analyses, weighting down/up pre-WW1 bowling/batting figures respectively. It is high time the ODI analyses is also done this way. This has been explained in depth later.

2. The second concerns the late order batsmen. I had given equal weighting of 0.25 to each of these 4 batsmen. Most readers have accepted this. However I myself felt that it is wrong to treat Akram at the same level, as a batsman, say, as Sikander Bakht. The weightings, explained later, have been graded now.

3. The third change concerns home advantage. Barring the great teams, most other teams struggle outside their home country and do well in their own backyard. The advantage of 50000 (give or take a few thousand) fans at Kolkatta or Lahore or MCG or Kingston rooting for the home team can never be ignored. Though some might say that India enjoy home advantage wherever they play.

1. Decade-level adjustments

To do this I have split the matches into four decades, the (swinging) 1970s, the (exciting) 1980s, the (nervous) 1990s and the (Twenty20-driven) 2000s. Please see the following table, first for batting and then for bowling. Incidentally this concept itself deserves of an independent post.

In both tables I have used the base factor as the All match numbers, which is presented in the first column. I concede that this is heavily weighted towards the later years. However there is no other way. If I take the median match (no.1354) as a cut-off point, that match itself was played as recently as 1998. So whatever one does, this problem will remain.

ODI Matches - Analysis by Decade - BATTING

	All Matches	1970s	1980s	1990s	2000s
Matches played	2703	82	516	933	1172
Batsmen innings	46968	1418	8838	16266	20446
Balls bowled	1445956	46208	277516	505727	616505
Runs per match	414	369	393	414	426
Runs per innings	23.83	21.36	22.96	23.76	24.44
% of all-matches avge	100.0%	89.6%	96.3%	99.7%	102.5%
Runs per ball	0.774	0.656	0.731	0.764	0.811
% of all-matches avge	100.0%	84.7%	94.4%	98.7%	104.7%

a. There is a clear increase in the Runs per match, which has been done mainly to show the trend.

b. Runs per innings, which is used to avoid the not outs impact, has clearly shown a move up, from 21.36 during the 1970s to 24.44 for the current decade matches.

c. Similarly, the scoring rate (runs per ball) has shown a clear move upward, from 0.656 (Rpo of 3.94) during the 1970s to 0.811 (Rpo of 4.86) now.

The adjustment is done in the following manner.

The Batting Index figures are adjusted by the Decade adjustment values. In other words, the Batting Average Index is divided by 0.896 for the 1970s teams, by 0.963 for the 1980s teams, by 0.997 for the 1990s teams and by 1.025 for the current teams. Similarly the Batting Strike Rate Index is divided by 0.847 for the 1970s teams, by 0.944 for the 1980s teams, by 0.987 for the 1990s teams and by 1.047 for the current teams.

ODI Matches - Analysis by Decade - BOWLING

	All Matches	1970s	1980s	1990s	2000s
Matches played	2703	82	516	933	1172
Balls bowled	1445956	46208	277516	505727	616505
Team Runs conceded	1119374	30292	202884	386508	499690
Wickets captured	38120	1156	7097	13215	16652
Wkts per match	14.10	14.10	13.75	14.16	14.21
Bowling Average	29.36	26.20	28.59	29.25	30.01
% of all-matches avge	100.0%	89.2%	97.4%	99.6%	102.2%
Balls per wkt	37.9	40.0	39.1	38.3	37.0

a. It is surprising, maybe not so, that the average number of wickets captured per match has remained fairly constant over these 30-odd years.

b. The bowling averages have shown a clear move upwards from 26.20 during the 1970s to 30.01 for the current decade. A minor concession, likely to have little impact on the final numbers, is made in that the bowling average for this purpose is calculated based on the team runs and team wickets.

c. The balls per wkt figures show a slight reduction as time has gone by, with the difference being only around 7.5%. It's given here only for information.

The adjustment is done in the following manner.

The Bowling Index figures are adjusted by the Decade adjustment values. In other words, the Bowling Index is multiplied by 0.892 for the 1970s teams, by 0.974 for the 1980s teams, by 0.996 for the 1990s teams and by 1.022 for the current teams.

Maybe it's not perfect, but this significant tweak has gone a long way in redressing the imbalance, as the results show.

2. Changing the weightings given to late order batsmen

Jeff Grimshaw has demonstrated that the higher average batsmen would, most probably, be able to bat through their 50 (or whatever) overs without even approaching the late-order batsmen. On the other hand, the lower-average, quicker-scoring batsmen might need the late-order batsmen often. It is, however, essential that we recognize the quality of late-order batsmen. After all, Vettori and Martin are poles apart, when it comes to batting. Hence the weightage is changed, as follows.

No. 8 Batsman: 0.40

No. 9 Batsman: 0.30

No.10 Batsman: 0.20

No.11 Batsman: 0.10

3. Home Advantage

I have effected a 5% increase for all the Index values for home teams for reasons already explained. This value is not applied for the hundreds of matches played in neutral venues. The only question is, why 5%, why not 2.5% or why not 10%. I have no answer other than my gut feel that the additional weighting cannot exceed the value assigned for Fielding.

The revised tables are summarized below.

Batting

1. 2004 2196 1 AUS (vs Nzl) 19.95 20.68 40.63;
Gilchrist A.C, Hayden M.L, Ponting R.T, Lehmann D.S, Martyn D.R, Symonds A, Clarke M.J.
(after 21 other Australian teams (as compared to 107 Australian teams earlier))
23. 1999 1390 2 SAF (vs Win) 18.80 20.63 39.43
Kirsten G, Gibbs H.H, Kallis J.H, Cullinan D.J, Cronje W.J, Rhodes J.N, Pollock S.M.
(after 44 other teams)
68. 2005 2237 2 IND (vs Pak) 18.35 20.27 38.62 (Match lost)
Sehwag V, Tendulkar S.R, Dhoni M.S, Ganguly S.C, Dravid R, Yuvraj Singh, Kaif M.

Bowling

1. 1981 0116 2 WIN (vs Eng) 1.62 39.53 41.15
Roberts A.M.E, Holding M.A, Garner J, Croft C.E.H + Richards/Gomes.
2. 2001 1670 2 AUS (vs Win) 2.55 38.57 41.12
Warne S.K, Lee B, Bracken N.W, McGrath G.D, Symonds A.
3. 1981 0115 1 WIN (vs Eng) 1.37 39.53 40.90
Roberts A.M.E, Garner J, Holding M.A, Croft C.E.H + Lloyd/Gomes.
4. 2000 1552 2 AUS (vs Ind) 2.58 38.22 40.80
Warne S.K, Lee B, Fleming D.W, McGrath G.D, S.R.Waugh.
5. 2000 1622 2 AUS (vs Saf) 2.56 38.21 40.77
Warne S.K, Lee S, Gillespie J.N, Lee B, McGrath G.D.

It is in Bowling that these changes are felt a lot. The top 5 teams are now composed of West Indian and Australian teams since the Australian bowlers have got their Indices adjusted accordingly.

Team Strength

1. 2001 1670 2 AUS (vs Win) 39.47 38.57 2.55 80.59
Gilchrist A.C, Waugh M.E, Ponting R.T, Bevan M.G, Lehmann D.S, Martyn D.R, Symonds A,
Warne S.K, Lee B, Bracken N.W, McGrath G.D.
(after 24 other Australian teams (as compared to 144 Australian teams earlier))
26. 1983 0189 1 WIN (vs Ind) 37.28 38.24 2.15 77.67
Greenidge C.G, Haynes D.L, Richards I.V.A, Logie A.L, Lloyd C.H, Gomes H.A, Dujon P.J.L,
Marshall M.D, Roberts A.M.E, Holding M.A, Garner J.
(after 19 other Australian/West Indian teams)
46. 2002 1918 1 SAF (vs Pak) 37.48 37.17 2.45 77.10
Smith G.C, Gibbs H.H, Dippenaar H.H, Kallis J.H, Rhodes J.N, Boucher M.V, Pollock S.M,
Klusener L, Hall A.J, Donald A.A, Ntini M.

You can note the significant change. The 1983 West Indian team moves up considerably. The top 100 now has teams from Australia, West Indies and South Africa.

The best teams for all the 10 Test-playing countries can be viewed by clicking here.

