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22 July 2008 COMPARING THE RECORD
TEAM SCORES By Charles Davis 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 depends also 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 #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 790/3 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.] |
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17 June 2008 Gibbs Update (see also 30
May 2007 and 7 July 2007) Back from holidays,
where some more detail was found regards the unique 8 for 6 spell against
India by Lance Gibbs at Bridgetown in 1962. The Barbados Advocate gives some useful detail not available
elsewhere, including the times of each wicket, and in combination with other
sources, an over by over sequence of sorts is possible. One complication is
that some sources, including Wisden,
give the length of the spell as 15.3 overs with 14 maidens. The Advocate, and one or two other sources,
say 16.3 overs with 14 maidens, and on close inspection, this appears to be
correct. The following
reconstruction distills various sources, but is based on the Advocate account, starting with Gibbs
being brought on for Worrell just before 2 o’clock. Prior to this spell,
Gibbs had bowled 37 overs without success. The overs in Gibbs’ spell are
numbered. The overs at the other end, mostly bowled by Solomon, are given in
italics. Note that there was no new ball taken in an innings that lasted
185.3 overs. When Gibbs was brought back on, there had been no wicket for
close to 100 overs, and the partnership between Sardesai and Manjrekar had
produced just 98 runs. The score, 149/2 off 142 overs at lunch, was now 158/2
off 153 overs. 1.
Wicket
maiden (Sardesai, 60 in 392 mins) 2:00pm Solomon, maiden 2.
One run
to Umrigar. Solomon, maiden 3.
Double
wicket maiden (Manjrekar 51 in 259 minutes, Pataudi 0, 2nd ball).
2:11 Solomon, maiden. India now 159 off 159 overs. 4.
To 10.
Seven overs with six maidens, and one over for 5 runs. Solomon bowled at
the other end, conceding 10 runs. For 25 mins, Borde faced Gibbs and Umrigar
faced Solomon. 11. Wicket maiden (Umrigar, 10 with 1x4) 2:45,
Borde 6 not out. Solomon, maiden 12. Maiden Solomon, conceding two runs from Borde plus a bye 13.
Double Wicket maiden (Borde, 8 with 1x4, Engineer 0, 2nd ball)
3:00 Solomon, boundary by Durani, plus two singles (Durani, Nadkarni) 14.
Wicket maiden (Durani, 5 with 1x4) 3:07. Gibbs spell at this point is
14-12-6-7 Solomon, maiden 15. Maiden. At this point India had scored 183 runs in 182 overs. Solomon’s last over, with a
single to Nadkarni, single to Desai and 2 leg byes. Solomon’s spell:
21 overs for 24 runs, no wickets. 16.
Maiden Sobers on, maiden 17.
Desai (1) out off third ball. 3:22pm All out
for 187 off 185.3 overs in 474 minutes. This
sequence confirms that Gibbs took his last 5 wickets without conceding a run.
Oddly enough, none of the sources mention this, though they mention his 3 for
1 spell earlier. It may have escaped notice because it was stretched over a
period of 12 overs during which runs were scored at the other end. |
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For
comments, or to contact Z-score (Charles Davis) email statz334 at iprimus dot com dot
au (The address is like this to avoid
SPAM. Type the address in the usual format) |
12 May 2008 The
website/blog
Cricket Buzz has produced a list of “50 Best
Cricket Blogs”, and included this site on the list. So there is a compliment.
Thanks, guys. Actually, I didn’t know there were 50 cricket blogs, best or
otherwise, but with millions of people blogging, I suppose it is not
surprising. So Near but So Far (Written for Cricinfo) When Virender Sehwag strode to the Chennai wicket on the fourth day of the recent Test against South Africa, 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, say that 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 have been dismissed. 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 that batsmen encounter above 300 can also be seen when we look more closely, at 20-run increments
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