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.

	Mark Taylor played 186 Test innings, and opened the batting in each of them © Getty Images

Where does a batsman bat in Tests? Has he opened always? Has he been shunted around? Which batsmen have had the luxury of always (or almost) batting in the same position? Here is a new measure to explore these aspects of batting, which I had briefly mentioned in my previous post. I've written a program to analyse the position at which every batsman has batted in his entire career, and average these. The positions of 1 and 2 are combined into a single position, 1, since it really does not matter who faces the first ball; other positions are numbered from 3 to 11. The batting position values are totalled and divided by the number of innings each batsman played, thus arriving at the Batting Position Index (BPI) for each player. In addition, the mean variance for all these positions has been worked out. This is the average of the absolute variances from the BPI. Let me explain this. Let us say that a batsman batted at No. 4 in 10 innings. His BPI is 4.0. Let there be another batsman who batted 4 times at No 3, twice at No. 4 and four times at No. 5. His BPI is also 4.0. However the Mean Variance for the first batsman is 0.0, indicating no departure from the mean position while the Mean Variance for the second batsman is 0.8, indicating quite a bit of shuffling around of the batting position. I have adopted the mean variance rather than the standard variance since the distribution is not Standard or Gaussian. The distribution of batting positions does not have a pattern. A player tends to bat around his favourite (and/or) productive positions. There may be a case for using standard deviation. Since I do not have a master's degree in statistics, I have resorted to using my common sense which tells me that I should use the mean deviation rather than standard deviation. The other value which has been determined is the most often batted position for each batsman and the percentage of total for this position. There is a strong correlation between this % value and the Mean Variance. As this percentage value approaches 100, the Mean Variance approaches 0.0. A few notes about the Batting Position Index. A BPI of 1.0 indicates that the batsman has always played in the opening position, while a BPI of 11.0 indicates that the batsman has similarly always batted last for his team. These are the extremes, and fairly clear. On the other hand a BPA of 5.0 does not indicate that the batsman always batted at No.5, since he could have batted 25 times at No. 4 and 25 times at No. 6. However a BPI of 4.15 generally indicates that he might have batted more at No. 4 while a BPA of 4.90 indicates that he would have batted more often at No. 5. Keep this in mind while you look at the numbers. A number of interesting facts came to light and are presented below. Let us see some tables. '~' indicates a left-handed batsman. These are current upto Test no 1854, the third Test between Sri Lanka and England played at Galle. A minimum of 50 innings has been taken as the minimum qualification.

A minimum of 50 innings has been taken as the minimum qualification.

Batsman	L	Cty	Tests	Inns	BPTot	BPIdx	MeanDev	Freq	Batpos (%)
Border A.R	~	Aus	156	265	1245	4.7	0.98	89 @	4( 33.6)
Waugh S.R		Aus	168	260	1410	5.42	0.74	142 @	5( 54.6)
Stewart A.J		Eng	133	235	842	3.58	1.97	77 @	1( 32.8)
Lara B.C	~	Win	131	232	876	3.78	0.52	148 @	4( 63.8)
Tendulkar S.R		Ind	142	229	983	4.29	0.61	185 @	4( 80.8)
Gooch G.A		Eng	118	215	313	1.46	0.83	184 @	1( 85.6)
Gavaskar S.M		Ind	125	214	269	1.26	0.53	203 @	1( 94.9)
Atherton M.A		Eng	115	212	249	1.17	0.43	197 @	1( 92.9)
Waugh M.E		Aus	128	209	886	4.24	0.57	170 @	4( 81.3)
Gower D.I	~	Eng	117	204	812	3.98	0.72	91 @	4( 44.6)
Haynes D.L		Win	116	202	209	1.03	0.03	201 @	1( 99.5)
Inzamam-ul-Haq		Pak	120	200	930	4.65	0.91	98 @	4( 49.0)
Warne S.K		Aus	145	199	1649	8.29	0.82	113 @	8( 56.8)
Dravid R		Ind	115	197	640	3.25	0.78	146 @	3( 74.1)
Boycott G		Eng	108	193	199	1.03	0.16	191 @	1( 99.0)
Boon D.C		Aus	107	190	478	2.52	1.05	111 @	3( 58.4)
Kallis J.H		Saf	111	189	712	3.77	0.62	91 @	4( 48.1)
Javed Miandad		Pak	124	189	798	4.22	0.57	140 @	4( 74.1)
Cowdrey M.C		Eng	114	188	684	3.64	1.33	54 @	5( 28.7)
Jayasuriya S.T	~	Slk	110	188	367	1.95	1.77	152 @	1( 80.9)
Taylor M.A	~	Aus	104	186	186	1	0	186 @	1(100.0)
Ponting R.T		Aus	112	186	751	4.04	1.34	121 @	3( 65.1)
Walsh C.A		Win	132	185	1965	10.62	0.65	122 @	11( 65.9)
Richards I.V.A		Win	121	182	758	4.16	1.07	63 @	5( 34.6)
Sobers G.St.A	~	Win	93	160	807	5.04	1.2	57 @	6( 35.6)
Bradman D.G		Aus	52	80	292	3.65	1.24	56 @	3( 70.0)
Jones A.H		Nzl	39	74	223	3.01	0.11	70 @	3( 94.6)