Not considered

1. Career-to-date average or recent form adjusted values instead of career average

I evaluated this option but decided not to do the change. The reasons are many. Richards is an outstanding 47.00(Avge) / .887(Strt) batsman. If his mid-career figures were lower or his recent form was not good, that does not make him any lesser, at any time in his career. Similarly for other great players such as Tendulkar, Lara, Wasim Akram, McGrath et al. The other reason is that between the 11 players these numbers would get evened out. The last reason is that this will involve too much work, for very little improvemet.

2. RPI instead of Batting Average

This was also considered seriously. I did not do this because that meant I would be going away from the widely accepted Batting Average. It is true that a Hussey or Bevan might gain in view of the high number of Not outs. However this is more than compensated by the fact that they would have had very little time to settle down, they would have to throw the bat around and in general play for the team score. The early batsmen, on the other hand, may be hampered by the high number of dismissals. However they would have time to settle down, play themselves in and in general play longer innings.

3. Consider the two Bowling parameters separately

This was also a good suggestion. However, I could not get away from the fact that the bowling average is a composite value of the two components (Bowling Average = Strike Rate x Accuracy). I also did some trial calculations. These showed that the impact of splitting the two components would be minimal. Hence I retained the Bowling Average.

4. Finally the Fielding

Everyone knows that Jonty Rhodes was a great fielder. But then how great a fielder was he? Was he greater than Colin Bland, Roger Harper, Ricky Ponting et al or not? Is there a quantifiable and verifiable measure available? Even run-outs started getting attributed to specific fielders only recently. Possibly the greatest fielding display of all time was effected by Richards during the 1975 World Cup final against Australia. His three run-outs do not find a place on the scorecard.

We do not have a measure for fielding. Until we get that (even then what about the earlier matches) it will be impossible to quantify fielding. I am not going to do a subjective error-prone Fielding Index. Instead I have done a low weighting of 5% for Fielding, done using the available Catches/Stumpings values.

I have also resisted the temptation to come out with an all-time best world team. That is outside the scope of this team-oriented analysis and I want to avoid making the mistake I made in my previous post. Surely there will be another time when such an analysis will be done.

	Joel Garner averaged 18.85 in ODIs, the lowest among bowlers with at least 50 wickets © PA Sports

Post-Note:

"I urge readers to read and understand the reasoning behind the analysis. It is NOT to determine the best ODI team across years or teams. Rather it is to determine the best team that walked on to the field, as 11 players. Many comments have been made ignoring this fact. So much so, no comment which lists the readers' favourite team will be published. Let me add that over 50 comments have gone unpublished because of this."

For my next post, I wanted to stay away from Test cricket, on which most of the recent It Figures posts have been. At the other extreme we have Twenty20, which has had an all-pervading presence on almost all the channels on television, and the web and print media as well. That leaves the often-ridiculed form of cricket, one-day internationals. I never thought I would say this, but I have already started longing for ODI cricket.

This time I have taken for analysis a topic which I had looked at for Tests, and am now adapting to ODIs: how strong is an ODI team and how do the teams compare over the 37 years of ODI cricket? Where does the 2007 Australian team stand when compared to the West Indian teams of early 1980s, or for that matter the Australian teams of the late 1990s? It has turned out to be a fascinating study.

The one significant advantage we have when comparing ODI teams is that even the 1975 West Indies team had players most of us [barring those below 30, who would anyhow be familiar with them] have seen. It is not very difficult to identify with Viv Richards, Ian Chappell, Clive Lloyd, Michael Holding etc. unlike in Test cricket, where George Lohmann, with a Test bowliing average of 10.76, was born nearly 143 years ago. It isn't easy to relate to either fact.

A team is as strong as its batsmen, bowlers and fielders are. If we consider fielding as part of the bowling, these two main areas have to be given equal weightage. ODI laws might be tilted towards the batsmen, but the role of bowlers can never be underestimated. This happens even in the Twenty20 game.

Hence I have given a weightage of 50 for batting and 50 for bowling (further split as 45 for bowling and 5 for fielding). Because there is no quantified data for fielding per se, the weightage for fielding is in reality for catching/stumping. This also explains the low weightage.

The one thing I want to ensure is that this analysis will comprise only of measurable, objective parameters. The other areas such as captaincy, recent form, home advantage etc. are intangibles and subjective. A captain is only as good as his team is. Recent form has more relevance in Test matches. Home advantage is a mirage. The non-Australian strokemakers would love to play on the bouncy Australian pitches and the non-New Zealand seam/swing bowlers would love to bowl in Auckland or Hamilton.

Readers might be tempted to send the usual comments that these are obvious and why should there be a need to do analysis. Let me remind such readers that their conclusions would be based on error-prone subjective inferences and also not indicate how much a team is better than another. My results are based on objective analysis and indicate the quantitative differentials between teams.

Batting

ODI batting consists of two distinctly measurable and independent factors: how many runs are scored and how fast they are scored. In other words, the batting average and the strike-rate. No one can question the decision to treat these two parameters equally.

The average is taken rather than the lesser known and acceptable runs per innings or my own development, the extended batting average. The average is a widely accepted measure and presents the best method of measuring runs scored. Only two batsmen in ODI history, Michael Bevan and Michael Hussey, have averages higher than 50 (among those with a minimum of 20 innings), mainly because of their number of not-outs. However this is partly rectified by limiting the average to 50.0 for these two batsmen.

There is no problem with strike-rate. That is available as a straight computation of runs scored / balls faced. The averages and strike-rates of the top seven batsmen in the team's batting order are summed. The averages and strike-rates for batsmen nos. 8 to 11 are given a 25% weightage each. The arrived total is divided by eight and the Team Batting Average and Team Strike-Rate are arrived at.

The batting average index points are determined by dividing the team batting average by two. The maximum value for this is 25.0.

The strike-rate index points are determined by multiplying the team strike-rate (runs per ball) by 25.0. The maximum value for this is just over 25.0. Only one batsman in ODI history, Shahid Afridi, has a career strike rate of over 1.00.

Care is taken that these full values are applied only for career aggregates of 1000 runs and above. Otherwise Arvind Kandappah of Canada and Alex Obanda of Kenya will single-handedly make their team's batting averages huge. These two have Bradmanesque career batting averages of 97.0, although scoring only 97 and 194 runs respectively.

 SNo. Year MtNo I Team   vs     AvIdx  SRIdx  Bat


   1. 2005 2257 2 AUS (vs Bng) 19.89 20.99 40.87

      (Gilchrist, Hayden, Ponting, Martyn, Clarke M, 

       
Symonds, Hussey).   

   2. 2005 2261 2 AUS (vs Eng) 19.91 20.90 40.81

   3. 2005 2259 1 AUS (vs Eng) 19.67 20.78 40.45

   

Next 105 teams are Australian, followed by

 109. 2005 2282 2 ICC (vs Aus) 18.15 20.47 38.62

        (Sangakkara, Sehwag, Kallis, Lara, Dravid, 

         Pietersen, Flintoff, Afridi)

Next 16 teams are Australian, then

 126. 2004 2202 1 IND (vs Bng) 18.06 20.43 38.49

        (Sehwag, Tendulkar, Ganguly, Dravid, Kaif, 

         Yuvraj Singh, Dhoni). 

Then another 5273 teams

5400. 2004 2172 1 USA (vs Aus)  3.27  9.73 13.00

5401. 1979 0067 1 CAN (vs Eng)  5.05  7.85 12.91

5402. 1979 0070 1 CAN (vs Aus)  4.76  6.98 11.74

Note: Out of the 2703 matches considered, two matches were abandoned without even the team information being available.

The first 108 teams in the batting list are Australian. These 108 matches have come over a nine-year period, from 1999 to 2008, a period of total Australian domination, punctuated by three World Cup wins. The three batsmen who have been part of almost all these matches are Adam Gilchrist, Ricky Ponting and Andrew Symonds.

Bowling

Like batting, bowling also has two components, the bowling strike-rate and accuracy. However, unlike batting, the bowling average is a fantastic measure since it encompasses both these key measures in a single value. Consider the following.

                  Runs Conceded

Bowling Average = -------------

                  Wickets Taken


Rewriting this as

                  Runs Conceded     Balls Bowled

Bowling Average = -------------  x  -------------

                  Balls Bowled      Wickets Taken

This can be written as

Bowling Average = Bowling Accuracy x Bowling Strike-Rate.

