Z-score’s Cricket Stats Blog May 2007 –Mar 2008
3 March 2008
Hanging in There
It is well known that some batsmen are better than others when it comes to going on to very big scores after getting a start. The differences between individuals can be surprising; for an extreme recent example look at two of today’s top opening batsmen, Matthew Hayden and Virender Sehwag. A comparison of the last 10 Tests centuries for each batsman shows a remarkable contrast.
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; better for now 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
Average Size of all scores over 100
Minimum 10 Test Centuries
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.
Highest Century Averages (batting average of runs beyond the century mark)
Minimum 10 Test Centuries
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.
The Lowest Century Averages (batting average of runs beyond the century mark)
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. Yes, it is a funny game, this cricket.
Finally, here is a similar list for “Half-Century Average”, the batsmen most likely to go on to big scores after reaching 50.
Highest Half-Century Averages (batting average of runs beyond a score of 50)
Minimum 20 Test Half-Centuries
24 January 2008
What are the fastest and slowest Test innings of all time?
A simple question like this is actually tricky, thanks to the extreme range of possible scores. Comparing innings large and small, based on scoring speed alone, is unsatisfactory. For instance, Adam Gilchrist’s 102 off 59 balls in 2006 was considerably faster that Nathan Astle’s 222 off 168 balls in 2002; both were freakish innings, but which was the more remarkable?
One way to answer this is by measuring how far each innings deviates from normal innings of similar size. To do this, we take every innings of a given size and 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 at Adelaide in 1980. This is 1.75 standard deviations faster than the average, so the innings gets a z-score of -1.75. Likewise, the slowest innings of 76 was 315 balls by Glenn Turner in 1971, with a z-score of +3.2.
To compare many innings of different sizes, the process must be repeated for all possible scores. This process gives big innings a better rating than smaller innings of a similar speed, because it is more difficult to score rapidly for longer periods.
So which innings have the most extreme z-scores? At fast end of the scale, the results look like this:
The most Extreme Fast Innings
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 a further back in time.
The most Extreme Slow Innings
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. Hanif, at modern over rates, would take more than five hours for his 20 runs, while Alec Bannerman’s 91 would probably take more than two full days in the modern game. 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 at 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 a very large number of innings with data available. 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.]
20 December 2007
From now on, some of my material will be appearing on the Cricinfo website under the It Figures blog. You can leave comments there. Here is my first contribution to that blog…
Some of the more intriguing Test records cannot be found by looking at traditional scorecards. Hat-tricks are a prime example, but there are endless possibilities. I recently came across a case, at the Oval in 1886, of WG Grace scoring 60 runs while his batting partner, W Scotton, remained scoreless, stuck on 21. I wondered, what is the greatest number of runs scored while one batsman remained scoreless? I knew of one example greater than Grace. In his legendary 232 at Trent Bridge in 1938, Stan McCabe scored the last 66 runs of the Australian innings, while batting with Chuck Fleetwood-Smith.
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.
Monopolising the Scoring in Tests (since 1999)
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.
UPDATE: Another Gilchrist special, at Edgbaston 2001, has been found (by Dean) and is now listed in the table. One historical case, Kris Srikkanth at the SCG 1985/86, has also come to light (thanks SBI). Srikkanth added 51 runs while Gavaskar was on 27; to top it off, Srikkanth was batting with a runner.
30 November 2007
The stats blog at Cricinfo has an item by Ananth Narayanan on a new way to calculate batting averages. It is only of minor interest, since it adjusts traditional averages by less than 2%, and therefore tells us very little that is new about the top players.
However, there is a question arising. The method uses a player’s previous ten innings as a guide to the likely outcome of a not out innings. The phrases “reasonable to expect” and “fair to assume” are used, which means it hasn’t actually been proved that this is useful. So what is better at predicting a player’s next innings, his last ten innings or his career average?
Well, it is the latter, if you compare apples with apples. I have looked at the complete careers of all players with 80 or more innings, and found that a player’s career average comes slightly closer to predicting the score than his average over his previous ten innings. More importantly, there is more ‘scatter’ in the results using just the last ten. The standard deviation using career average as a predictor is 37.7, but using the last ten it is 41.0.
This implies that recent form is not an especially good guide to a player’s next innings.
The method also has a curious twist: it does not allow scores above a player’s previous top score to be predicted. This seems to imply that a player who has never scored a century never will score one.
There is an interesting counter-example. In his first 28 Test innings, Garfield Sobers had a top score of 80 and an average of 34. He then scored 365 not out in his next innings, and his next ten innings scored six centuries, with an average of 185.8. However, in the following seven innings after this purple patch he failed to reach 50.
Well maybe it is a little unfair to cite a single extreme example, but the issue of form or momentum in sports is an interesting one that tends to fail under the statistical blowtorch. I have seen this in golf stats, and others have looked at sports like basketball, and the same finding arises: in the long run, a player’s overall ability is a better guide to future performance than his recent results. With hindsight, there is some ‘momentum’ in the Sobers case, but really, the sequence of scores offered little hint that the purple patch was about to begin; perhaps more importantly, nor did the scores foretell when it would end.
Incidentally, that average of 185.8 over ten innings by Sobers is the highest by any player, although Kallis and Tillakaratne have come close, thanks to clusters of unbeaten innings. Bradman’s best was 154.5.
UPDATE 1: within a week of my writing that last paragraph, Kumar Sangakkara has surpassed Sobers by scoring 1185 at 197.5 in his last 10 innings. His 92 and 152 vs England makes him the first player to score 150s in four consecutive Tests, and the first to exceed 200 runs in a match in four consecutive tests.
It is remarkable, though, that in total number of runs even Sangakkara is almost 200 short of Bradman’s best of 1370 runs in 10 innings in 1930.
UPDATE 2: A very interesting take on this question from David Barry.