The top five batsmen have batted in middle order positions. Allan Border has batted at No. 4 for most of his career while Steve Waugh has batted a position lower. Alec Stewart and Brian Lara have batted higher up the order with Stewart getting his numbers lower because of his frequent opening stints. Lara's most batted position is No. 4. Sachin Tendulkar has batted slightly down the order, while Dravid has batted at No. 3 most of the times in his career. Now we get to the batsmen specialising in opening positions. Graham Gooch has batted lower down more often than Sunil Gavaskar or Michael Atherton. Desmond Haynes' index is interesting. He has batted only once other than the opening slot, and that was in the last innings he ever played in his career. He batted at No. 8 and scored 15 against England in 1994. Why he batted at that position is quite a mystery. Boycott batted at lower positions twice in a single Test. Most of the top batsmen in this group have mean variance values below 1, indicating a reasonably settled existence in the opening or middle order slots. The only exception is, of course, Alec Stewart, with a high value of 1.97. Note also the somewhat high variance value for Jayasuriya, indicating long tenure at positions 1 and 2, and a few innings way down the order. Richards, surprisingly, has batted at No. 5 most. This explains his slightly higher BPI. Walsh averages 10.62, indicating a near-permanent residency at No. 11. Andrew Jones makes an interesting examples. He has the highest occupancy % of a single batting position among the middle-order batsmen, 94.6% at No. 3, only four times batting away from this position. He is the only batsman with a 90+% occupancy of a batting position among the non-opening, and non-No. 11 batsmen.

Now a table of Opening batsmen who have never vacated their assigned slots.

Batsman	L	Cty	Tests	Inns	BPIdx	MeanDev	Freq	Batpos (%)
Taylor M.A	~	Aus	104	186	1.00	0.00	186 @	1( 100.0)
Hayden M.L	~	Aus	91	162	1.00	0.00	162 @	1( 100.0)
Slater M.J		Aus	74	131	1.00	0.00	131 @	1( 100.0)
Lawry W.M	~	Aus	67	123	1.00	0.00	123 @	1( 100.0)
Strauss A.J	~	Eng	43	81	1.00	0.00	81 @	1( 100.0)
Hunte C.C	~	Win	44	78	1.00	0.00	78 @	1( 100.0)
Srikkanth K		Ind	43	72	1.00	0.00	72 @	1( 100.0)
Imran Farhat	~	Pak	27	51	1.00	0.00	51 @	1( 100.0)

These are die-hard opening batsmen who have frowned at doing anything else. The fact that this list is headed by four Australians - and three of them from recent times - seems to indicate the importance they place on the opening position in particular, and a sense of permanence in their batting orders in general. Even when Taylor struggled, they did not try to push him down to No. 4 or 5. What about those other opening stalwarts like Gavaskar, Boycott, Hutton, Hobbs, Sutcliffe, Haynes and Greenidge? Well, Gavaskar batted at No. 4 in quite a few matches. Sutcliffe batted at No. 6 in a single match. Hobbs batted low down in a few matches. Boycott batted at No. 4 a few times. Similarly Haynes and Greenidge went off their opening positions for no more than a couple of innings. Note Mark Taylor's perfect index value of 1.00. He has batted in the opening slot in each of the 186 innings he has played for Australia. This is the highest number of innings by an opener without vacating his slot.

A list of the real rabbits.