There is no need to measure these two factors independently. It is sufficient to take the single composite measure, bowling average and work on it.

Unlike the batting computation, the bowling averages of the best five bowlers is taken and divided by five. This is because it is expected the team would use their best five bowlers. Even if Jacques Kallis bats at No. 3, he is likely to be used as a bowler if he is one of the best five. Whether he bowls in the concerned match or not is outside the scope of this analysis since this study only measures how strong a team potentially is, not how strong the team actually was.

Here also care is taken that bowlers with less than 50 wickets have their figures scaled down suiitably. Otherwise Gary Gilmour, with 16 career wickets at 10.31, will completely tilt the figures of the late-1970s Australian teams.

The bowling index is determined by subtracting the Team Bowling Average from 60.0. Since the best bowling average for qualifying bowlers [minimum 50 wickets] is 18.85 by Garner, the highest value will not exceed the maximum weightage given to bowlers, of 45.

For both batting and bowling, I have also taken the full career figures rather than the career-to-date figures in view of the complexity of calculation and the fact that we are averaging and the minor differences tend to get ironed out.

Fielding

Only catches and stumpings are considered. The values for all 11 players are added, divided by 11, and multiplied by two to get a team fielding average. The highest value is 1.95 and the maximum index value is 3.90. It is obvious that this figure will be strongly influenced by the wicketkeeper's figures. A per match average rather than catches/stumpings aggregate is taken to be fair to weaker teams.

 SNo. Year MtNo I Team   vs    Fld   Bow   Tot


   1. 1981 0116 2 WIN (vs Eng) 1.55 38.65 40.20

      (Roberts, Holding, Croft, Garner)

   2. 1982 0134 2 WIN (vs Pak) 2.25 37.79 40.03

   3. 1982 0135 2 WIN (vs Aus) 2.25 37.79 40.03

Next 21 teams are West Indian, then

  25. 2001 1670 2 AUS (vs Win) 2.44 35.95 38.38

Then another 5374 teams

5400. 1979 0070 1 CAN (vs Aus) 0.17 10.00 10.17

5401. 1979 0067 1 CAN (vs Eng) 0.17 10.00 10.17

5402. 1979 0064 1 CAN (vs Pak) 0.17 10.00 10.17

The first 24 teams in the batting list are West Indian teams. These 24 matches have come over a six-year period, from 1981 to 1987. The two bowlers who have been part of almost all these matches are Holding and Garner.

Final Team Strength

This arrived by adding the batting, bowling and fielding indices. The maximum is 100, making it easier to see things in perspective.

 SNo. Year MtNo I Team   vs     Bat   Bow  Fld  Team


   1. 2001 1670 2 AUS (vs Win) 38.95 35.95 2.44 77.34

      (Gilchrist, Waugh M, Ponting, Bevan, Lehmann, Symonds,

       Martyn, Warne, Lee, Bracken, McGrath).   

   2. 2004 2180 1 AUS (vs Eng) 39.28 35.39 2.56 77.23

      (Gilchrist, Hayden, Ponting, Martyn, Lehmann, Clarke M, 

       Symonds, Lee, Gillespie, Kasprowicz, McGrath).   

   3. 2004 2172 2 AUS (vs Usa) 39.28 35.39 2.56 77.23

       (Same as previous team)      

   4. 2004 2131 2 AUS (vs Zim) 39.10 35.30 2.69 77.09

   5. 2003 1951 2 AUS (vs Ind) 39.47 35.02 2.43 76.91

Next 140 teams are Australian, then

 146. 1982 0139 2 WIN (vs Aus) 33.82 37.79 2.25 73.86

      (Greenidge, Haynes, Richards, Gomes, Lloyd, 

       Bachhus, Dujon, Roberts, Holding, Clarke ST, Garner).

Next 19 teams are Australian/West Indian, then

 166. 2005 2282 2 ICC (vs Aus) 38.62 32.75 2.28 73.65

      (Sangakkara, Sehwag, Kallis, Lara, Dravid, 

       Pietersen, Flintoff, Shahid Afridi, Pollock S, 

       Vettori, Shoaib Akhtar, Muralitharan).

Then another 5233 teams

5400. 1975 0024 1 EAF (vs Ind) 13.06 10.00 0.52 23.58

5401. 1979 0067 1 CAN (vs Eng) 12.91 10.00 0.17 23.07

5402. 1979 0070 1 CAN (vs Aus) 11.74 10.00 0.17 21.91

The first 145 teams in the list are Australian. These 145 matches have come over a nine-year period, from 1999 to 2008, a period of total Australian domination, punctuated by three World Cup wins. The five players who have been part of almost all these matches are Gilchrist, Ponting, Symonds, Brett Lee and Glenn McGrath.

Finally I have done another "fourth dimension" formation. Australia have had the best batting teams ever and West Indies, the best bowling teams ever. Let us combine the two into one all-time great ODI team. Take the first seven players from the Australian 2005 team [Match no. 2257] and add to it the best four bowlers from the 1981 West Indies side [Match no. 116]. Given below is the final squad.

Just to round up the analysis, this all-time great team has an index value of 77.05, which is lower than the Australia 2005 figure. This has been caused no doubt by the loss of batting and fielding points of the Australian team (Watson/Lee/Gillespie/Kasprowicz are much better batsmen and fielders than the West Indian bowling quartet). However, the team listed below is an outstanding one with a superb bowling attack.

Adam Gilchrist

Matthew Hayden

Ricky Ponting

Damien Martyn

Michael Clarke

Andrew Symonds

Michael Hussey

Andy Roberts

Michael Holding

Colin Croft

Joel Garner.

Readers should not forget that this not necessarily the best ODI Team of all time, It has been formed by merely taking the first 7 players from the best ever Batting line-up and adding the 4 bowlers from the best ever Bowling line-up.

Theoretically this team can be further improved by taking in Tendulkar, Richards, Dhoni, Wasim Akram, Shane Warne et al. That is a different day and different motivation. For the present let us enjoy the combination of two different eras.

If we tamper with this team, the charm would be lost. The Australia-West Indies combination would be missing. After all, these two countries have dominated the ODI scene during these 37 years, West Indies during the first ten years and Australia, the last 20.

ODI Analysis - by decade

Batting	AllMats	1970s	1980s	1990s	2000s
Matches played	2703	82	516	933	1172
Runs scored	1119374	30292	202284	386508	499690
balls bowled	1445956	46208	277516	505727	616505
Batsmen innings	46968	1418	8838	16266	20446

	Brian Lara: the one batsman who managed to add another 100 after getting a triple hundred © Mid-day

When Virender Sehwag strode out on the fourth day of the recent Test against South Africa in Chennai, he already had 309 runs to his name. There would have been a great many fans wondering how far he could go: could he top Brian Lara’s 400?

Statistics, however, indicate the fans were very likely to be disappointed [as they were]. The truth is that while 309 and 400 sound like reasonably similar scores, they are not. In fact, it is harder for a batsman to add another 100 runs if he has already made 300, than it is at almost any other score.

There have now been 22 Test triple-centuries, enough for some statistics. Only one of those triples has gone on to produce the magic 400, while 17 others have been dismissed before reaching that mark. Only one out of 18: that is only a 5.6% conversion rate. (The other four innings finished not out between 300 and 399; it is better not to include them in this calculation.) It is interesting to compare this to the conversion rates at other scores:

Conversion rates in 100-run increments

Score range	No. of dismissals	No. of successes	Conversion rate
0-99*	33,822	2942	8%
100-199	2334	279	10.7%
200-299	192	22	10.3%
300-399	17	1	5.6%

*0-99 data involves only recognised batsmen (#1-6 in batting order). “Number of successes” refers to the number of innings that have passed through the specified range without dismissal, e.g., for 0-99 it refers to the number of centuries.

While interesting, this data is not very robust for the 300-399 range. If the next batsman to make a triple-century happens to go on to 400, the conversion rate will almost double [to a rate similar to the 300-400 conversion rate in first-class cricket of 11%]. However, the difficulty batsmen encounter above 300 can also be seen when we look more closely, at 20-run increments.

