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.