26 November 2007
There are some comments about Shane Warne’s Test career in the “Longer Articles” section. These were written for a book “On Ya Warnie” by Ken Piesse. If you can get by the book’s hideous cover, it is an entertaining read, and avoids too much hero-worship. The stats were written in September.
20 November 2007
Against Australia, Sri Lanka averaged 29 with the bat and 118 with the ball. With a difference of 89 runs per wicket, this makes it the most one-sided Test series in history (if you ignore some of Bangladesh’s efforts). Apart from part-timer Sanath Jayasuriya, no Sri Lankan bowler finished the series with an average of better than 100. That’s a far cry from their previous experience against Bangladesh in July, when every bowler averaged better than 30, and Murali took 26 wickets in three Tests at 10.8. In that series, Sri Lanka average 95 runs per wicket to Bangladesh’s 17, a record difference for any three-Test series. The Sri Lankans were probably poorly served by that series.
It was a relief, in such a train wreck of a series, to see some class emerge from the bat of Kumar Sangakkara. Sangakkara had scored unbeaten double centuries in his previous two innings, but coming as they did against Bangladesh, they will be come to be counted for much less than his 192 at Bellerive. With his 57 in the first innings, KS has now scored 200 or more runs in three consecutive Tests, a feat that eluded Bradman, and achieved previously only by Wally Hammond in 1928/29. With consecutive scores of 200*, 222* and 57, Sangakkara just missed out on Sachin Tendulkar’s record of 497 runs between dismissals in Tests, registering 479. He has scored 1285 runs at 128.5 in his last eight Tests, with a top score of 287 and five scores over 150.
After 130 years of Test cricket, you don’t often see a one-ball innings that is unique, but Dilhara Fernando managed it at Bellerive. Never before in a Test has a batsman been out first ball for two runs. There have been two batsmen run out first ball for one run; Geoff Arnold at the WACA in 1974, and Nixon Mclean at Port Elizabeth in 1998. Dougie Walters (who ran out Arnold) was once run out first ball for two in a Sheffield Shield match, but that was probably the only such occurrence in Australian first-class cricket.
UPDATE: interesting to see, just after the above was written, Sachin Tendulkar run out for one off one ball against Pakistan. However, Tendulkar, as in a number of other similar instances, was not run out off the same ball he faced.
Mike Hussey continues his freakish career. He now has almost 2000 runs at an average of 86. Bradman did better over his first 2000, but no other batsman in history comes close. Watching Hussey at Bellerive, the was a feeling of inevitability about his century, perhaps the same impression that Bradman so often created. The odd thing, though, about Hussey’s extraordinary Test career is a lack of giant scores, even though he has several triple-centuries to his name in lesser cricket. If he starts bringing those sort of scores to Test matches, watch out bowlers.
Phil Jaques will be thrilled to establish himself, but you have to wonder about the standard of bowling in Test cricket these days (apart from the Aussies, of course). One thing that Jaques has in common with Hayden, Hussey, Clarke and Gilchrist is that they all have better averages in Tests than in Pura Cup/Sheffield Shield cricket. In Hussey’s case, his Test average is more than double his domestic first-class average. When so many players have better performances at the top level than at the next level down, something must be topsy-turvy.
Australia, by scoring 4/551, 5/542 and 2/210 is the first team to average over 100 runs per wicket in all innings of a series. The only other team to average over 100 for three consecutive innings was India in 2003/04, when they scored 7/705 and 2/211 against Australia in Sydney in 2003/04, and then 6/675 against Pakistan a couple of months later.
Rhett Lockyear is the first substitute in a Test match to be credited with two run outs in one match. And this from a player not even on Tasmania’s contract list.
13 November 2007
The First Double-Century Partnership?
When trawling through the detailed records of the very early Test matches, one thing does become clear: things were not always exactly what they seemed. Only a few of the first Tests are represented by surviving complete scorebooks (five out of the first 17 matches). The scores of the others, now accepted as “official” scores, were in fact originally drawn from published sources including newspapers.
The trouble is that these sources do not always agree. Usually, the discrepancies are trivial, but occasionally they might have some minor importance. A case in point is the third Test of the 1881/82 series, the seventh Test match played. In Australia’s first innings, Percy McDonnell scored 147 and Alick Bannerman 70; their partnership for the fourth wicket of 199 was the highest in Tests up to that time. But now there is some doubt about the exact number of runs.
There is some confusion in the reports of this match. McDonnell’s score is variously given as 145, 146 and 147, extras 14 or 16, and Australia’s total as 260 or 262. However, as it happens, the reports in the Sydney Morning Herald and other sources are so detailed that the innings can be reconstructed stroke-by-stroke, or over-by-over (but not quite ball-by-ball). Every over and every scoring stroke, including sundries, can be accounted for by combining the Herald and Daily Telegraph reports.
The discrepancy that arises boils down to a single ball in the 129th over, a dropped catch by Barlow off McDonnell from the bowling of Midwinter, when the score was 200 and McDonnell 116. It either went for two runs or four runs; the sources vary. If it is the latter, as seems likely, then McDonnell’s score of 147 and Australia’s 262 stand. However, if so, the fall of the fourth wicket must be adjusted from 215 to 217: the partnership becomes 201 runs, and therefore takes its place ahead of the 207 by Scott and Murdoch in 1884 as the first Test partnership over 200 runs.
Looking at it closely, it may be that confusion arose because the score was altered retrospectively, perhaps in consultation with the umpires. While the scores of McDonnell and Australia were corrected, the fall of wicket was not.
The only viable alternative is that McDonnell scored 145, Australia 260, and Midwinter took 2 for 73. Fortunately, Australia eventually won the match by six wickets by hitting a boundary that gave them enough runs to win in either case.
The corrected falls of wicket are 4/217 (not 215), 5/230 (not 228), 6/237 (not 235), 7/246 (not 244), 8/248 (not 245), 9/255 (not 252), and 10/262.