Conversion rates in 20-run increments

Score range	No. of dismissals	No. of successes	Conversion rate
100-119	1105	1791	62%
120-139	581	1087	65%
140-159	329	667	67%
160-179	209	414	66%
180-199	110	279	72%
200-219	96	142	60%
220-239	50	84	63%
240-259	22	55	71%
260-279	19	30	61%
280-299	5	22	81%
300-319	7	14	67%
320-339	5	7	58%

Note the similarity of the pattern at the 200-run mark and the 300-run mark. As batsmen approach 200, their conversion rate rises, only to fall suddenly after reaching the milestone; the same thing happens at 300. A dismissal between 280 and 299 is a rare thing.

It is also striking that a batsman’s ability to add runs once he has reached 300 [67% and 58% for 300-319 and 320-339] is, in effect, no better than for those who have just reached 100 [62% and 65%].

Further perspective can be gained by looking at the one batsman who did make it to 400, Brian Lara at St John’s in 2004. In that innings, Lara played with caution and great focus after reaching 300, taking 178 balls to go from 300 to 400 [56 runs per 100 balls]. This is probably the slowest progression from 300 to 400 in first-class cricket: in doing this under very benign conditions when quick runs were called for, Lara also sacrificed any chance his team had of winning the match.

Few triple-centurions take this approach. The surprisingly high rate of failures after reaching 300, when scoring should be easiest, is probably a combination of mental exhaustion and the need for quick runs in those circumstances. The typical scoring-rate for triple-centurions in their first 300 runs is about 63 runs per 100 balls, but for runs beyond 300 [apart from Lara], the rate is over 80 runs per 100 balls, in time-limited Tests.

	Jack Hobbs made his highest Test score of 211 as England hammered 503 runs on a single day at Lord's in 1924 © The Cricketer International

Test cricket has changed in many ways over the decades; to the statistician, one of the most striking is the speed at which it is played. By that, I don’t mean the speed of bowling or scoring, though these are important, but simply the sheer amount of cricket that gets played in any given hour or day. Today, it is rare to see even 90 overs bowled in six hours, but in days gone by, 140 or even 150 overs in a day was commonplace. On the second day of the Lord’s Test of 1946, India and England wheeled through no fewer than 161 six-ball overs.

For spectators, it must have been rich entertainment when batsmen were on the attack. One of the most productive innings came at Lord’s in 1924, when England put South Africa’s bowlers to the sword, scoring 503 runs on the second day, for just two wickets, in less than five-and-a-half hours. England scored 200 runs before lunch and another 223 between lunch and tea. While 200 or more in one session is rare enough, keeping it up for two sessions in a row appears to be unique.

While doing a bit of general research, I came across more details of this Test in the original scorebook, thankfully preserved by the archivists at Lord’s. The 200 before lunch was greatly assisted by the bowlers getting through 57 overs (!) in an extended session. Jack Hobbs made his highest Test score, 211 off 300 balls. Hobbs was not given to collecting giant scores, and the Times commented that towards the end he batted as though he “seemed to think someone else might as well have a turn at batting”. One of those others was Frank Woolley, one of the most aggressive batsmen of his generation, who scored 134 not out off 123 balls, fine hitting in any era.

A tally of 223 runs in one session raises the question of records. Where does it stand? No one seems to have assembled a list before, so here is my attempt. This is one record that favours old-time Tests, but there are a few modern entries [all involving “minnows”]. Pre-War Tests in England predominate, mainly because sessions and days in other countries in the days of high over-rates tended to be shorter than in England. (a pre-War Test day in England was often six-and-a-half hours, but in Australia only five hours.) I have examined only those Tests that had specified tea breaks; tea breaks were not always taken in Tests before 1910.

In fact, there are quite a few extreme cases from sessions that were extended beyond the normal two hours, for various reasons. These have been put into a separate list. Note that all of the two-hour cases were the lunch-tea session, whereas all of the extended-session cases are in the opening or closing sessions.

Most runs in a two-hour (maximum) session

236 (43 overs) Aus v SA, Lunch-Tea, Joburg 1921 (119 off 85 balls by Jack Gregory)

233 (41 overs) Eng v Pak, Lunch-Tea, Nottingham 1954 (Denis Compton 173)

231 (45 overs) Eng v NZ, Lunch-tea 3rd day, Leeds 1949 (both teams batted)

223 (43 overs) Eng v SA, Lunch-Tea, Lord’s 1924

220 (47 overs) Eng v NZ, Lunch-Tea, Wellington 1933 (Wally Hammond 151)

208 (32 overs, 100 minutes) Aus v SA, lunch-tea, Sydney 1910/11

207 (29 overs) Aus v Zimbabwe Lunch-Tea Perth 2003 (both Matt Hayden and Adam Gilchrist scored centuries in the session)

Most runs in a longer session

249 (33 overs) SA v Zim, post-tea 1st day, Cape Town 2005

244 (58 overs, 165 minutes), Eng v Aus, post-tea, Oval 1921

239 (45 overs, 140 minutes), Eng v NZ, pre-lunch, Lord’s 1937 (two teams)

223 (35 overs, 150 minutes) Eng v Ban, post-tea, Chester-le-Street 2005 (Marcus Trescothick 127)

221 (150 minutes) Eng v SA, pre-Lunch, Oval 1935 (Les Ames 123)

219 (35 overs, 150 minutes) NZ v Zimbabwe, post-Tea, Harare 2005 (Daniel Vettori 127)

~210 (150 minutes) Eng v India, pre-Lunch, Oval 1936

208 (47 overs, 154 minutes) Aus v SA, post-tea, Melbourne 1910/11 (Victor Trumper 133)

200 (57 overs, 150 minutes) Eng v SA, pre-Lunch, Lord’s 1924

Readers are invited to submit others that I may have overlooked.

********

Speaking of remarkable sessions, I was asked if India, all out for 76 against South Africa in Ahmedabad, had become the first team to be bowled out before lunch on the first day of a Test match. Not quite, as it happens, but there appears to be only one precedent, and that was 112 years ago. In the Lord’s Test of 1896, Australia was bowled out for 53 in 85 minutes, allowing England to reach 37/0 before lunch.

India also became the first team to be bowled for less than 100 after scoring over 600 in their previous innings in the same series. Sri Lanka once went from 713/3 to all out 97 in consecutive innings in 2004, but as their opponents were Zimbabwe and Australia respectively, it’s not quite the same thing.

	When Virender Sehwag gets a hundred, he usually goes on to make it a big one © Getty Images

It is well known that some batsmen are better than others when it comes to going on to very big scores after getting a start. The differences between individuals can be surprising; for an extreme recent example look at two of today’s top opening batsmen, Matthew Hayden and Virender Sehwag. A comparison of the last 10 Tests centuries for each batsman shows a remarkable contrast.

Test hundreds by Hayden and Sehwag

Hayden	Sehwag
138	130
111	195
118	309*
110	155
137	164
102	173
153	201
124	254
123	180
103	151

In this table, Sehwag has scored 912 runs after reaching 100, while Hayden has mustered only 219. In fact, Hayden has converted only one of his last 15 Tests centuries into a 150, whereas Sehwag has clocked up nine conversions in a row (a world record; not even Bradman managed this).

The contrast might be more understandable if Sehwag was by far the superior batsman, but of course this is not the case. Hayden scored his last ten centuries in the space of just 45 innings, where Sehwag needed 68 innings; Hayden averaged 60.0 in that time to Sehwag’s 54.2. Sehwag even spent some time on the Indian reserves bench in that time.

A deeper understanding of this might require an excursion into psychology; it’s better for the moment to leave it simply as an intriguing difference between two great players.

A wider examination of such differences is quite straightforward; just calculate the “century average” of all players. One way is to take a simple average of all Test centuries (ignoring the effect of not-outs); the leaderboard looks like this:

Average size of all scores over 100 (at least 10 Test hundreds)

Batsman	100s	Average
Don Bradman	29	186.0
Kumar Sangakkara	16	180.9
Zaheer Abbas	12	179.8
Virender Sehwag	13	174.6
Brian Lara	34	173.2
Dennis Amiss	11	170.8
Sanath Jayasuriya	14	168.3
Wally Hammond	22	167.5
Bob Simpson	10	164.6
Marvan Atapattu	16	161.5
Herschelle Gibbs	14	159.0
Graeme Smith	13	158.6
Mahela Jayawardene	21	157.6

Now any measure of scoring that puts Don Bradman on top is all right by me, but there are better ways of doing this. Bradman, after all, made some very big scores in “timeless” Tests that would be curtailed under modern conditions, and that would bring down the average size. An alternative is to take a standard batting average of the centuries, accounting for not-outs.

