Trivia - batting July 6, 2008

Extrapolating high scores in Tests

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Comments have now been closed for this article

  • Ron on October 19, 2008, 10:17 GMT

    Interesting bit of analysis. However, it is not enough to look at the expected value of the extrapolated score. What is the variance? My guess is that it'd be fairly high.

  • Alex on August 10, 2008, 11:49 GMT

    PS to my earlier comment: earlier commenters were even more confused than I thought (even managed to confuse me too). Jayasuriya's innings in the big total against India was only 340, nowhere near a record. The 374 by Jayawardene was after Haydn's 380 AND after Lara's 400*.

  • Alex on August 10, 2008, 11:39 GMT

    Re Jayawardene "eclipsing" Lara. According to Cricinfo's best batting performances, he only made 374, so he certainly did not eclipse Lara. That feat was achieved by Matthew Hayden with his 380 against Zimbabwe. Of course, as you mentioned in your response to Slog Unlimited, Lara later regained the record with his 400 not out.

  • santhosh kudva on August 2, 2008, 16:56 GMT

    ... i think one more factor needs to be considered in this analysis. the team composition. a team like australia is likely to amass more runs for the last five wickets than the west indies team would during its entire innings...or better still give a teamwise breakup...

  • Ananth on July 12, 2008, 0:50 GMT

    Charles, an excellent analysis. I know a few people have already commented on this. I personally think the most dominating innings of all time is West Indies 790 for 3 because Sobers and Walcott were still batting and they still had two batsmen yet to come. Non-statistically, I am convinced that that would have been the only innings capable of reaching 1000. I had done a similar study on ODI innings and there the Australian total of 434 for 4 (a losing score) stood at the pinnacle.

  • Chris on July 11, 2008, 12:04 GMT

    To Azad Ahmad.. Do you think SL will score more than 952.. were Aus able to score thatmuch against the same bowling - NO!. And i find this record quite selfish, if it were the Australians... they would have forced the second innings by declaring at 700 odd.

  • Abhay Goyal on July 11, 2008, 8:15 GMT

    I believe you may be right till some extent but I beleive there is a certain patience of a batsman playing in the middle. In these days,its very difficult for batsmen to play a long test like knock and stay in the middle for long hours. And see if each batsman scores over a 100 in the team then the score reaches somewhere near 1000 mark. Thats a very difficult mark and also one needs to be very bold not to go for declaring. Remember, Captain Dravid once declared Indian innings at a stage when tendulkar was at the crease on 194*. Wow, 952 was a very good score, Hats off to Srilanka. 790 runs scored by westindies was still far from the 1000 mark and it was clas of lara that more than 50% of the runs were his.

  • SRAM on July 10, 2008, 21:47 GMT

    Were the scores considered at the time of declaration or at the time of the last wicket to fall? For instance a 600/5 decl might have been a 300/4 when the 4th wicket fell. The fall of the 5th wicket might be just round the corner and one could consider the score to be 600/6.

    [Response: It cannot be predicted statistically whether a wicket is 'just around the corner'. There is no particular level of a partnership, once it is past 20 runs or so, where a fall of wicket suddenly becomes more or less likely.]

  • Amer - Canada on July 10, 2008, 18:31 GMT

    Charles, Interesting. I remember in 86/76 Pakistan posting a huge total vs England at the Oval. I think it was around 600+. I was expecting to see that innings here.

    [response: Pakistan were all out for 708 at the Oval in 1987.]

  • Slog Unlimited on July 10, 2008, 16:49 GMT

    Seriously, I just read a comment in which someone said that in that 952/6 by SL, Jayasuriya went all over the park to eclipse Lara! Man, that's impossible! Lara's 400* knock was after Jayasuriya's, which means Lara actually eclipsed Jayasuriya! Learn simple cricket history, then talk Statistics!

    [Response: Lara did hold the world record at the time, with his 375.]

  • Ron on October 19, 2008, 10:17 GMT

    Interesting bit of analysis. However, it is not enough to look at the expected value of the extrapolated score. What is the variance? My guess is that it'd be fairly high.

