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January 30, 2008

Trivia - batting

Extreme batting - fastest and slowest innings in Tests

Charles Davis
Nathan Astle pulls to the boundary, South Africa v New Zealand, 4th Test, May 6, 2006
 © ESPNcricinfo Ltd
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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 – in terms of runs scored – calculate the average (or mean) balls faced, and then calculate the standard deviation, which is a measure of the spread or variability of the data. We can then give the most exceptional innings a z-score (the number of standard deviations from the mean) which becomes a measure of how extraordinary the innings were.

An example may help clarify this. Let’s look at all innings of exactly 76 runs in Test matches. We have balls faced data for 119 such innings. The average number of balls faced is 161 and the standard deviation of this data is about 49.

The fastest known innings of 76 in Tests was off 72 balls by Viv Richards in Adelaide in 1980. This is 1.75 standard deviations faster than the average, so the innings gets a z-score of -1.75. Likewise, the slowest innings of 76 was 315 balls by Glenn Turner in 1971, with a z-score of +3.2.

To compare many innings of different sizes, the process must be repeated for all possible scores. This process gives big innings a better rating than smaller innings of a similar speed, because it is more difficult to score rapidly for longer periods.

So which innings have the most extreme z-scores? At fast end of the scale, the results look like this:

The fastest innings
Batsman Runs Balls Match Venue & year z-score
Viv Richards 110 58 WI v Eng Antigua, 1986 -2.58
Nathan Astle 222 168 NZ v Eng Christchurch, 2002 -2.54
Adam Gilchrist 102 59 Aus v Eng Perth, 2006 -2.45
Chris Cairns 82 47 NZ v Eng Lord’s, 2004 -2.36
Jack Gregory 119 81 Aus v SA Johannesburg, 1921 -2.34
Jacques Kallis 54 25 SA v Zim Cape Town, 2005 -2.34
Kapil Dev 89 55 Ind v Eng Lord’s, 1982 -2.33

Recent innings are prominent in this list, a sign of the speed of the modern game. Still, no batsman has reached quite the extremes of Viv Richards in his record-breaking century in 1986. I wonder what it is about English bowling that has attracted so many extreme innings.

At the other end of the scale, we must go further back in time.

The slowest innings
Batsman Runs Balls Match Venue & year z-score
Hanif Mohammad 20 223 Pak v Eng Lord’s, 1954 7.90
Alec Bannerman 91 620 Aus v Eng Sydney, 1892 7.88
Herbie Collins 40 340 Aus v Eng Manchester, 1921 7.66
John Murray 3 100 Eng v Aus Sydney, 1963 7.15
Yashpal Sharma 13 159 Ind v Aus Adelaide, 1981 6.90
Geoff Allott 0 77 NZ v SA Auckland, 1999 6.80

It is interesting to see a wide range of scores, from 0 to 91, appearing on this list. Modern cricket watchers can only wonder at the extremes represented here. In terms of time, Hanif would have, going by modern-day over-rates, taken more than five hours for his 20 runs, while Alec Bannerman’s 91 would probably take more than two full days. Apart from Bannerman, every other batsman who has faced 620 or more balls in a Test innings has scored well over 200 runs, and the most balls faced (known) in reaching a century is 525 by Colin Cowdrey in 1957. Perhaps it is no wonder that Bannerman, unlike his more adventurous brother Charles, never scored a Test century.

Of course, there are quite a number of past innings for which balls faced are unknown, so we don’t know exactly where they may fit on the scale, but we can still make some estimates. Of particular interest is Dilip Sardesai’s 60 against the West Indies in Bridgetown in 1962. Sardesai was at the crease for 155 overs, and probably faced over 450 balls; if so, his z-score would be 7.93. His dismissal in that match started an extraordinary collapse that saw Lance Gibbs take eight wickets for six runs.

A postscript puzzle: innings of four runs, on average, involve fewer balls faced than innings of three runs. There is a logical reason for this (for readers to ponder).