Some care is required. For a proper comparison of the ability to progress beyond 100, the first 100 runs of each century must be set aside, otherwise anomalies occur. (For example, a batsman scoring 100 not out, 100, and 100 not out would end up with a century average of 300 even though he has never scored a single run past 100.) By ignoring the first 100 runs in each century, a score of exactly 100 becomes equivalent to a duck in a normal batting average, while a score of 100 not-out will have no effect on the average, equivalent to a score of 0 not-out. This is fair enough, since a score of 100 not-out tells us nothing about a player’s ability to score after reaching 100.

It is interesting that, when you calculate such averages, many batsmen come up with a century average similar to, or just a little higher than, their ordinary batting average (for example, Jacques Kallis 57.4, Greg Chappell 56.1, Allan Border 55.0, Sunil Gavaskar, 51.9, Adam Gilchrist 49.6, Marcus Trescothick 45.1; this applies even to Bradman, 108.0). However, there are notable exceptions, and Sehwag is among them.

Highest century averages (batting average of runs beyond the hundred

Batsman	100s	Average
Kumar Sangakkara	16	129.4
Don Bradman	29	108.4
Andy Flower	12	100.0
Wally Hammond	22	99.0
Dennis Amiss	11	97.4
Zaheer Abbas	12	95.8
Javed Miandad	23	85.6
Dean Jones	11	82.7
Marvan Atapattu	16	82.0
Brian Lara	34	77.8
Garry Sobers	26	77.5
Virender Sehwag	13	74.6
Sachin Tendulkar	39	71.7
Len Hutton	19	71.1

When it comes to converting hundreds into giant scores, Kumar Sangakkara is a phenomenon. In his last thirteen Test centuries, he has been dismissed below 150 only once, while scoring six double-centuries plus that umpire-truncated 192 against Australia. It is also quite curious that, in addition to Sangakkara and Marvan Atapattu, the Sri Lankans Sanath Jayasuriya (68.3) and Mahela Jayawardene (67.2) are also in the all-time top 20.

Lowest century averages (batting average of runs beyond hundred)

Batsman	100s	Average
Allan Lamb	14	22.0
Mohinder Amarnath	11	25.3
Mark Waugh	20	25.8
Mushtaq Mohammad	10	25.8
Andrew Strauss	10	26.5
Alvin Kallicharan	12	26.7
Damien Martyn	13	26.7
John Wright	12	28.0
Nasser Hussain	14	28.7
Colin Cowdrey	22	8.9
Michael Atherton	16	28.9

At the other end of the scale, while it is not surprising to see Mark Waugh (highest score 153) near the extreme, it is intriguing to compare his century average with his brother, who averaged 67.2. Honourable mention should go to Graeme Wood, who, with only nine centuries, did not qualify for the list, but whose century average was only 17.4. Wood was out for exactly 100 in three of his nine tons.

And what of Matt Hayden? His century average is 39.0, quite low, but it would be much lower still without his 380 against Zimbabwe. In fact, imagine if Hayden’s 380 had never happened, and we were to try to predict the major Australian batsmen most likely to ever make such a score. Hayden would have to be just about the least likely, with the exception of Mark Waugh.

Finally, here is a similar list for half-century averages, the batsmen most likely to go on to big scores after reaching 50.

Highest half-century averages (batting average of runs beyond the 50)

Batsman	50+ scores	Average
Don Bradman	42	123.4
Dennis Amiss	22	86.1
Wally Hammond	46	85.3
Jimmy Adams	20	82.6
Virender Sehwag	26	77.0
Kumar Sangakkara	40	75.5
Marvan Atapattu	33	74.4
Garry Sobers	56	72.7
Dean Jones	25	69.8
Steve Waugh	82	69.2
Zaheer Abbas	32	68.6
Sachin Tendulkar	88	67.1
Brian Lara	82	65.8
Ricky Ponting	73	65.5

Postscript

My previous post on the fastest and slowest innings attracted some lively comments. Some thought that the calculation was too complex, others thought that it needed more sophistication. The numbers of these comments seemed about equal, so perhaps I was doing something right.

Some pointed out that, because the distributions are skewed, comparing scores of different sizes could be unreliable. This is valid, up to a point. One could probably normalise the distributions, perhaps by taking the logarithms of the balls faced. This is a nuance that must await some future day; this is a cricket blog, not a statistics journal. My gut feel is that the results would not be significantly different if a fancier approach was taken.

Someone asked about Hanif Mohammad’s epic 337 against the West Indies. This is tricky, firstly because we don’t know the balls faced, and secondly because there are so few innings of similar size to compare it with. However, the z-score can be estimated at 6.42.

If you like, check out a detailed analysis of this innings on my blog. Scroll down to 23 June 2007.

Inevitably, there are those who come onto blogs like this to cleverly inform us that “statistics don’t tell the whole story” (or words to that effect). I have been following cricket stats for 40 years or so, and I have never heard anyone, statistician or otherwise, claim that stats DID tell the whole story. Just enjoy stats for what they are, an important dimension of the game.

	Nathan Astle's 168-ball 222 against England ranks second in the list of fastest innings © Cricinfo Ltd

What are the fastest and slowest Test innings of all time?

A simple question like this is actually tricky, thanks to the extreme range of possible scores. Comparing innings large and small, based on scoring speed alone, is unsatisfactory. For instance, Adam Gilchrist’s 102 off 59 balls in 2006 was considerably faster that Nathan Astle’s 222 off 168 balls in 2002; both were freakish innings, but which was the more remarkable?

One way to answer this is by measuring how far each innings deviates from normal innings of similar size. To do this, we take every innings of a given size – in terms of runs scored – calculate the average (or mean) balls faced, and then calculate the standard deviation, which is a measure of the spread or variability of the data. We can then give the most exceptional innings a z-score (the number of standard deviations from the mean) which becomes a measure of how extraordinary the innings were.

An example may help clarify this. Let’s look at all innings of exactly 76 runs in Test matches. We have balls faced data for 119 such innings. The average number of balls faced is 161 and the standard deviation of this data is about 49.

The fastest known innings of 76 in Tests was off 72 balls by Viv Richards in Adelaide in 1980. This is 1.75 standard deviations faster than the average, so the innings gets a z-score of -1.75. Likewise, the slowest innings of 76 was 315 balls by Glenn Turner in 1971, with a z-score of +3.2.

To compare many innings of different sizes, the process must be repeated for all possible scores. This process gives big innings a better rating than smaller innings of a similar speed, because it is more difficult to score rapidly for longer periods.

So which innings have the most extreme z-scores? At fast end of the scale, the results look like this:

The fastest innings

Batsman	Runs	Balls	Match	Venue & year	z-score
Viv Richards	110	58	WI v Eng	Antigua, 1986	-2.58
Nathan Astle	222	168	NZ v Eng	Christchurch, 2002	-2.54
Adam Gilchrist	102	59	Aus v Eng	Perth, 2006	-2.45
Chris Cairns	82	47	NZ v Eng	Lord’s, 2004	-2.36
Jack Gregory	119	81	Aus v SA	Johannesburg, 1921	-2.34
Jacques Kallis	54	25	SA v Zim	Cape Town, 2005	-2.34
Kapil Dev	89	55	Ind v Eng	Lord’s, 1982	-2.33

Recent innings are prominent in this list, a sign of the speed of the modern game. Still, no batsman has reached quite the extremes of Viv Richards in his record-breaking century in 1986. I wonder what it is about English bowling that has attracted so many extreme innings.

At the other end of the scale, we must go further back in time.