  • Alex on August 10, 2008, 11:49 GMT

    PS to my earlier comment: earlier commenters were even more confused than I thought (even managed to confuse me too). Jayasuriya's innings in the big total against India was only 340, nowhere near a record. The 374 by Jayawardene was after Haydn's 380 AND after Lara's 400*.

  • Alex on August 10, 2008, 11:39 GMT

    Re Jayawardene "eclipsing" Lara. According to Cricinfo's best batting performances, he only made 374, so he certainly did not eclipse Lara. That feat was achieved by Matthew Hayden with his 380 against Zimbabwe. Of course, as you mentioned in your response to Slog Unlimited, Lara later regained the record with his 400 not out.

  • santhosh kudva on August 2, 2008, 16:56 GMT

    ... i think one more factor needs to be considered in this analysis. the team composition. a team like australia is likely to amass more runs for the last five wickets than the west indies team would during its entire innings...or better still give a teamwise breakup...

  • Ananth on July 12, 2008, 0:50 GMT

    Charles, an excellent analysis. I know a few people have already commented on this. I personally think the most dominating innings of all time is West Indies 790 for 3 because Sobers and Walcott were still batting and they still had two batsmen yet to come. Non-statistically, I am convinced that that would have been the only innings capable of reaching 1000. I had done a similar study on ODI innings and there the Australian total of 434 for 4 (a losing score) stood at the pinnacle.

  • Chris on July 11, 2008, 12:04 GMT

    To Azad Ahmad.. Do you think SL will score more than 952.. were Aus able to score thatmuch against the same bowling - NO!. And i find this record quite selfish, if it were the Australians... they would have forced the second innings by declaring at 700 odd.

  • Abhay Goyal on July 11, 2008, 8:15 GMT

    I believe you may be right till some extent but I beleive there is a certain patience of a batsman playing in the middle. In these days,its very difficult for batsmen to play a long test like knock and stay in the middle for long hours. And see if each batsman scores over a 100 in the team then the score reaches somewhere near 1000 mark. Thats a very difficult mark and also one needs to be very bold not to go for declaring. Remember, Captain Dravid once declared Indian innings at a stage when tendulkar was at the crease on 194*. Wow, 952 was a very good score, Hats off to Srilanka. 790 runs scored by westindies was still far from the 1000 mark and it was clas of lara that more than 50% of the runs were his.

  • SRAM on July 10, 2008, 21:47 GMT

    Were the scores considered at the time of declaration or at the time of the last wicket to fall? For instance a 600/5 decl might have been a 300/4 when the 4th wicket fell. The fall of the 5th wicket might be just round the corner and one could consider the score to be 600/6.

    [Response: It cannot be predicted statistically whether a wicket is 'just around the corner'. There is no particular level of a partnership, once it is past 20 runs or so, where a fall of wicket suddenly becomes more or less likely.]

  • Amer - Canada on July 10, 2008, 18:31 GMT

    Charles, Interesting. I remember in 86/76 Pakistan posting a huge total vs England at the Oval. I think it was around 600+. I was expecting to see that innings here.

    [response: Pakistan were all out for 708 at the Oval in 1987.]

  • Slog Unlimited on July 10, 2008, 16:49 GMT

    Seriously, I just read a comment in which someone said that in that 952/6 by SL, Jayasuriya went all over the park to eclipse Lara! Man, that's impossible! Lara's 400* knock was after Jayasuriya's, which means Lara actually eclipsed Jayasuriya! Learn simple cricket history, then talk Statistics!

    [Response: Lara did hold the world record at the time, with his 375.]

  • Prabhu on July 10, 2008, 15:29 GMT

    This is a badly designed model. A better model to use might be some kind of survival analysis using weibull distribution or that sort.

    [Response: there was a survival analysis of sorts used in the iterative analysis mentioned at the end of the article.]

  • Jeff on July 10, 2008, 12:55 GMT

    What about the 1st Test of the 2001 Ashes? The Aussies were 495-5 with Martyn (great batsman) and Gilchrist (best no. 7 ever) well set. They then had Warne (best test no 8 ever?), Lee (great no. 9) and Gillespie (scorer of a test double ton) still to come.