Batsman	L	Cty	Tests	Inns	BPIdx	MeanDev	Freq	Batpos (%)
Chatfield E.J		Nzl	43	54	10.96	0.06	52 @	11 ( 96.3)
Chandrasekhar B.S		Ind	58	82	10.93	0.16	75 @	11 ( 93.8)
McGrath G.D		Aus	124	138	10.92	0.21	128 @	11 ( 92.8)
Valentine A.L		Win	36	51	10.90	0.14	46 @	11 ( 90.2)
Malcolm D.E		Eng	40	58	10.84	0.32	49 @	11 ( 84.5)
Danish Kaneria		Pak	51	69	10.78	0.43	55 @	11 ( 79.7)
Tufnell P.C.R		Eng	42	59	10.75	0.48	44 @	11 ( 74.6)
Alderman T.M		Aus	41	53	10.62	0.76	42 @	11 ( 79.2)
Walsh C.A		Win	132	185	10.62	0.65	122 @	11 ( 65.9)
Willis R.G.D		Eng	90	128	10.61	0.54	78 @	11 ( 60.9)

Not a very surprising list. All confirmed rabbits. Is there a batsman who has ALWAYS batted at No.11? If a player has a long enough career, he inevitably bats at least once or twice in some other position, and thus has a BPI different from 11. The nearest we get to a perfect rabbit is in the form of Chatfield, who has batted at No.11 a total of 52 times and at No.10 twice, both times because of injuries to other batsmen. Chatfield has scored 18 zeros (dismissed or otherwise) out of these 54 innings. McGrath has batted at positions earlier than No.11 a few times. Similarly Chandrasekhar has achieved promotion a couple of times. Valentine and Malcolm complete the perfect list of rabbits. Chandrasekhar's batting average is the lowest in this collection. Chris Martin of New Zealand, almost the perfect no.11, just misses the cut, having played 49 innings. he has batted at no.11 a total of 46 times, gaining promotion 3 times to no.10. Oh! that is wrong. As David Barry has pointed out, Martin was moved upto no.10 (probably very reluctantly) because Vettori, Bond and Cummings were absent in the three innings respectively. A true no.11, then Martin is.

Batsmen who have a Mean Deviation of 0.00 (All opening batsmen!)

Batsman	L	Cty	Tests	Inns	BPIdx	MeanDev	Freq	Batpos (%)
Taylor M.A	~	Aus	104	186	1.00	0.00	186 @	1( 100.0)
Hayden M.L	~	Aus	91	162	1.00	0.00	162 @	1( 100.0)
Slater M.J		Aus	74	131	1.00	0.00	131 @	1( 100.0)
Lawry W.M	~	Aus	67	123	1.00	0.00	123 @	1( 100.0)
Strauss A.J	~	Eng	43	81	1.00	0.00	81 @	1( 100.0)
Hunte C.C	~	Win	44	78	1.00	0.00	78 @	1( 100.0)
Srikkanth K		Ind	43	72	1.00	0.00	72 @	1( 100.0)
Imran Farhat	~	Pak	27	51	1.00	0.00	51 @	1( 100.0)

and one very close to 0.00

Chatfield E.J

Nzl

43

54

10.96

0.06

52 @

11 ( 96.3)

This is the same list of omni-present opening batsmen already presented, re-displayed here to emphasise the fact that the opening slots have a sense of permanency attached to them. We have already talked of Chatfield.

Non-opening batsmen who have a Mean Deviation of 0.00 (Below 50 innings played)

Batsman	L	Cty	Tests	Inns	BPIdx	MeanDev	Freq	Batpos (%)
Jayawardene H.A.P.W		Slk	17	19	7.00	0.00	19 @	7 ( 100.0)
Hayward M		Saf	16	17	11.00	0.00	17 @	11 ( 100.0)
Aamer Nazir		Pak	6	11	11.00	0.00	11 @	11 ( 100.0)
Mohsin Kamal		Pak	9	11	11.00	0.00	11 @	11 ( 100.0)
Renneberg D.A		Aus	8	13	11.00	0.00	13 @	11 ( 100.0)
Mpofu C.B		Zim	6	12	11.00	0.00	12 @	11 ( 100.0)
Owens M.B		Nzl	8	12	11.00	0.00	12 @	11 ( 100.0)

and

Patterson B.P

Win

28

38

10.97

0.03

37 @

11 ( 97.4)

Prasanna Jayawardene, the current Sri Lankan wicket-keeper leads this list with 19 batting stints, all at position 7 (including the test which finished now). The maximum number of innings played by a batsman whose entire career was spent in the No. 11 position is 17, by Nantie Hayward of South Africa. West Indies’ Pattrick Patterson has had one promotion, out of 38 attempts, from 11 to 10.