The slowest innings

Batsman	Runs	Balls	Match	Venue & year	z-score
Hanif Mohammad	20	223	Pak v Eng	Lord’s, 1954	7.90
Alec Bannerman	91	620	Aus v Eng	Sydney, 1892	7.88
Herbie Collins	40	340	Aus v Eng	Manchester, 1921	7.66
John Murray	3	100	Eng v Aus	Sydney, 1963	7.15
Yashpal Sharma	13	159	Ind v Aus	Adelaide, 1981	6.90
Geoff Allott	0	77	NZ v SA	Auckland, 1999	6.80

It is interesting to see a wide range of scores, from 0 to 91, appearing on this list. Modern cricket watchers can only wonder at the extremes represented here. In terms of time, Hanif would have, going by modern-day over-rates, taken more than five hours for his 20 runs, while Alec Bannerman’s 91 would probably take more than two full days. Apart from Bannerman, every other batsman who has faced 620 or more balls in a Test innings has scored well over 200 runs, and the most balls faced (known) in reaching a century is 525 by Colin Cowdrey in 1957. Perhaps it is no wonder that Bannerman, unlike his more adventurous brother Charles, never scored a Test century.

Of course, there are quite a number of past innings for which balls faced are unknown, so we don’t know exactly where they may fit on the scale, but we can still make some estimates. Of particular interest is Dilip Sardesai’s 60 against the West Indies in Bridgetown in 1962. Sardesai was at the crease for 155 overs, and probably faced over 450 balls; if so, his z-score would be 7.93. His dismissal in that match started an extraordinary collapse that saw Lance Gibbs take eight wickets for six runs.

A postscript puzzle: innings of four runs, on average, involve fewer balls faced than innings of three runs. There is a logical reason for this (for readers to ponder).

[Notes for the statistically-minded: this process works quite well when we have data available for a very large number of innings. However, it does require some smoothing and trend-fitting at higher, rarer scores (above 120). Note also that the distributions are skewed, so z-scores of fast innings are different in magnitude to slow ones, and at the fast end of the scale the calculation is not very useful for innings of less than 40 runs. However, the process is still useful as long as we just compare fast with fast, and slow with slow.]

	Jacques Kallis averages 71.84 at No. 4 © Getty Images

My blog post from January 9 has received a fair number of comments. Some of the readers have raised relevant queries and points which deserve a response. Here is my attempt to answer them, and also check out the best batsmen at each position.

The opening-position conundrum

A couple of readers have suggested that the two openers be allotted a number other than 1.00. The two suggestions offered are 1.5 or 2.0 for both openers. Both suggestions have their merits. 1.5 is more correct since the total for the two batsmen comes to 3.0 which is the sum of 1 and 2. However it does not look good as 1.0 or 2.0 would do. Allotting 2.0 to both batsmen is probably the better solution since it allows one to maintain continuity in numbers from 2.0 to 11.0. The other major benefit is that when an opener bats at 3.0, the variance will be a more correct 1.0 than the somewhat bloated 2.0 as is currently the case. Hence I have decided to allot both openers 2.0 and re-do the tables.

There will be no changes for the batsmen who have never opened. There will be no changes (other than a mean value of 2.0 as against the current 1.0) for the omni-present openers. For batsmen such as Boycott and Gavaskar there will be very little change. The change is significant only for those batsmen like Alec Stewart who have moved up and down the order quite frequently. Some of the key batsmen are compared below.

These are current up to the recently concluded second Test between New Zealand and Bangladesh.

Batsman            L Cty  Tests Inns BPTot  BPIdx MeanDev  Freq Batpos (%)
Revised
Stewart A.J          Eng   133  235    919   3.91   1.56    77 @  1( 32.8)
Previous
Stewart A.J          Eng   133  235    842   3.58   1.97    77 @  1( 32.8)
Revised
Jayasuriya S.T     ~ Slk   110  188    519   2.76   1.44   152 @  1( 80.9)
Previous
Jayasuriya S.T     ~ Slk   110  188    367   1.95   1.77   152 @  1( 80.9)
Revised
Langer J.L         ~ Aus   105  182    440   2.42   0.55   115 @  1( 63.2)
Previous
Langer J.L         ~ Aus   105  182    325   1.79   0.90   115 @  1 (63.2) 

It can be seen that the BP Index values are higher because the opening positions are assigned values of 2.0 instead of 1.0. However, more significantly, the Mean Variance values are significantly lower for all these players. These are probably the correct values. Alec Stewart remains the one who has been most tossed around, but he can derive some comfort from a mean variance value of around 1.5.

Just for the record, the top 25 batsmen in the revised table are listed in order of innings played. As per Steve Procter's suggestion, the Standard Deviation has been calculated and shown.

Batsman         L Cty  Tests Inns  BPIdx  M Dev   Freq Batpos (%) StdDev


Border A.R      ~ Aus   156  265    4.70   0.98    89 @  4( 33.6)   1.14

Waugh S.R         Aus   168  260    5.42   0.74   142 @  5( 54.6)   0.95

Stewart A.J       Eng   133  235    3.91   1.56    77 @  1( 32.8)   1.79

Tendulkar S.R     Ind   144  233    4.29   0.60   189 @  4( 81.1)   0.71

Lara B.C        ~ Win   131  232    3.78   0.51   148 @  4( 63.8)   0.65

Gooch G.A         Eng   118  215    2.31   0.57   184 @  1( 85.6)   0.80

Gavaskar S.M      Ind   125  214    2.21   0.44   203 @  1( 94.9)   1.42

Atherton M.A      Eng   115  212    2.10   0.25   197 @  1( 92.9)   0.49

Waugh M.E         Aus   128  209    4.24   0.56   170 @  4( 81.3)   0.67

Gower D.I       ~ Eng   117  204    4.00   0.71    91 @  4( 44.6)   0.87

Haynes D.L        Win   116  202    2.03   0.03   201 @  1( 99.5)   0.42

Dravid R          Ind   117  201    3.29   0.78   146 @  3( 72.6)   1.00

Inzamam-ul-Haq    Pak   120  200    4.66   0.91    98 @  4( 49.0)   1.15

Warne S.K         Aus   145  199    8.29   0.82   113 @  8( 56.8)   1.18

Kallis J.H        Saf   114  194    3.77   0.61    96 @  4( 49.5)   0.79

Boycott G         Eng   108  193    2.02   0.13   191 @  1( 99.0)   0.80

Boon D.C          Aus   107  190    2.85   0.61   111 @  3( 58.4)   0.84

Ponting R.T       Aus   114  190    4.02   1.34   125 @  3( 65.8)   1.46

Javed Miandad     Pak   124  189    4.24   0.57   140 @  4( 74.1)   0.71

Jayasuriya S.T  ~ Slk   110  188    2.76   1.44   152 @  1( 80.9)   1.72

Cowdrey M.C       Eng   114  188    3.84   1.09    54 @  5( 28.7)   1.28

Taylor M.A      ~ Aus   104  186    2.00   0.00   186 @  1(100.0)   0.00

Walsh C.A         Win   132  185   10.62   0.65   122 @ 11( 65.9)   0.63

Greenidge C.G     Win   108  185    2.03   0.13   182 @  1( 98.4)   0.72

Vengsarkar D.B    Ind   116  185    3.67   0.81    74 @  3( 40.0)   1.03

Highest averages at different batting positions

This is another interesting request. It would be of considerable interest to see the highest averages at different batting positions, with a qualification of at least 1000 runs at that position. Some surprises are in store for us.

Opening: Sutcliffe H        Eng  4522      61.11

No surprise to see Herbert Sutcliffe at the top. He was amongst the best three openers of all time. He is followed by Bruce Mitchell with 2390 runs @ 56.90.

No.3:    Bradman D.G        Aus  5078     103.63

Again no one should be surprised to see the greatest ever batsman at this position, with a 100+ average, the only instance of a such an average. He is followed by Ken Barrington with 2626 runs at 77.24.

No.4:    Kallis J.H         Saf  5675      71.84

Jacques Kallis' consistency at this position is well-known and this accounts for his overall average of high 50s. Surprisingly he is followed by Sourav Ganguly with 1143 runs @ 71.44. Have the Indian selectors/captains missed a trick there?

No.5:    Worrell F.M.M      Win  1189      59.45

This is a proof of the domination of the famous Ws. They occupy the first three places. Frank Worrell is followed by Clyde Walcott with 1599 runs @ 59.22.

No.6:    Chanderpaul S    ~ Win  2087      63.24

Another surprise, or perhaps not. The difficulty opposing bowlers have in dismissing Shivnarine Chanderpaul is shown by his outstanding average at this pivotal position. He is followed by Salim Malik with 1591 runs @ 56.82.