    Against a 4 man England attack of Gough (quite good), Caddick (average), White & Giles (very ordinary) who must have been tired and demoralised?

    Surely this must rank as one of the highest scoring innings ever…?

    Oh, what’s that you say? They collapsed to 576 all out? And mark Butcher took 4 wkts?

    I don’t believe it. The great Aussie side of 2001 would never have done that. Please can you rewrite the statistics to show what I think they should have got?

    What about SA at The Oval 2003? They were 345-2. And this was the team that scored 594-5 and 682-6 earlier in the series. Surely they would have gone on to score at least 700…? Don’t try and tell me they collapsed to 484 all out…

    (WARNING: this post contains irony)

    [Response: we naturally tend to remember the really extreme innings which go on and on, but forget the other innings with similar potential which don't.]

  • Bob the Builder on July 10, 2008, 11:26 GMT

    Interesting statistics. I was just wondering whether you considered the fall of wicket in these calculations. A 700/3, for example, could have actually been 400/3 and have carried on for a 300 run partnership, which could change the way the scores would have gone. Hope that makes sense ... nice work though

    [Response; there is surprisingly little difference between the future scoring potential of a partnership that stands at 50 runs and one that stands at 200 runs (involving recognised batsmen). This is one of those things that people have a hard time getting their heads around, but it also ties in to the finding that teams on 300 for 5 and 600 for 5 have similar scoring potentials.]

  • tintin on July 10, 2008, 9:18 GMT

    What distribution have you assumed for the predicted scores? I think you have assumed a normal distribution and this is probably not the case - do you have evidence for this? If not then I think your statistics are somewhat suspect

    [Response: I did not calculate a distribution, merely averages. The distributions appear normal to a first approximation.]

  • fouzan taha on July 10, 2008, 8:47 GMT

    i have remember india in several matchers they tried to drow instead of winning the match,they are not taking risk,and making boring whole world

  • Michael Jones on July 10, 2008, 8:03 GMT

    For the sake of argument, though, let's compare the 952/6 and 790/3 in terms of the averages of the remaining batsmen - this is still flawed, as it assumes that the number of runs that a batsman is likely to score after a given point is the same regardless of his score at that point. Nevertheless, let's try it:

    Sri Lanka: 952 + Kaluwitharana (26) + Vaas (24) + Pushpakumara (9) + Muralitharan (12) + Silva (2) = 1025

    West Indies: 790 + Sobers (58) + Walcott (57) + Smith (32) + Alexander (30) + Gibbs (7) + Atkinson (16) + Gilchrist (5) + Dewdney (2) = 997

    In both cases the answer is almost exactly the same as that given by Charles's method, so maybe there's something to be said for it after all!

  • Michael Jones on July 10, 2008, 7:28 GMT

    Yes, of course any analysis of this sort is "useless", since conducting it has no effect on matches already completed, and it can never be definitive because no statistical model can take account of all the factors involved - adding up the averages of the remaining batsmen might give a slightly more accurate answer, but doing so for every single innings in the list would take ages and people would still object on the grounds that there was no consideration taken of the bowling attack, pitch, match situation etc. The point is that it's still interesting to do the analysis, you just have to remember not to take it too seriously - no-one is saying that Sri Lanka would definitely have made more than any other team given the chance to bat on, only that, based on the average number of runs that a team adds after a particular score, it's probable that they would have.

    [Response: well said. The analysis is all this but nothing more, although you might be surprised that extending it into other areas can be fruitful, and that it is even possible to make money from it.]

  • Sorcerer on July 10, 2008, 6:56 GMT

    Travis

    Did Sobers also recount that he was caught behind on 342 but the umpire could not give him out without risking jeporady to his life and property in WI, as the batsman was still 23 short of a new world record?

    Plus Idon't think Bradman could have averaged over 70 in today's game given how scientific bowlers' regime and training has become. Just look at the way the bowlers in the 30s and 40s used to amble in and observe their chubby physiques - can you really compare majority of them to today's even Sidebottoms or Muralis?

  • Udit on July 10, 2008, 6:36 GMT

    Kudos to you Mr. Davis. I understand and agree with some of the counter points presented. However there are some limits to how far and how much you can utilize statistics and I believe you are doing quite well.

