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.

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:

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:

(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

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

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]

• 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.
  

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.
  

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

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)

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

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)

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

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)

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

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)

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

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)

• Jadeja A 92 (109)

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)

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

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)

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

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)

• Stewart A.J 91 (126)

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)

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

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)

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

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)

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

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)

• Vengsarkar D.B 50 (46)

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)

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

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

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.

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.

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

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.

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

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

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.

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:

*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.

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

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:

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.

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.

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.

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

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:

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.

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

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) 

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.3:    Bradman D.G        Aus  5078     103.63

No.4:    Kallis J.H         Saf  5675      71.84

No.5:    Worrell F.M.M      Win  1189      59.45

No.6:    Chanderpaul S    ~ Win  2087      63.24

No.7:    McMillan B.M       Saf  1051      58.39

No.8:    Vettori          ~ Nzl  1136      42.07

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

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.

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:

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.

Comments (10)

November 12, 2007

Posted by S Rajesh at in Trivia - batting

Martin zeroes in on records

	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

Comments (12)

November 9, 2007

Posted by Andrew Samson at in Trivia - batting

Of ducks and drakes

	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.

Comments (16)