No.7:    McMillan B.M       Saf  1051      58.39

Brian McMillan has outdone quite a few fancied others at this position. He is followed by the mercurial Gilchrist with 3864 runs @ 49.62.

No.8:    Vettori          ~ Nzl  1136      42.07

Can anyone deny Vettori's claims to an allrounder position when he bats like this at No. 8. He improved his No. 8 position average in the recently concluded Test with an aggressive 94. He is followed by Mark Boucher with 1034 runs at 34.47.

No batsman has scored 1000 runs at Nos.9, 10 and 11. Just for the record, Shaun Pollock has scored 534 runs @ 41.08 at No. 9 (min 500 runs). W. Oldfield has scored 263 runs at 26.30 at No.10 (min 250 runs). Brian Statham has scored 348 runs @ 13.92 at the No.11 position (min 250 runs).

Just to complete the analysis and in anticipation of reader demands, I have given below the best batting position, runs and average for a few key batsmen, with the proviso that a minimum of 1000 runs should have been scored in that position.

Tendulkar       4  9573  57.32 
Dravid          3  7444  57.26
Laxman          6  2130  48.41
Ponting         3  7062  66.00
S.R.Waugh       5  6754  56.28
Lara            3  3749  60.47
Richards        3  3508  61.54
Sangakkara      3  5557  61.07
Inzamam-ul-haq  4  4867  52.90
...
Warne           8  2005  19.10
Vaas            8  1703  24.33
Kumble          7  1087  20.13
and
CS Martin      11    64   2.46

Chris Martin had an average of 2.00 (that is the BPI of an opener) until his last innings against Bangladesh when he reached his best ever score of 12 not out, increasing the average to 2.46. In the current Test he remained unbeaten on 0, thus remaining at the majestic figure of 2.46. The million-dollar question is if he will ever get 100 Test runs and reach a double-digit score again.

	Mohammad Yousuf scored 67 runs while his partners didn't contribute a single one against India in 2004 © AFP

Some of the more intriguing Test records cannot be found by looking at traditional scorecards. Hat-tricks are a prime example, but there are endless possibilities. I recently came across a case, at The Oval in 1886, of WG Grace scoring 60 runs while his batting partner, W Scotton, remained scoreless, stuck on 21. I wondered, what is the greatest number of runs scored while one batsman remained scoreless? I knew of one example greater than Grace: in his legendary 232 at Trent Bridge in 1938, Stan McCabe scored the last 66 runs of the Australian innings, while batting with Chuck Fleetwood-Smith.

Are there any modern parallels? This is where Cricinfo’s ball-by-ball archive, with more than 400 Tests since 1999, comes in. Make a suitable database out this archive and it can be searched for feats like this.

It’s not as simple as it sounds, but some results are in. Bear in mind also that the archive was set up more as a detailed commentary than an “official” statistical source, and contains gaps. Anyway, here are some results for extreme domination of scoring.

Monopolising scoring in Tests since 1999

Batsman (Total score)	Runs	Incl extras	Scoreless partner (s)	Versus	Venue & year
Mohammad Yousuf (112)	67	74	Moin Khan, Mohammad Sami, Saqlain Mushtaq, Shoaib Akhtar	India	Multan, 2004
Adam Gilchrist (138*)	65	69	Shane Warne, Brett Lee, Jason Gillespie, Glenn McGrath	South Africa	Cape Town, 2002
Kumar Sangakkara (100*)	64	66	Farveez Maharoof, Lasith Malinga, Muttiah Muralitharan	New Zealand	Christchurch, 2006
Sanath Jayasuriya (253)	58	70	Dilhara Fernando	Pakistan	Faisalabad, 2004
Andy Flower (183*)	56	63	Henry Olonga	India	Delhi, 2000
Tatenda Taibu (153)	52	54	Douglas Hondo	Bangladesh	Dhaka, 2005
Justin Langer (123)	51	56	Matthew Hayden	New Zealand	Hobart, 2001
Tapash Baisya (66)	51	51	Mohammad Rafique, Enamul Haque jr	New Zealand	Chittagong, 2004

Mohammad Yousuf went from 23 to 90 in 22 overs in that Multan Test, and saw three wickets fall while his partners added nothing, so that edges out McCabe as the most extreme case. McCabe, though, totally monopolised the scoring; there were no extras. Fleetwood-Smith still holds the record for watching his partner score while not scoring himself, although the total of 66 runs was exceeded by Dilhara Fernando if you include extras.

Perhaps the most remarkable example is the Langer-Hayden case, given that Hayden is normally such a heavy hitter. To find a more extreme example of one recognised batsman outscoring another, you have to go back to WG in that Oval Test of 1886. (Langer, incidentally, was the first batsman to reach a half-century in the first 10 overs of a Test match, a feat since emulated by Marcus Trescothick).

Readers who know of (or suspect) other extreme cases are invited to suggest them.

First let me explain the reasons for undertaking this whole exercise of extended batting averages:

The purpose was not to replace the conventional batting average. It was a suggestion to complement the batting average.

It was not a Tendulkar v Lara article. Their figures were just used for comparison.

Let me start by replacing the first para of my article with the following, just to put to bed the Tendulkar v Lara arguments. Consider the following two outstanding batsmen, among the best of their generation.

Richards and Kallis in Tests

Batsman	Tests	Innings	Not-outs	Runs	Average
Viv Richards	105	182	12	8540	50.24
Jacques Kallis	111	189	31	9197	58.31

Richards’ average is nearly eight behind Kallis', but is he that far behind? One of the main reasons for the difference in average has been the wide disparity in not-outs between the two, 12 against 31. It might be partly because of the way Richards played, almost always in an attacking mode. Both Richards and Kallis have similar Batting Position Index values - which is the average batting position at which a batsman has batted in - of 4.16 (Richards) and 3.77 (Kallis), indicating almost similar batting positions. This analysis seeks a way to normalise such situations.

Now to respond to some of the comments that came in:

The 1500 runs cut-off wasn’t meant to exclude Vinod Kambli, as someone suggested (Kambli is incidentally one of my favourite players). It was determined that the overall runs per Test for a top-order batsmen was around 75. The 1500 runs meant that one would have played 20 tests, which is a fair number of games. It also allowed me to include Hussey, which ensured further discussion on this phenomenal cricketer. Selecting the top 25 batsmen was again done to allow to include Lara and Pietersen, who were two of the 5 batsmen whose EBA was greater than their Batting Average.

The average of last ten innings could be construed as an arbitrary decision. Come to think of it, if I had taken five innings, it would have seemed too few, while 20 might have seemed too many. Ten innings represents about seven tests, which in turn is a minimum of two Test series.

Chris made a valid point about the order of the first table, stating that it should have been ordered by batting average rather than the EBA. A valid point, and I apologise for overlooking the significance. Unfortunately I had split the EBA-ordered wide table into two smaller ones and should have re-ordered the same.

A number of people have commented that this exercise was not needed since the final EBA table is more or less the same as the batting average table. My argument is that the result does not invalidate the analysis process.

The question of not-outs

The extension of not-out innings has attracted the most comments and rightly so. The approach I have taken can be construed as arbitrary. However it must be remembered that what has been done is neither a statistical extension nor a simulation-based computation. It is a fourth-dimension prediction and should be taken as it is. I can only repeat that the EBA should be taken to complement the current and much more understood batting average. The EBA can never be a substitute for batting averages since the common man can neither compute the same on his own nor understand the same easily.

When the concept was first created, the batting average was added to the not-out innings. It was only when I reworked the same concept for this blog did I change it slightly to include current form.

Some of the responses to the not-out issue have been interesting. Stuart says:

A batting average measures the number of runs between dismissals. If you get 20* and 27, that is equivalent to a single innings of 47 for your batting average. It also means you cobbled together 47 runs before you got out, whether it was over two innings or one. As it stands, interpreted correctly, a batting average is a perfect measure and needs no adjustments or fiddling.

That’s a fine analysis, and we could take this as an additional measure.

One of the best alternatives, and quite simple to implement also, was provided by Arvind Agarwal. It is given below.