  • Rosh on July 10, 2008, 4:22 GMT

    I agree with Marcus in that Bradman would most definitely have averaged over 100 had he been playing today. Remember he most often had to play against Tait, Farnes, Larwood, Voce, Bowes, Verity, Bedser and co. - there simply aren't that good a line-up of bowlers today. Now had this question been for the late 70s and early 80s it most certainly would have been a case of an average around, I would say, 90 for the Don. Roberts, Holding, Garner, Marshall, Croft, Hadlee, Imran Khan, Kapil Dev, Willis, Underwood, Bedi, Chandra & Venkat(70s only) would have certainly brought his average down a little. This is of course assuming that Australia did meet Clive Lloyd's men quite often at that time.

  • pranavjh on July 9, 2008, 17:27 GMT

    Very interesting analysis indeed. I do think however that there are at least two other factors that must be considered -

    a) Number of overs - it gives an indication of the conditions as well as brings in the aspects of (how many) new balls being taken and evens out analysis a bit further.

    b) Size of the ground - this adds to the fatigue factor of the players (both teams). Additionally, scoring 900 on a 75m boundry ground is easier than scoring 750 on an 85m boundry ground.

    [Response: the size of ground is a factor that is interesting but is hard to study because actual figures for ground size are hard to come by, except for Austrlia and England.]

  • Navin on July 9, 2008, 16:44 GMT

    The matches are played to win. Indians in that match I think declared for 537 in order to put pressure on Lankans. But at the start of the fifth day the Lankans went on the field only for records. Jayasurya trying to eclipse Lara and so on. As I am Indian I can give their examples. Lords 1990 Gooch declared 653/4 to win the match, which he did. India declared at 600/4 in Sydney 1985-86. India again declaring at 633/5(or6) in Kolkata against Aussies 1997-98.(All the top six getting past 50) India won that match. Indian declaring at 705-7 against Aussies at Sydney 2003-04(one stage 650-5). India against Pakistan at Multan 675-5 (Sachin notout 194). Some matches were won some were drawn. But the objective was to win those matches but in Srilanka-India match there was no intention to win that match for Lankans. So they might have finished on 1028 or 1528. It did not matter as with more time they would have tried to break more batting records.

  • Vasu on July 9, 2008, 15:07 GMT

    Given the fact that some of the Pakistani bowlers were injured, the probability that the WI innings would have gone beyond 996 is pretty high. WOnder if the model takes into account the condition of the bowlers etc.

  • John Clifford on July 9, 2008, 11:17 GMT

    I note with interest that the projected score of 1028 is still well short of Victoria's 1107 in 1926/7 - still the highest first class score. As a proud and passionate Victorian I just thought I should mention it !!!!

  • Marcus on July 9, 2008, 9:15 GMT

    I'd like to second Priyankara's suggestion for some sort of comparison regarding batsmen of different eras, which is something I'd find very interesting. I remember you doing a similar analysis for bowlers of different eras in the Australian Wisden a while ago, so I'm sure it's possible. However, unlike Priyankara, I'm positive that Bradman would still end up on top- if he batted on today's flat pitches against today's weak attacks then he'd surely average more than 99.94.

  • Swati Kulkarni on July 9, 2008, 7:57 GMT

    Tushar had made a very valid comment above - especially about the current state of the partnership and batting average of the batsmen yet to get out. Would like to hear the author's opinion on this.

  • samarth on July 8, 2008, 21:22 GMT

    This is the beauty of statistics, it makes even the dullest minds start to think on different possibilities. Mr. Davis, you have done a fine job. please do some more extrapolations in future. I would like to second monkeyfuel's opinion of Duckworth/lewis system and powerplays. pleaase have a look at that.

  • offcutter on July 8, 2008, 20:06 GMT

    I am not sure what Mr Davis is trying to get at. Extrapolations without a whole host of indegenous and exogenous elements can lead to many conclusions and most records may debated.