(Incidentally, the analysis in either case requires that the batsmen, not out overnight, went to the wrong ends when play started on the third day. I wonder how often this has happened.)
The re-scoring of this innings means that over-by-over, or ball-by-ball, accounts have been completed for all of the first 17 Test matches up to late 1884. Two or three of these Tests were analysed by John Kobylecky, the others by myself.
Unfortunately, extending this analysis forward in time will be very problematic for some Tests. From 1884 on, the style of reporting in Australian newspapers changed, with far more interpretation applied by the commentators and less narrative reporting. It is only possible to re-score from newspaper accounts in a few cases of extreme scoring, such as Bonnor’s hectic 128 at the SCG in 1884/85 (at 90 minutes for the first 100, still the fastest century in an Australian Test).
The 1886 series in England is particularly wanting in detail. However, it is possible to come up with a framework for one extraordinary innings, WG Grace’s 170 at the Oval. His partnership of 170 with the professional Scotton, who scored only 34, remains the most lop-sided opening stand of its size in Tests. Scotton probably faced as many as 275 balls in his innings, and at one point remained stuck on 21 for about 75 balls (67 minutes), during which time Grace scored 60 runs (plus three sundries) with 10 boundaries.
Grace, for his part, scored 130 runs in 160 minutes after lunch, off about 195 balls. It is interesting that tea breaks were not taken in those days, so technically, Grace made these runs in a session of play, and it probably should be recorded among the records for must runs in a session, at least as a footnote. Grace finished with 170 off about 320 balls.
17 September 2007
The “Fastest-Scoring Batsmen in Tests” section has been updated. Note the entry of Mahendra Dhoni straight into the Top 10 now that he has his 1000 runs in Test cricket. There are some small changes for old-timers as well, as new information becomes available. However the estimate for Victor Trumper’s speed has not changed with the new data on balls faced for 1903/04.
3 September 2007
Compromise of the Anomalies
I have commented before on the problems that sometimes arise when original Test scorebooks are examined in detail. This can drain confidence in the accuracy of older records. Trustworthy alternative figures are elusive, so we may have to live with a bit of uncertainty.
One of the most problematic scores is of an important Test, the first of the 1903/04 series. It was a great six-day match containing two great innings, the 287 by Reg Foster (still the highest score on Test debut), and Victor Trumper’s famous reply, 185 not out in 230 minutes. As a curiosity, it was probably the first series that was explicitly contested for “The Ashes” as a regular contest, a concept promoted by Pelham Warner, the English captain. A scorebook for this Test survives in the MCC archives; I attempted to re-score this into modern form a few years ago , but encountered numerous anomalies. I have attempted this again, armed with better software and half a dozen detailed newspaper accounts from the time.
Even though a full re-score has now been achieved, the anomalies remain numerous. One important problem is that the batsmen’s strokes do not always add up to the total. Monty Noble scored 133, apparently, but his strokes add up to only 128, while Trumper’s innings adds up to 187 not 185. Foster’s score does add up to 287, but his last two listed strokes, for one and two, cannot be found in any of the bowler’s analyses. There has to be suspicion that these strokes were added afterwards to make it add up.
Trumper’s last two strokes are listed as a four and a two, but again, these are absent from the bowling analysis. In this case, one newspaper confirms Trumper’s last strokes as a four and a two off Arnold’s last over. Perhaps they were not included in the bowling analysis to make the bowling add up. We really don’t know. There are more than a dozen overs in Australia’s second innings where problems of this type arise, and a similar number in England’s first innings.
There are some issues with the order of some overs. In England’s first innings, a wicket listed in Howell’s 19th over must have actually been taken in his 18th. There are a number of such problems, probably because the scorer was using double rows for each bowler, putting an over in each row alternately, but sometimes inadvertently departing from this approach.
There are many other little problems, too many to list. I should say, though, that about 90% of the score is in good shape, so reasonable estimates of balls faced can be made, 490 in Foster’s case and 245 for Trumper. Trumper reached 100 off close to 100 balls in 94 minutes. Foster’s innings came in two distinct parts, scratching his way to 73 off about 200 balls on the second day, then soaring to 287 (213 off 290 balls) on the next; he scored his last 50 runs off 32 balls.
One indicator of the problems is conflict between published figures for runs conceded by the bowlers. The figures in Wisden follow the scorebook, but newspaper figures for England’s innings differ, as shown below:
Note that the figures in the Melbourne Age do not add up.
The re-score figures are a compromise among the anomalies. There are thousands of permutations of alterations possible, so it is likely that the best compromise has not been found. Although the problem data can be beaten into shape to reproduce the agreed batsmen’s scores and falls of wickets (using the written accounts as support), it does not, at this stage, exactly reproduce published bowling figures.
20 August 2007
More on the Most Remarkable Bowling Sequences
I reported on some unusually successful bowling spells (or sequences) in earlier posts. A few readers such as Sreeram pointed out other examples that had been missed, so I did some actual research and turned up some more. The results can be found here . This list will remain linked under “Unusual Records” at the top of the page.
So we now have five cases of sequences of 5/0, starting with Hugh Tayfield in 1953/54. I noted that Waqar Younis had completed his 5/0 in 13 balls (albeit against Bangladesh), so I set up an extra list of the fewest balls required to take five wickets (regardless of runs conceded). It is curious that no cases of five in fewer than 13 balls has been found, given that there are three cases of four wickets in five balls (Allom, Old, and Wasim Akram). Perhaps they exist, and other researchers can help.
The fastest that any bowler has reached 5 wickets from the start of his innings bowling, is the 19 balls for Ernie Toshack against India at the ’Gabba in 1947/48.
Naturally, most of these remarkable sequences involved tailend batsmen. A few did not; at some stage I will go through these and label them. One amazing sequence not on the list is SF Barnes 5/6 (including 4/1) at Melbourne in 1911/12, which started with the second over of the match on a good batting wicket.