[Notes for the statistically-minded: this process works quite well when we have data available for a very large number of innings. However, it does require some smoothing and trend-fitting at higher, rarer scores (above 120). Note also that the distributions are skewed, so z-scores of fast innings are different in magnitude to slow ones, and at the fast end of the scale the calculation is not very useful for innings of less than 40 runs. However, the process is still useful as long as we just compare fast with fast, and slow with slow.]

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Posted by Single Kontakt zum Flirten aus Berlin on (February 6, 2011, 18:03 GMT)

Dig the well before you are thirsty.

Posted by Deepak on (February 15, 2010, 11:57 GMT)

how are slowest innings anything but the ducks?

Posted by Andy on (March 7, 2008, 8:54 GMT)

Very interesting comments by Mick on Feb 1 and Madhan on Feb 11. :)

Posted by Madhan on (February 11, 2008, 14:18 GMT)

One question. Would not the batsman's innings be better compared with how the other batsmen performed in the same match. An e.g., in a match of run rate 3, an innings with run rate 6 per over could be better rated than a match where everyone scored at 5.5 and one batsmen scored 6 per over. Just a thought.

Posted by Bharat L. Sud on (February 10, 2008, 7:07 GMT)

Loved the use of z-stats, allows comparison across different scores thus making them comparable. Am using similar standardization approaches in my research in marketing! Maybe one thing that could add to this is to also use the approach suggested by Ritwik and use both measures, together, to come up with fastest and slowest innings. Another thing, maybe control for the average run/strike rates in that year, so in the 1950s a 50 of 70 balls might be fast but today it is average. Regarding Sarojini Kumar's point, yes cricket is simple and we might be complicating it, but this is just for fun beyond the cricket matches, not too serious stuff but allows another perspective at some great innings.

Posted by anders on (February 1, 2008, 17:11 GMT)

Top work. The balls-per-innings distribution has the strong scent of a lognormal, to me (a wise man once said to me: given the choice of living in a world where everything was logged or a world where nothing could be, he'd choose Planet Logarithm every time!)

Posted by caspian on (February 1, 2008, 14:02 GMT)

"Rate the innings at the milestones, ie rate both Gilly and Richards' innings at 100, and all the 300 scores would be rated at 100, 150, 200, 250 as well as the 300. Its obvious Gilchrist's and Richard's innings should be directly compared and not broken into 2 exclusive subsets. Statistics are so good to abuse."

This is a rather good idea. It would be a lot easier to judge the 300+ scores this way.

Great article, by the way. I'm curious as to what the average amount of balls faced for a duck is, as well.

Posted by Somasekhar on (February 1, 2008, 8:17 GMT)

Nice article. If only it can be related to the total runs scored in the match so that a perspective of the degree of difficulty involved (read pitch and playing conditions) can be also be achieved.

Posted by Srijoy on (February 1, 2008, 7:23 GMT)

Aaaaarrrgghhh!!! Numbers!!! Is this cricket or an algebra lesson? a+b-x+z-score = Boring! Let the bat do the scoring and Duck for all you're Worth!

Posted by Sailesh on (February 1, 2008, 4:50 GMT)

Sarojini, it is okay to keep quiet once in a while!

@Charles: Interesting analysis. I have a suggestion to partially alleviate the problem of thin data. A score of, say, 55, and a score of 56 (or 54, for that matter) are not really different. So, when computing the mean and SD of a score of 55, you can include all innings with scores 54 or 56 (maybe even 53 and 57). This will not entirely solve the problem for higher scores, but it will atleast smooth the data for scores less than 100.

Also, instead of computing the z-score as a function of the deviation from mean, you can create probability distributions by fitting curves for each score (which would take care of the problem of asymmetric spreads) and compute a one-tailed likelihood for each innings. This will also make comparisions between different scores more meaningful, by eliminating the implicit assumption that the distributions for all scores are the same.

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