  • Priyankara Nanayakkara on July 8, 2008, 19:57 GMT

    Sir, - In the same manner can you analyse the statistics of Donald Bradman against all test playing nations in present day and with modern technology whehter he can be classed as the best batsman of all time when comparing with modern day grears like Sachin , Sanath, Gilchrist etc. It is my opinion that Sir Donald is NOT the greaset had he played cricket in present times and we are not doing justice to present heroes of cricket if we do not come to conclusion and the only way is the same way as it is done " Extapolating high scoring cricket" Please analys and show us/Thanking you - Priyankara Nanayakkara

  • Travis on July 8, 2008, 17:45 GMT

    In the book "Garfield Sobers Most Memorable Matches" Sobers recalled how Conrad Hunte, who scored 260 in that innings, had been keeping track of the then record second wicket partnership of 451 and got himself run out going for a stupid single in an attempt to break the record.

    If it wasn't for that the West Indians would still be batting.

  • frank davis on July 8, 2008, 17:43 GMT

    Given that Sobers and Walcott were not out 365 and 88 respectively, chances are one of them may well have fallen soon and so i'd say that a further 200 runs was probably about par...

    Although if you read the account of the game, Pakistan only had 2 fit bowlers in the side, both of whom had bowled a lot of overs. For example Sobers 365th run came of Hanif Mohammed who took one test wicket in his whole career. It just makes you wonder how many Sobers may have finished with, especially as when he reached 365 the crowd poured onto field in celebration and cutailed play for that day. Would he have beaten Lara to 400?

    Frank

  • Anand on July 8, 2008, 11:57 GMT

    Hi Charles:

    Just out of cuiosity Why werent the following scores projected? India 675-5 vs Pakistan at Multan (Sachin was still at the crease on 194) and Pakistan's 581-3 vs India at Hyderabad (Miandad was on 280*)?

    [Response: they are both on the list.]

  • Vikram Maingi on July 8, 2008, 11:04 GMT

    It seems Charles Davis is taking only a couple of factors (runs scored and wickets lost) into consideration for extrpolating the scores. I think these 2 factors are too few to extrapolate the final scores. When the morale of the fielding team is so down, even the tail-enders make merry.

  • Vikram Maingi on July 8, 2008, 11:04 GMT

    It seems Charles Davis is taking only a couple of factors (runs scored and wickets lost) into consideration for extrpolating the scores. I think these 2 factors are too few to extrapolate the final scores. When the morale of the fielding team is so down, even the tail-enders make merry.

  • monkey fuel on July 8, 2008, 11:04 GMT

    Nice troll Mr Davis! The average cricket fan has no grasp of the theoretical statistics that you allude to using, and is bound to post stuff like "OMG how can any team only make 200 for their last 7 wickets!!!1!". You've hit on a sure fire way of getting them all riled up. Your analysis is interesting, but I have some doubts that the amount of data you have to work with is enough that we can take the results with anything other than a large pinch of salt. How about addressing a usefult topic: like how you would adapt the Duckworth Lewis system to take power plays into account? That's a long overdue change in my humble opinion.

  • Sorcerer on July 8, 2008, 6:31 GMT

    I doubt if the SL world record against India of 952 runs can ever be surpassed, but for a match involving the hard-hitting Aussie batting line-up on an Aussie pitch against Bangladesh.

  • Rukicee on July 8, 2008, 0:57 GMT

    India scored 537 and batted 2 whole days on a dead flat track. It was best that SL went for the record as there was no way any team could have won. Also Sanath was on fire and almost beat Lara's record at the time. Good luck to any team passing this score now. Lanka Rocks!

  • Anjo on July 7, 2008, 23:13 GMT

    Regardless of its relevance or consequence to cricket, I must admit I am intrigued by the extrapolation. I am going to assume that you trained your model on a set of data and then attempted to extrapolate based on the training weights, but my big question is whether you had sufficient data for accurate training, particularly for the really high scores. The trends for the lower order are quite interesting; does this or a similar pattern emerge for all first class matches? One big advantage of incorporating first-class matches is you will have a huge base for training. You could then compare and perhaps find weights which mark the transition to Tests or just extrapolate for all first class. But I don't know, maybe you've done all this, but I would certainly welcome the chance to discuss the methodology employed. Only if you're willing and interested of course, the last time I tried discussing methodology with a blogger on It Figures, I was told not to impinge on Intellectual Property!