Readers are welcome to add to these. Here is a list of sequences that could belong on the list (most probably do not), but which I do not have exact data for.
I hope to add more categories to the “Unusual Records” list, some from earlier blog posts.
3 August 2007
Here’s a piece I wrote recently for a magazine.
Head to Head: The Best (and Worst) Batsmen Against Australia’s Great Bowlers.
One of cricket’s attractions is the fact that while it remains a team sport, it is in essence also a series of one-on-one contests. On the subject of contests between individual batsmen and bowlers, commentators tend to offer impressions, because detailed statistics on how particular batsmen go against specific bowlers are often hard to come by.
In the afterglow of the great careers of Glenn McGrath and Shane Warne, It is worth investigating who performed best and worst against them. Some basic information is easy to find. We do know, from conventional Tests scores, how often each bowler dismissed each batsman, but not who actually scored the runs they conceded. For that, we need ball-by-ball information. In recent years, this has become available online.
This doesn’t extend back far enough to cover the whole careers of these bowlers, but we do have near-complete information since 1999. So, for more recent times, we can answer the question: who were the most effective batsmen against Warne and McGrath?
The batsmen with the best averages against Shane Warne’s bowling are listed in Table 1. We are looking here at those who have faced at least 200 balls and scored 100 runs off Warne. The stats include Australia’s 1999 tour in the West Indies and all Tests since.
Table 1. Best batting averages against Shane Warne 1999-2007
This is an interesting mix of the very best batsmen of the era, and a few outsiders. It shows a surprising number of batsmen whose averages against Warne were as good or better than their overall career averages. Tendulkar’s record against Warne is particularly impressive; he has played 12 Tests against Warne stretching back to 1991, but Shane only ever got him three times. Gary Kirsten’s name at the top may be a bit misleading, given that he was dismissed on five other occasions by Warne before 1999. He is also one of the few leading opening batsmen with a good record against Warne, as Table 2 will show. This lists some well-known batsmen who struggled against Warne.
Table 2. Prominent batsmen who failed against Warne 1999-2007.
Qualification: 3 dismissals.
Curious to see five opening batsmen among the eight in Table 2. Perhaps it shows that they were where they belonged in the batting order.
Looking at the top performers against Glenn McGrath, a different picture emerges.
Table 3. Table 1. Best batting averages against Glenn McGrath 1999-2007
This shows how few top batsmen ever got the measure of McGrath. The great modern Indian batsmen, who enjoy excellent overall records against Australia, all struggled to various degrees against McGrath. A couple even appear on the list of McGrath “bunnies”, in Table 4.
Table 4. Prominent batsmen who failed against McGrath 1999-2007.
Mike Atherton gets the prize for worst combined performances against McGrath and Warne, averaging 16.6 overall. Of course, Atherton played Tests before 1999 that are not included in this survey, but his reputation as McGrath’s bunny, (out 19 times overall to McGrath, and ten times to Warne) suggest that he might have wished he played in another era.
It is clear that of the two bowlers, McGrath has much the better record against top-class batsmen. It was already known that Warne counted proportionally more lower-order players among his victims that just about any bowler in history. This might have been because Australia bowl their opposition out more often than any other team, or because Warne didn’t open the bowling. However, the new figures suggest that the very best batsmen, especially those from the middle-order, seemed to have worked Shane out.
One other observation: most of the batsmen who succeeded against one bowler failed against the other. No important batsmen surpassed his own career average against both bowlers; Kallis was the nearest thing to a success against both. (Curiously, while most failed against one or the other, not many good batsmen failed against both.) When both bowlers were in the Australian team, no batsman found the going easy. Call it synergy: a sign that cricket is a team sport after all. It certainly helps explain how Australia did not lose a home Test for ten years, as long as Warne and McGrath were both in the team. Both Warne and McGrath knew defeat at times, but almost never as team mates.
Postscript: there could be much else written about a survey like this. For example, I noticed that Brian Lara’s success against Warne was something he inflicted on all spinners. He even averaged, incredibly enough, 124.0 against Muralitharan, and his average against the top six spinners of recent years was no less than 96.6. A story for another time, perhaps.
29 July 2007
Having now rummaged through various folders in my archive, it is worth putting together the information gathered so far on the best Test bowling spells (or, more correctly, bowling sequences). Thanks also to Mohan Menon for some of these. If readers can add to this list, please get in touch.
Update: Sreeram has supplied a couple more, Lawson and Imran below. I must admit to a blind spot when it comes to records against Bangladesh.
9/16 (46 balls) JC Laker 9/37 Eng v Aus Manchester 1956
8/4 (~36 balls) GA Lohmann 8/7 Eng v SA Johannesburg 1895/96
8/6 (~95 balls) LR Gibbs 8/38 WI v Ind Bridgetown 1961/62
7/1 (32 balls) CEL Ambrose 7/25 WI v Aus Perth 1992/93
7/2 (~22 balls) GA Lohmann 8/7 Eng v SA Johannesburg 1895/96
7/4 (7/1, plus 3 nb) (33 deliveries) Sarfraz Nawaz 9/86 Pak v Aus Melbourne 1978/79
7/5 (~85 balls) LR Gibbs 8/38 WI v Ind Bridgetown 1961/62*
7/8 (22 balls)
JC Laker 9/37 Eng v Aus
6/0 (18 balls) JJC Lawson 6/3 v Bangladesh Dhaka 2001/02
6/6 (45 balls) S Haigh 6/11 Eng v SA Cape Town 1898/99
6/8 (28 balls) SJ Pegler 7/65 SA v Eng Lord's 1912
6/8 (36 balls) H Ironmonger 6/18 Aus v SA Melbourne 1931/32
6/9 (6/7, plus 2 nb)(23 deliveries) 6/7 AER Gilligan Eng v SA Birmingham 1924
6/9 (56 balls)
CV Grimmett 7/83 Aus v SA
5/0 (18 balls) BKV Prasad 6/33 Ind v Pak Chennai 1998/99
5/0 (~30 balls) LR Gibbs 8/38 WI v Ind Bridgetown 1961/62*
5/1 (17 balls)
GR Hazlitt 7/25 Aus v Eng The Oval
5/3 (5/1, plus 2 nb) (17 deliveries) 9/86 Sarfraz Nawaz Pak v Aus Melbourne 1978/79
5/3 (25 balls) Imran Khan 8/60 Pak v Ind Karachi 1982/83*
5/4 (~28 balls) J Briggs 8/11 Eng v SA Cape Town 1888/89
Note that Hazlitt’s sequence was the last 17 balls he bowled in Test cricket.