Now for the list of batsmen who have been tossed around a lot (High Mean Deviation)

Batsman	L	Cty	Tests	Inns	BPIdx	MeanDev	Freq	Batpos (%)
Rhodes W		Eng	58	98	5.06	3.39	43 @	1 ( 43.9)
Abid Ali S		Ind	29	53	4.85	3.17	21 @	1 ( 39.6)
Prabhakar M		Ind	39	58	4.09	3.05	30 @	1 ( 51.7)
Mongia N.R		Ind	44	68	4.84	3.00	30 @	7 ( 44.1)
Engineer F.M		Ind	46	87	3.77	2.96	48 @	1 ( 55.2)
Mankad M.H		Ind	44	72	3.56	2.94	40 @	1 ( 55.6)
Blackham J.M		Aus	35	62	7.45	2.45	16 @	8 ( 25.8)
de Villiers A.B		Saf	32	58	3.17	2.30	34 @	1 ( 58.6)
Macartney C.G		Aus	35	55	4.07	2.23	28 @	3 ( 50.9)
Grout A.T.W		Aus	51	67	8.57	2.20	29 @	9 ( 43.3)
Stewart A.J		Eng	133	235	3.58	1.97	77 @	1 ( 32.8)

Wilfred Rhodes is one of the very few who has batted in positions 1 to 11. Ravi Shastri, another 1 to 10 batsman, has a BPI of 4.93 and a Mean Variance of 1.74. Abid Ali has batted consistently in the opening slots and in the late order. Note the presence of five Indians among the top six, indicating a propensity for the Indian selectors to have stop-gap opening combinations more often than others. Alec Stewart is a special case worthy of separate discussion. Having played 235 innings, he has batted 77 times at No. 1 (only a third of the innings). Otherwise he has been shunted around to almost all the top-order batting positions, with No. 6 being the next highest. He has batted in 3, 4 and 5 quite frequently. He is the only batsman who has played over 130 Tests and 230 innings and has a mean variance of nearly 2. There is no doubt that he would have achieved more than an average of 39.56 if he had a settled batting slot.

Batsmen who have batted in the same position for many an innings

Batsman	L	Cty	Tests	Inns	BPIdx	MeanDev	Freq	Batpos (%)
Gavaskar S.M		Ind	125	214	1.26	0.53	203 @	1 ( 94.9)
Haynes D.L		Win	116	202	1.03	0.03	201 @	1 ( 99.5)
Atherton M.A		Eng	115	212	1.17	0.43	197 @	1 ( 92.9)
Boycott G		Eng	108	193	1.03	0.16	191 @	1 ( 99.0)
Taylor M.A	~	Aus	104	186	1.00	0.00	186 @	1 ( 100.0)
Tendulkar S.R		Ind	142	229	4.29	0.61	185 @	4 ( 80.8)
Gooch G.A		Eng	118	215	1.46	0.83	184 @	1 ( 85.6)
Greenidge C.G		Win	108	185	1.05	0.17	182 @	1 ( 98.4)
Waugh M.E		Aus	128	209	4.24	0.57	170 @	4 ( 81.3)
Hayden M.L	~	Aus	91	162	1.00	0.00	162 @	1 ( 100.0)
Jayasuriya S.T	~	Slk	110	188	1.95	1.77	152 @	1 ( 80.9)

Gavaskar and Haynes head this list having batted more than 200 times in their respective positions. Tendulkar has had a settled tenure at No.4 and Mark Waugh a similar comfort zone.

Barring these two, the other batsmen are all opening batsmen

Batsman	L	Cty	Tests	Inns	BPIdx	MeanDev	Freq	Batpos (%)
Dravid R		Ind	115	197	3.25	0.78	146 @	3 ( 74.1)
Waugh S.R		Aus	168	260	5.42	0.74	142 @	5 ( 54.6)
Botham I.T		Eng	102	161	6.23	0.69	94 @	6 ( 58.4)
Marsh R.W	~	Aus	96	150	6.91	0.46	123 @	7 ( 82.0)
McGrath G.D		Aus	124	138	10.92	0.21	128 @	11 ( 92.8)

Dravid, as expected, has played at No. 3 a total of 146 times, often walking in during the first 5 overs. Steve Waugh has batted at No. 5 a total of 142 times. Not so surprisingly Glenn McGrath has batted at No. 11 the most number of times.
PS: Quite a few readers have expressed that the Runs Per Innings value could also be used as an alternate measure for the Batting Average as compared to EBA. I had used this measure in most of my earlier simulation exercises, especially ODI. It presents a simple computation methodology as compared to EBA. The best thing to do is to leave the batting average as the main measure for analysis and leave the other two as alternative measures which could be used to complement the established measure.