  • leartiste2001 on July 7, 2008, 21:37 GMT

    I think Sri Lanka would have made more than the projected 1028. They were on fire at this stage, and they did it against quite a good opponent (India). How many of these records resulted in wins? I always wonder why do teams bat for records instead of going for a team win? Wouldn't it be better to have a low scoring win than a huge scoring (boring) draw?

  • Beburg Zehri on July 7, 2008, 21:22 GMT

    Good attempt. Most projected scores do make sense while some simply don't. In your formula, you have underestimated the lower order and tail. A slight improvement/research there might produce better projected scores.

  • sashi on July 7, 2008, 18:40 GMT

    once again statistics shows its shortcomings! the people who saw the sri lankan innings against india would surely say that it would have been impossible for them to get beyond 1000! and a west indian team at its peak and losing just 3 wickets for 700 odd runs can surely go beyond 1200 as even the tailenders then were good hitters of the leather ball. but as we all know the beauty of cricket is its unpredictability and test cricket, more so! :)

  • Sorcerer on July 7, 2008, 18:11 GMT

    There is no doubt Sri Lanka's demolition of India - 952/6 was always going to take the top spot. I just wonder how SL's 713/3 against Zim would have added just 200 more given that they were being scored against an extremely weak bowling attack. Anyhow, good job done by charles.

  • Ryan on July 7, 2008, 17:07 GMT

    There is always one! Nanagaswaami, you are that one. My club captain is the greatest...! Followed by My high school coach.

    Enjoyed the article Charles, tough assignment though I suppose with the lack of data at the higher end of the scores but interesting none the less. I wonder, does the Duckworth/Lewis calculations work on a similar theory? And would the record for highest ODI innings' be surpassed if 2nd innings wins were taken into account. I'm thinking of along the lines of the match involving Brendan McCullum's assault on Bangladesh in their recent ODI series at home and the like.

    Keep up the good work.

    Ryan

  • Amar on July 7, 2008, 14:32 GMT

    sri lanka scoring 952/6 also at one stage were 790/3. so it doesnt mean that west indies who were 790/3 would have necessarily crossed the score of 952

  • Jeff on July 7, 2008, 13:55 GMT

    Great insight on the number of runs added at diff scores when 5 wickets down.

    Contrary to some of the other posters, it makes perfect sense to me.

    How often have you seen a team in trouble at 50-5 stage a fightback and get themselves up to a reasonable score?

    About as often as you see a team cruising along at 500-5 and then collapsing to 600 all out as the lower order get carried away.

    And in response to "anonymous" regarding his doubting that the Windies of 1958 might have lost their last 7 wkts for 200 runs, this is the batting they had left in that inns:

    O Smith (career ave 31.7), F Alexander (30.0), L Gibbs (7.0), E Atkinson (15.8), R Gilchrist (5.5), D Dewdney (2.4)

    Hardly the most formidable lower order in test history (combined ave for all 6 = 92)

    Given that Sobers and Walcott were not out 365 and 88 respectively, chances are one of them may well have fallen soon and so i'd say that a further 200 runs was probably about par...

  • Tushar Kardile on July 7, 2008, 12:58 GMT

    IMHO, the model is flawed. Not only that but it does not consider some vital aspects of batting composition of a team and state of the innings. e.g.

    1. How many batsmen the team is playing with.

    2. What is the score of the unbeaten batters? e.g. first 3 men out on 200 each and no 4 and 5 just in is different from the first 3 out on 100 each and no 4 and 5 batting on 150 each. In later case, wicket no 4 and 5 are likely to fall much earlier than in earlier scenario.

    3. Batting average of batsmen yet to bat and that of the ones that are out. e.g. SL's no 7 was Kalu. Had it been more prolific no 7 like Gilly, the projected score would be different.

    Also, generally tailenders do not add much even after a huge score by top half, because they are not interested in adding many runs, but are interested in adding quick runs and get the opposition in. If they know they have eternity to bat until, they will more likely than not hang on and score 25-30% of what top guys scored.