I have not included subsets of listed sequences unless they involved fewer runs than the whole sequence. For example, Ambrose naturally recorded 5-1 and 6-1 as part of his record spell, but these are not listed separately.
25 July 2007
Update on the longest spells. Thanks to Sreeram and Mohan Menon, two more 50-over spells have been found. We now have:
354 balls (59 overs) Hirwani at the Oval 1990.
352 balls (44 eight-ball overs), AMB Rowan, Durban 1948/49.
322 balls (53.4 overs) Hugh Tayfield, Saf v Eng, The Oval 1955.
308 balls (51.2 overs) Tom Veivers Manchester 1964.
300 balls (50 overs) George Giffen, Sydney 1894/95.
300 balls (50 overs) Mohammad Nazir, Pak vs Ind, Nagpur 1983/84 (unconfirmed).
Also thanks to Mohan Menon, there is some more information around on the best spells in Test matches. At Chennai in 1998/99, BKV Prasad took his last 5 wickets for 0 in 18 balls for Ind v Pak. He also took a wicket with his second ball in the next Test.
Lance Gibbs spell has been discussed below, and mention was made of spell of 5 for 1 by Hazlitt (17 balls) and Botham (28 balls). No one has taken six wickets in a spell at such low cost; the best reported by Menon is 6 for 6 off 45 balls by S Haigh at Cape Town in 1898/99.
Of course, there are the spells of 7 for 1 by Sarfraz and Ambrose. It is worth mentioning that using modern scoring protocols, Sarfraz’s spell was actually 7 for 4, since he bowled three no-balls. Ambrose’s spell would be unaffected.
One might add that Jim Laker took 9 for 16 off his last 46 balls in the first innings during his 19 for 90 at Old Trafford; the last 7 cost 8 runs (22 balls, fewer than Ambrose or Sarfraz), and the last 5 cost 3 runs (14 balls).
Update update: in the fifth Test of 1948/49 at Port Elizabeth, in England’s first innings, Athol Rowan bowled a 14 (8-ball) over spell before stumps, changed ends, and bowled another 28 overs from the other end the next morning: 336 balls in all with only one minimal change. At one stage, Rowan and NBF Mann together bowled 376 balls unchanged.
17 July 2007
There are some standard Test records that are fairly straightforward to determine, given a complete set of standard (Wisden-style) scorecards. Most runs most wickets, highest scores – while it can take some work, these can be found by interrogating said scorecards. There is another type of records that is more elusive, and cannot be derived from basic scores. Most runs off an over, best bowling spells, even hat-tricks. Such records, if they are published at all, often depend on research of anecdotal reporting.
Sometimes there is
little to be found on what might be an interesting subject. One such is the
longest unchanged bowling spell by a single bowler. The spell of 59 overs
(354 balls) by Narenda Hirwani at
The Durban Test of 1948/49 is famous for its finish, with England winning by two wickets off the last possible ball of the match, the only such victory in Tests. In the first innings, England had scored a fairly pedestrian 253, under conditions favouring spin. Off spinner Athol Rowan bowled 44 overs. The surviving scorebook gives no obvious clue to the length of the longest spell. It is only when it is re-scored over-by-over that it becomes clear that Rowan bowled his overs completely unchanged.
Being eight-ball overs, that gives Rowan a spell of 352 balls, just two short of Hirwani, and the longest spell up to that time.
Rowan and Mann bowled the last 46 overs of that innings.
The only other spells of 300 balls or more by a single bowler that I know of are 308 (51.2 overs, not 55.2 as sometimes stated) by Tom Veivers at Old Trafford in 1964, and 300 (50 overs) by George Giffen in Sydney in 1894/95. Readers may know of others.
On the last day, the South African tailenders made a real effort to force a draw. Rowan himself scored 15 off 100 balls, but he was out-stonewalled by Lindsay Tuckett, whose 3 from 82 balls belongs in the pantheon of low slow innings. At one point there was no score for 48 balls, and Compton bowled nine consecutive maidens. Unfortunately, Cuan McCarthy, arguably the worst batsman ever to play Tests (with a top score of 5 in 24 innings), only lasted 3 balls for his usual duck, and the door was open for England.
The final innings makes for an interesting re-score, of course. Nowadays we would regards a target of 128 off 216 balls as simple, but the light was poor and the pitch very two-paced towards the end. England were reduced to 74 for 6 with 15 overs to go, but declined to appeal against the light. Compton and Jenkins turned the game around, mostly with singles, but it was left to tailenders Bedser and Gladwin (who faced the last ball) to fall over the line. There was only one boundary in the last 22 overs, perhaps reflecting the field settings. That came in the last over, which also featured 3 leg-byes. In the end, the fact that South Africa conceded 33 sundries in the match to England’s 11 made a big difference.
15 July 2007
No Worse, There is None
(Apologies to Hopkins)
Bangladesh continue to plumb new depths of incompetence in Test cricket. They are now demonstrably weaker than Zimbabwe before their ejection from Tests.