EBA = Batting Average x (1 - (Not Out Inngs / Total Inngs) ^ 2. The computed values are:
Lara = 52.80 (0.998 x Average)

Sachin = 53.82 (0.980 x Average)

Bradman = 97.93 (0.980 x Average)

Ponting = 58.08 (0.977 x Average)

M Hussey = 82.04 (0.945 x Average)

My gut feel is that Arvind's computations match mine almost completely without getting into any of the not-out extension complications and very easy to compute. Again this has to be taken as an additional measure rather than a replacement of the batting average.

There have been suggestions to take into account the match conditions, bowling attack etc., but it would be too complicated an exercise for this simple task. Similarly, the idea of using weighted averages instead of using the average of the last ten innings is a good one, but it makes the process more difficult and the results difficult to comprehend for the non-statiscally oriented people.

Glossus has suggested considering only those innings in which the batsman was dismissed, and ignoring the not-out innings. The table below has the results for this exercise.

Out batting average, and extended batting averages

Batsman	Tests	Career average	Out batting average	Extended batting average
Don Bradman	52	99.94	83.83	97.81
Michael Hussey	18	86.18	69.05	81.34
George Headley	22	60.83	45.61	61.33
Herbert Sutcliffe	54	60.73	54.64	60.54
Graeme Pollock	23	60.97	54.43	59.68
Everton Weekes	48	58.62	54.88	58.53
Ricky Ponting	112	59.40	49.46	58.52
Wally Hammond	85	58.46	46.19	58.43
Garry Sobers	93	57.78	44.06	58.16
Ken Barrington	82	58.67	50.37	58.11
Eddie Paynter	20	59.23	48.31	57.71
Jack Hobbs	61	56.95	53.34	56.52
Jacques Kallis	111	58.21	42.42	56.43
Len Hutton	79	56.67	47.89	56.41
Kumar Sangakkara	68	55.74	46.16	56.26
Clyde Walcott	44	56.69	51.03	56.14
Rahul Dravid	113	56.26	47.60	55.54
Mohammad Yousuf	77	55.72	48.84	55.28
Sachin Tendulkar	141	54.94	44.33	53.90
Dudley Nourse	34	53.82	47.49	53.40
Brian Lara	131	52.89	49.76	52.97
Kevin Pietersen	30	52.69	50.44	52.84
Greg Chappell	87	53.86	44.57	52.79
Matthew Hayden	91	52.57	49.19	52.50
Javed Miandad	124	52.57	41.97	51.62

Charles Davis, in his blog , has commented on this computation. Some of the answers to Charles can be found elsewhere in this article. Our first basis was the career average and would probably have been more apt. However I must point out to Charles that the "not exceeding the highest score" idea was only done to prevent extremely high scores, especially when batsmen (like Sangakkara/Yousuf/Kallis) are going through an outstanding run of form. That restriction may not be needed if the career average is used. However I must point out that the standard deviation differential between the career average and last 10 innings, according to Charles himself, is less than 10%. Charles, many thanks for your comments.

	A familiar end to a Chris Martin innings © AFP

Chris Martin further enhanced his already considerable reputation as the classic tailender with a near-perfect game at the Wanderers: played eight balls (which, some might argue, was six more than necessary), scored 0 runs, out twice. His 19 Test ducks mean he is fast moving up the all-time list, and is already in the top 15, after a mere 34 matches.

As Mathew Varghese pointed out in his post-match stats piece after the Johannesburg Test, Martin is already the proud holder of three records – the most number of pairs in Tests, the most zeroes in Tests between South Africa and New Zealand, and in Tests at the Wanderers.

The table below shows just how far ahead of the rest of the pack Martin is: in 25 completed innings, he has failed to get off the mark 19 times. Taking a cut-off of 20 dismissals in Tests, Martin is far ahead of his nearest competitor, Danish Kaneria. If he continues at his current rate of a duck every 1.79 Test, Martin will get his 44th – and go past Courtney Walsh’s world record – in his 79th match.

Highest duck factor, as a % of innings dismissed (at least 20 dismissals)

Player	Dismissed innings	Ducks	% of ducks
Chris Martin	25	19	76.00
Danish Kaneria	34	20	58.82
BS Chandrasekhar	41	23	56.10
Danny Morrison	45	24	53.33
Ewen Chatfield	21	11	52.38
Allan Mullally	23	12	52.17
Phil Tufnell	30	15	50.00
Dilip Doshi	28	14	50.00
Manjural Islam	22	10	45.45
Corey Collymore	25	11	44.00

Meanwhile, here’s a response to the queries about genuine batsmen with the most propensity to score ducks. Taking a cut-off of 50 Test innings, and an average of at least 30, India’s Pankaj Roy comes out on top. Among specialist batsmen, Marvan Atapattu and Steve Waugh have the most number of ducks – 22 – but while Atapattu makes it to the list below, Waugh’s zeroes came over 260 innings, which means his percentage was only 8.46.

Batsmen with highest duck percentage in Tests (at least 50 innings, with an average of at least 30)

Batsmen	Innings	Average	Ducks	% of ducks
Pankaj Roy	79	32.56	14	17.72
Derek Randall	79	33.38	14	17.72
Keith Arthurton	50	30.71	8	16.00
Roy McLean	73	30.29	11	15.07
Marvan Atapattu	154	38.91	22	14.29
Mike Smith	78	31.64	11	14.10
Andrew Flintoff	110	32.51	15	13.64
Kamran Akmal	59	30.82	8	13.56
Chandu Borde	97	35.59	13	13.40
Frank Woolley	98	36.08	13	13.27

	Courtney Walsh: a true giant in the art of making zeroes © AFP

Ah, The Duck – nothing troubles the scorers more, despite what any commentator may tell you. Especially if it is a quick one and you are still entering all the details of the previous wicket. A duck is almost as much of a symbol of non-batsmanship as scoring a century is of batting ability.

In 1996, Danny Morrison passed the record for most ducks in Test cricket amid a blaze of publicity and memorabilia. Bhagwat Chandrasekhar had held the record with 23 at that stage. Morrison subsequently passed the baton (if you will excuse the truly abysmal pun) to Courtney Walsh, who still holds the record with 43. Muttiah Murailtharan has been dismissed first ball for a duck on no fewer than 14 occasions in Test cricket.

But, what about ducks in first-class cricket? Reg Perks, of Worcestershire and England (twice, in 1939), collected 156 ducks in his first-class career, which is a record. Perks was not the world’s worst batsman: he scored 8956 runs, including 14 fifties, at an average of 12.20 in 595 first-class matches.

But a major candidate for champion duck maker in first-class cricket is Kevin Jarvis of Kent and Gloucestershire. Jarvis is the only batsman with over 100 dismissals in first-class cricket to have ducks as more than 50% of his dismissals. In his 199 first-class innings he was not out 87 times and made 59 ducks, which represents 52.69% of the total innings in which he was dismissed. In all, Jarvis scored 403 runs at an average of 3.59. He did, of course, make up for this by taking 674 wickets. He reached 20 for the first, and only, time in his 255th first-class match (Gloucestershire v Hampshire at Portsmouth in 1989) and played only 5 more matches before retiring.

And what of Seymour Clark? He played 5 first-class matches for Somerset (all in 1930) and in 9 innings (two of which were not outs) he did not score a run. He did not take a wicket either. He was a wicketkeeper and presumably must have been a very good one just to get a game.

Then there is the 1, the much-neglected score. If a century is a mark of batting excellence and a duck is a mark of batting ineptitude, then a 1 must be the non-batsman’s equivalent of 99. I briefly considered nominating the word ‘drake’ for ones to go with ducks for noughts. But it would probably be considered inappropriate, in these egalitarian times, for the male of the species to represent a higher value than the female.

The most dismissals for 1 in Test cricket is 12 by Javagal Srinath and Glenn McGrath.

Three players have been dismissed for 1 eleven times in Tests: Curtly Ambrose, Courtney Walsh and, surprisingly, Rod Marsh. And Adam Sanford was an impressive 1-maker. He was dismissed eight times for 1 out of his 15 Test dismissals (53.33%), including each of his last 4 innings. Then there’s Walter Reader-Blackton. In addition to having a name that was almost as long as his first-class career (8 matches for Derbyshire between 1914 and 1921), he was also the first player to be dismissed for 1 in five consecutive first-class innings.

And another world record for Shane Warne. He has been dismissed for 2 more often than anyone else in Test cricket – 11 times.