  • Azad Ahmad on July 7, 2008, 12:38 GMT

    That record of 952 could yet be broken on indian near future tour of Srilanka given Indian recent absolutely useless Bowling.

  • nanagaswaami on July 7, 2008, 10:36 GMT

    wasim akram is the greatest by the way..exquisite article thou.....

  • saurabh somani on July 7, 2008, 4:52 GMT

    interesting analysis... however, from what ive understood you have treated all the teams equally in your analysis. i.e. if a team were 500/3 this would project to the same score no matter which team is batting - it could be the present australian or west indian teams, or it could be the zimbabwean team or whoever. somehow this doesn't seem right. shouldn't individual players' career performances count for something? in other words, if today's australia were at 500/3 i would back them to get a lot more than if today's west indies were at 500/3.

    [Response: you are correct, it is a straightforward analysis without the extra sophisticiation you mention, which would be very difficult because it would reduce the statistical sample size greatly. There might be some effect, but I think any team on 500 for 3 can be described as being dominant at least on the day; Zimbabwe, incidentally have never been there.]

  • David Barry on July 7, 2008, 4:09 GMT

    Akshay Dave: the unbroken seventh wicket partnership for Sri Lanka in their 6dec/952 was worth 31 runs, and was made in 36 minutes. Granted, there were several extras, but it was hardly a snail's pace.

    Because of Mahanama's slow scoring (a strike rate of 40 in an innings of 225), Sri Lanka actually improved their run rate after the 576-run partnership. Roughly 3.2/over while Jayasuriya was in, 4.3 afterwards.

  • Salmon on July 7, 2008, 3:02 GMT

    Quite an interesting analysis, with projected scores being less than what many people might think. I disagree with Jaytara - this is not meaningless, although admittedly it is hypothetical. The reality of course is that we will never know the answer to this question. Keep up the great work Charles.

  • Nauman on July 7, 2008, 2:35 GMT

    The beauty of cricket is that its unpredictable. To put bounds on what could be achieved on the field with the numbers that a computer can crunch is, to say the least, absolutely ridiculous. An innings of 700 for 3 would fold to 906, you can create a statistical model and justify it but its highly unacceptable to common man. At 700 for 3, you have lost only half of your top batsman. You looking at 3 more top-class batsman plus a wicket keeper and a couple of low-order all-rounders in the change room waiting to give the ball some spanking, I don't see how you lose your last 7 wickets for just 200 odd runs. More realistic would be that you add at least 350 runs to that 700 for 3. Statistical result start to sound even more unreasonable when you put into consideration that 700 for 3 could only be achieved against a pathetic bowling line up and an absolutely unresponsive pitch. How such combination can simply turn the tide is simply unheard of.

    [Response: I agree it sounds counterintuitive, and it can't be proven one way or another for teams on 700 for 3 because there are so few examples. However, as I pointed out, you would expect similar from teams that are 500 for 3; there are enough cases for analysis here and, and it can be shown that often they don't do as well as we might expect.]

  • Akshay Dave on July 7, 2008, 1:26 GMT

    While I do like the idea of extrapolating test innings, I am still not quite satisfied with the analysis. For eg. anyone who witnessed the Sri Lanka vs India game (whether on TV or live) will remember that the last hour (or two) of that innings produced barely any runs. In fact, Sri Lanka could have gone on for a full ninety over and barely made another 20 or 30 runs. In comparison, an innings that was going at a faster pace (and thus had more momentum) would easily end up farther than that.

  • Jaytara on July 6, 2008, 23:40 GMT

    Most cricket-lovers, including me, revel in statistics, but this is a meaningless exercise--- Charles Davis could have used his considerable talents in coming up with something more relevant.

  • Jonathan on July 6, 2008, 18:51 GMT

    West Indies v England at Antigua in 2004 was 751 for 5, not 751 for 4. Don't know if that's a misprint or what.

    [response: yes it is a typo, sorry]

  • Anonymous on July 6, 2008, 17:20 GMT

    personally i find it highly unlikely that any team - particularly the West Indies of old - would only add 200 runs for the loss of their last seven wickets.