Bangladesh’s loss to Sir Lanka at Kandy, by an innings and 193, was their fourth consecutive innings defeat in the space of six weeks, with a combined deficit of four innings and 756 runs. In all four matches, they have neither come close to making their opponents bat again, nor have they come close to bowling out their opponents even once. Without the intervention of rain, all the matches would have been finished early on the third day.
The series against Sri Lanka was the most one-sided 3-match series in Test cricket history. Twice before (in 1928 and 1994) teams have lost by an innings in all Tests of a 3-match series, but neither of the precedents was so totally lop-sided. Sri Lanka averaged 95 runs per wicket, Bangladesh 17(the latter is the worst by any team since India against New Zealand in 1969). The ratio of averages of 5.66 far exceeds that of any other 3-Test series, the previous record being 3.47 for India in England in 1974.
[Bangladesh did do worse in a 2-Test series in England last year, with a ratio of 9.4.]
In each case the match was effectively over before 40 overs had been bowled; in the first two Tests, the odds against a Bangladesh win rose beyond 100 to 1 before the end of the first session. In reality, it could have been worse still. There are signs that Sri Lanka went into cruise mode once they had gutted the Bangladesh batting.
Even compared to Zimbabwe, this is embarrassing. Zimbabwe did lose five straight by an innings just before they were turfed out. But in those matches they bowled their opponents out (or took 9 wickets) on each occasion, and only one score over 500 was recorded.
Kumar Sangakkara has just averaged 428 in the series, a record for a 3-Test series, by a margin of just one run, previously set by Daryl Cullinan for South Africa in New Zealand in 1998/99. Sangakkara now has consecutive unbeaten double-centuries under his belt, a Test first. With 422 runs since his last dismissal, other records beckon, but they would surely have a hollow feel.
7 July 2007
UPDATE on Gibbs record spell (first read 30 May, below)
The report of the Daily Gleaner does not really clarify the details of Gibbs’ spell, but instead it complicates it. Like most other sources, it gives the spell as 15.3-14-6-8, but it also says that, at the fall of the ninth wicket, the spell to that point was 14-12-6-7. One of these must be wrong, and if the latter is correct, then the six runs were scored in two different overs.
However, it does mention a spell of 3 for 1 in 3 overs, apparently in connection with the Pataudi dismissal. If so, then one run was scored off Gibbs between the dismissals of Sardesai and Manjrekar, presumably in the second over of the spell, and so the later sequence of 5 for 0 still stands, although the whole spell is either 15.3-13-6-8, or 16.3-14-8-6. It is curious, however, that the Gleaner does not mention the 5 for 0.
In any case, it transpires that Gibbs’ spell is not the best in a single session of Test cricket. Not if you accept the 2nd match of 1888/89 in South Africa as a Test match, which by an unfortunate historical accident, is the official case. In that match Johnny Briggs took 12 for 21 before lunch on the last day. South Africa started the day on 2/1 and were out for 47. Following on, they were 20/7 at lunch.
Of all the 1,800+ official Test matches, this match is probably the one least worthy of Test status. The series represented the entire first-class careers of three of the so-called “England” players, and there was no first-class cricket system in South Africa at the time. It is telling that while England’s captain, Bowden, is now listed as England’s youngest-ever captain, this fact, and this match, was not mentioned in Wisden’s obituary.
23 June 2007
Cricket’s Marathon Man
One curiosity of the cricket record books is that while we can identify the longest Test innings, its exact length is uncertain. Officially, Hanif Mohammad’s 337 at Bridgetown in 1958 lasted 970 minutes, but other sources, including Hanif himself, claim it was 999 minutes, a nice bookend for Hanif’s record 499 in first-class cricket a year earlier.
Hanif, in his autobiography, supports his claim with a recording he has of the radio broadcast of the end of his innings, which states 999 minutes. Without doubt the recording does say that, but that does not mean it is correct. It would be easy to make an error in adding up the times on the spur of the moment.
Unfortunately, no original scorebook of this match has been found. A scorebook of the series has recently surfaced in Pakistan, and it includes Sobers 365* later in the series, but the Bridgetown Test is missing from this book.
Until a scorebook is found, we will never know how many balls Hanif faced. However, the accounts of the innings in West Indian newspapers are quite detailed. What follows are the statistical gems found in the Jamaica Daily Gleaner, concentrating on Hanif’s batting in the match.
[Incidentally, Conrad Hunte’s claim, in his autobiography, that he hit the first two balls of his Test career(and the first two balls of the series) for four, is not confirmed by the Gleaner account, which mentions only a boundary off the fourth ball of the first over.]
Following the West Indies 579 on the second day, Hanif opened in the first innings, and scored five in the four overs before stumps. The following day he was second out for 17 at 39, in 45 minutes. Pakistan were bowled out at 2:23 for 106 in 148 minutes, 473 runs behind.
Pakistan followed on at 2:33, Hanif opening again. At tea, Pakistan was 79 for 0 in one hour, Imtiaz an aggressive 41. Hanif was dropped on 14. Imtiaz reached 50 in 71 minutes and the 100 partnership came up in 79 minutes. Hanif reached 50 in 123 minutes with five 4s, and the 150 came up in 130 minutes.
Imtiaz was out for 91 out of 152 in 137 minutes (12x4), and stumps was called at 161 for 1 in two and a half hours, after 50 overs, with Hanif 61 and Alim-ud-Din 1 not out. Attendance had been 9,700.
Hanif scored surprisingly well the next morning, though without hitting many boundaries, and reached 100 in 244 minutes, with only six fours. Lunch was taken at 219/1 (Hanif 100, Alim-ud-Din 18). After lunch the 100 stand was reached in 135 minutes, and Pakistan’s 250 in 275 minutes. Alim-ud-Din was out for 37 in 165 minutes at 264 (1x4), and the tea score was 295/2, Hanif 139, Saeed Ahmed 10 (in 60 minutes).
Hanif reached 150 in 393 minutes. Pakistan finished the day at 339 for 2 off 142 overs, Hanif 161 and Saeed 26. Hanif had scored 100 runs in 300 minutes in the day; 92 overs were bowled. There had been a four minute interruption because a mirror of a parked car was reflecting in the batsmen’s eyes.
On the fifth morning, a new ball was taken at 347 after three overs. The third-wicket stand reached 100 in 196 minutes. Saeed was dropped on 49 and reached 50 in 219 minutes, with 3 fours. The 400 came up in 534 minutes, and at lunch Pakistan were 405/2, Hanif 185 and Saeed 62. Saeed was out at the end of the fifth over after lunch, for 65 in 263 minutes (6x4). Hanif carried on unperturbed and reached 200 in 586 minutes with 17 fours. Scoring slowed, and the 450 came up in 662 minutes; at tea the score was 457/3, Hanif 216 in 656(?) minutes, and Wazir Mohammad 17. Between lunch at tea there had been 42 overs with 23 maidens.
At 473, Pakistan had wiped out the first-innings deficit in 688 minutes. Another new ball was taken, after 78 overs, with the score at 491. Hanif carried on, comfortably reaching 250 in 721 minutes with 21 fours, and the 500 was posted four minutes later. Hanif’s fourth consecutive century stand (unique in Tests) arrived in 179 minutes. Wazir at this stage had hit only one boundary. The day finished with Hanif on 270 in 755 minutes, with 22 fours. Wazir was on 31, the total 525. The West Indian bowlers had wheeled off 95 overs in the five-hour day.
It was “Groundhog Day” once again for the West Indies on the sixth morning, with Hanif walking to the crease for the fourth day in a row. Wazir was out for 35 in 213 minutes (1x4), after a partnership of 121. Hanif was tiring and slowing down, but there were no cracks in his concentration. At 290 he passed Hutton’s 797–minute record for the longest Test innings, but progress to a triple-century was delayed by lunch, Pakistan 566/3, Hanif 297, Wallis Mathias 9. The crowd was only 2,000. Fifteen minutes after lunch, Hanif finally ground past 300, reached in 860 minutes, with 23 fours.
Mathias couldn’t emulate the top order by sharing a century stand, and was out for 17 in 125 minutes at 598 (1x4). The 600 came up in 917 minutes, and the Pakistanis were at last in sight of saving the match. Hanif and captain AH Kardar saw the innings safely to tea at 623 for 5, Hanif on 334 in 965 minutes and in sight of the world record. He edged past Bradman’s and Hammond’s best scores, having batted three hours longer than those two record-breaking batsmen combined. But a few minutes after tea, he was caught behind off a routine edge, out for 337 in 973 minutes, with 24 fours. The score was 626.
With the match saved, Fazal Mahmood lightened up proceedings with two sixes off Collie Smith, and hit 19 in 20 minutes. He was out at 649, followed two minutes later, in the same over, by the sixteen-year-old Nasim-ul-Ghani (0). About ten minutes later, Kardar (23* in 100 minutes) was able to declare with the score at 657 for 8 in 1005 minutes, with an improbable lead of 184. There was just over half an hour for Hunte and Kanhai to bat, which they managed without difficulty, and the match was drawn after 1370 runs over six days.
The times given from the Daily Gleaner are mostly internally consistent, and are consistent with the known playing hours in that series (five-hour days, 90’ + 120’ + 90’). The only real problem seen with the account is that it gives Hanif a time of 214 minutes for his first 100, which it appears should be 244 minutes. This could easily be a typo.
In light of the details of this account, the alternative time of 999 minutes for Hanif is quite improbable.
Hanif batted for close to 309 overs. If he received half the strike, he would have faced about 930 balls. Similarly, his first innings can be estimated at 35 balls. The total of 965 balls is interesting in that, surprisingly, it would not actually be a Test record. Wally Hammond (119* and 177) faced 977 balls in the Adelaide Test of 1928/29. However, there remains a strong possibility that Hanif took more than half the strike, and he could even have faced more than 1000 balls in the match.
30 May 2007
Sardesai Grinds into the Records
An occasional search for the slowest Test half-centuries of all time has pointed the way to a most interesting day in Test history. At Bridgetown on the 28th March 1962, India, 2 for 104 overnight, was bowled out for 187 to lose by an innings and 30 runs to the West Indies. Sounds routine, but it was the progress of the innings that set a couple of records.
Firstly there was the innings of Dilip Sardesai, who scored 60 in no fewer than 392 minutes. From his overnight score of 41 in a less-than-blistering 248 minutes, Sardesai went to his 50 with somewhat more care, reaching 50 in 302 minutes. At this point he went right into his shell, his last 10 occupying an hour and a half.
We don’t know how many balls Sardesai faced, but he was at the crease for something very close to 155 overs. If he received half the strike, this comes to about 465 balls for just 60 runs. Slower than Bailey’s 68 off 427 in 1958/59, this would be a real record-breaker. Half the strike in this case would be perfectly reasonable assumption, since there were so many maiden overs. In such circumstances, strike tends to even out quite smoothly. There were no fewer than 32 maidens in the 48 overs bowled in the pre-lunch session of the final day, all faced by Sardesai and Manjrekar.
On this assumption, Sardesai’s 50 in 302 minutes is equivalent to about 357 balls faced, which would edge out Bailey’s 350 balls at Brisbane, and Jackie McGlew’s 343 balls at Johannesburg in 1957/58. Next on the list are Alec Bannerman, 330 balls at Sydney in 1891/92, and Charles Kelleway, 296 balls at Lord’s in 1912. Although there are many other 50s for which balls faced is unknown, there are few other clear contenders for the 300+ balls club. Nazar Mohammad’s record-breaking 124 against India is one. His 50 in 250 minutes is equivalent to 290 balls.