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  • Anonymous on July 6, 2008, 17:20 GMT

    personally i find it highly unlikely that any team - particularly the West Indies of old - would only add 200 runs for the loss of their last seven wickets.

  • Jonathan on July 6, 2008, 18:51 GMT

    West Indies v England at Antigua in 2004 was 751 for 5, not 751 for 4. Don't know if that's a misprint or what.

    [response: yes it is a typo, sorry]

  • Jaytara on July 6, 2008, 23:40 GMT

    Most cricket-lovers, including me, revel in statistics, but this is a meaningless exercise--- Charles Davis could have used his considerable talents in coming up with something more relevant.

  • Akshay Dave on July 7, 2008, 1:26 GMT

    While I do like the idea of extrapolating test innings, I am still not quite satisfied with the analysis. For eg. anyone who witnessed the Sri Lanka vs India game (whether on TV or live) will remember that the last hour (or two) of that innings produced barely any runs. In fact, Sri Lanka could have gone on for a full ninety over and barely made another 20 or 30 runs. In comparison, an innings that was going at a faster pace (and thus had more momentum) would easily end up farther than that.

  • Nauman on July 7, 2008, 2:35 GMT

    The beauty of cricket is that its unpredictable. To put bounds on what could be achieved on the field with the numbers that a computer can crunch is, to say the least, absolutely ridiculous. An innings of 700 for 3 would fold to 906, you can create a statistical model and justify it but its highly unacceptable to common man. At 700 for 3, you have lost only half of your top batsman. You looking at 3 more top-class batsman plus a wicket keeper and a couple of low-order all-rounders in the change room waiting to give the ball some spanking, I don't see how you lose your last 7 wickets for just 200 odd runs. More realistic would be that you add at least 350 runs to that 700 for 3. Statistical result start to sound even more unreasonable when you put into consideration that 700 for 3 could only be achieved against a pathetic bowling line up and an absolutely unresponsive pitch. How such combination can simply turn the tide is simply unheard of.

    [Response: I agree it sounds counterintuitive, and it can't be proven one way or another for teams on 700 for 3 because there are so few examples. However, as I pointed out, you would expect similar from teams that are 500 for 3; there are enough cases for analysis here and, and it can be shown that often they don't do as well as we might expect.]

  • Salmon on July 7, 2008, 3:02 GMT

    Quite an interesting analysis, with projected scores being less than what many people might think. I disagree with Jaytara - this is not meaningless, although admittedly it is hypothetical. The reality of course is that we will never know the answer to this question. Keep up the great work Charles.

  • David Barry on July 7, 2008, 4:09 GMT

    Akshay Dave: the unbroken seventh wicket partnership for Sri Lanka in their 6dec/952 was worth 31 runs, and was made in 36 minutes. Granted, there were several extras, but it was hardly a snail's pace.

    Because of Mahanama's slow scoring (a strike rate of 40 in an innings of 225), Sri Lanka actually improved their run rate after the 576-run partnership. Roughly 3.2/over while Jayasuriya was in, 4.3 afterwards.

  • saurabh somani on July 7, 2008, 4:52 GMT

    interesting analysis... however, from what ive understood you have treated all the teams equally in your analysis. i.e. if a team were 500/3 this would project to the same score no matter which team is batting - it could be the present australian or west indian teams, or it could be the zimbabwean team or whoever. somehow this doesn't seem right. shouldn't individual players' career performances count for something? in other words, if today's australia were at 500/3 i would back them to get a lot more than if today's west indies were at 500/3.

    [Response: you are correct, it is a straightforward analysis without the extra sophisticiation you mention, which would be very difficult because it would reduce the statistical sample size greatly. There might be some effect, but I think any team on 500 for 3 can be described as being dominant at least on the day; Zimbabwe, incidentally have never been there.]

  • nanagaswaami on July 7, 2008, 10:36 GMT

    wasim akram is the greatest by the way..exquisite article thou.....

  • Azad Ahmad on July 7, 2008, 12:38 GMT

    That record of 952 could yet be broken on indian near future tour of Srilanka given Indian recent absolutely useless Bowling.