It is intriguing that the Bridgetown match had already seen one extremely slow half-century. Frank Worrell had taken two hours to get into double figures, and 286 minutes to reach 50 on the way to 77 in 351 minutes. The 50 time is equivalent to 285 balls.
Sardesai and Manjrekar eventually added 98 in 248 minutes, off about 100 overs, with looking too troubled. Before lunch, Lance Gibbs had bowled 10 wicketless overs for just 5 runs, but after lunch he was a different proposition. Manjrekar had reached his 50 ten minutes after lunch, but a further ten minutes later, Gibbs returned to the bowling crease, immediately ending Sardesai’s vigil. In the third over of his new spell, he got Manjrekar for 51, and Pataudi second ball.
Borde and Umrigar held out for half an hour (one source says 40 minutes), but Gibbs got them both, ten minutes (presumably 2 Gibbs overs) apart. At 7 for 177, Gibbs then took a wicket each over (according to Times of India) until it was all out for 187 (in 470 minutes and 186 overs). Eight wickets had fallen for 29 in 78 minutes.
According to Wisden and Times of India, Gibbs’ final spell was 15.3-14-6-8 (one other source says 16.3 overs). This is the best performance in a single session by any bowler in a Test match. There may be some other records tied up in this. Going by the descriptions, and if the 15.3 overs, 14 maidens figures are correct, Gibbs’ sequence was something like:
1. Wicket maiden (Sardesai)
2. Maiden (possibly one run, see update above).
3. Double wicket maiden (Manjrekar, Pataudi).
4. To 10. Six maidens and one over for 6 (or 5) runs.
11. Wicket maiden (Umrigar)
13. Wicket maiden (Borde)
14. Wicket maiden (Engineer)
15. Wicket maiden (Durani)
16. Desai out off third ball.
The most likely sequence therefore includes a spell of 5 for 0, from the dismissal of Umrigar to Desai. There is a slight chance that the six runs conceded by Gibbs was actually in the 13 or 14th over, between Engineer’s and Durani’s dismissals. In this case Gibbs took 6 for 0 between dismissing Sardesai and Engineer. (There is a small chance that there was a single in the incomplete over, which would make the best spell 5 for 1, but this seems very unlikely.)
Either of these bowling sequences would be unique in Tests. There are two cases known of five wickets for one run, by Hazlitt in 1912 and Botham in 1981, but none (that I am aware of) of 5 for 0. Gibbs’ 8 for 6 is also unique, although there are two cases of 7 for 1 (Ambrose and Sarfraz). Readers may know of other extreme spells.
The patience showed by both batsmen and bowlers would be hard for a modern cricketer to fathom. It is intriguing that only one year after the famously entertaining 1960/61 series in Australia, Worrell would lead his team with such negativity. When Worrell commenced his 77 in 351 minutes, the West Indies had already achieved a first innings lead, and there was no pressure. Worrell was reportedly slow-hand-clapped for almost his entire innings.
The 1960/61 series has often been referred to as a cricketing renaissance. Subsequent events, such as this series and the 1962/63 Ashes, show that it was nothing of the sort. More of an anomaly, really. (see Update 7 July)
20 May 2007
One of my occasional correspondents, Shekhar, mentioned to me a criticism of the conventional way of calculating batting average, by two actuaries, Sanchit Maini and Sumit Narayanan. They even got an article into The Economist. The criticism is a familiar one, finding fault with the treatment of not out innings. Their solution is a curious one, treating all innings where the player exceeds his average number of ball faced as completed innings with dismissal.
The traditional average is still much to be preferred, for basic reasons. The principle is simple: for a batsman, scoring runs = good, getting out = bad. Divide one by the other (the batting average) and you have a measure that rises with the good and falls with the bad.
With deeper analysis, it can be shown that, for most batsmen, not out innings actually harm the batting average. This is because most batsmen find scoring a bit easier as their scores mount. A batsman on 50 has a better chance of scoring another 50 runs than he did on 20. As a result, in the long run, artificially truncating a batsman’s innings (by running out of partners, declaration, or winning) actually costs him more runs than his batting average. If cricket allowed all batsmen to complete all their innings, most would have a higher average, even if they have many not out innings supposedly ”boosting” their averages.
There are exceptions. If all of Mark Waugh’s Test centuries had been terminated when he reached 100 not out, his career batting average would have been higher. However, if this had been done to Steve Waugh, Steve’s average would have dropped, even though he would have enjoyed many more unbeaten innings. If Brian Lara had never been allowed to carry on after reaching 100, his average would have been dropped from 52.9 to 48.8, even though his number of not outs would have risen from 6 to 38.
When you think of it, equating unbeaten innings with dismissals assumes that every batsmen finishing not out faced immediate and inevitable dismissal if he had continued. This is obviously a fallacy.
As for the Maini/Narayanan solution, there may be some limited utility for the One-day game, but it seems rather arbitrary. It is interesting that they have to go back more than 50 years to find an obvious anomalous example, Bill Johnston’s 100 average in England in 1953. In fact, their solution would not work in the Johnston case, because we don’t know how many balls he faced that season.
Solutions like this also unfairly favour top-order batsmen over middle-order, because the top order players have their innings artificially truncated far less often. Having said that, one should also consider “runs per match” as a secondary stat, not so much as a measure of the batsman’s ability of performance, but as a measure of his influence over matches. This is especially so in the One-day game. One of the most severe flaws in the design of that game is the fact that middle-order batsmen often play little role. In the World Cup, anyone batting below #3 or 4 for Australia was either a cameo (Symonds) or completely redundant (Hussey).
I did work out a formula for an alternative ODI batting average, giving equal weight to standard average, runs per match, and scoring rate. It looked pretty good (perhaps I will post the list later), but such systems are, of course, arbitrary. It is hard to prove that they are superior to conventional calculations, and Maini/Narayanan make little attempt to prove the superiority of their own system.
An article by Mainin and Narayanan: