January 30, 2009

A consistency index for batsmen

Ric Finlay
Jack Hobbs batting at The Oval
Among batsmen with at least 5000 Test runs, Jack Hobbs has the best consistency index  © The Cricketer International
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One thing we admire in our cricketers is consistency. Full marks to the gritty player who scores 50 on a minefield, even though he gets out for 50 when well set on a featherbed. But do we admire so much his team-mate who gets a duck in the first instance, but makes amends by crashing an impressive 100 in the second? They have the same average - but do they provide the same value?

Consistency can measured by calculating the standard deviation, which, in simple terms, seeks to measure the average deviation that each score is from the overall mean. The lower the standard deviation, the lower the variation in the scores. We can obviously apply this to cricket scores, but a couple of issues need to be resolved: what to do with "not out" scores, and how can we use it to compare the consistency of players with different averages?

To resolve the first, I elected to add any uncompleted innings to the next innings, so that effectively, I was calculating the standard deviation of the runs made between dismissals. If the last innings was a "red ink", it was ignored.

To allow comparison of consistency between different players, I simply divided the calculated standard deviation by the batting average (ignoring the last innings if it was "not out").

I performed this exercise three times for Test cricketers; for those who scored at least 1000 runs, for those who scored at least 5000 runs, and for those who scored at least 10000 runs.

The first table lists the most consistent Test batsmen who have scored at least 1000 runs. Australia's Bruce Laird, who scored with such consistency without scoring a century in his brief late-70s career, heads the list, and is followed by the admirable Sutcliffe, whose consistency is astounding given the extent of his career. Alastair Cook and MS Dhoni are notable current players in this list.

Table 1: Consistency Index: Most Consistent (Minimum 1000 runs)
Batsman Team CI SD Average Matches Innings Not Out Runs
Bruce Laird Australia 0.75 26.48 35.29 21 40 2 1341
Herbert Sutcliffe England 0.78 47.22 60.73 54 84 9 4555
Douglas Jardine England 0.79 37.08 46.70 22 33 6 1296
Ashley Giles England 0.80 16.81 20.90 54 81 13 1421
Alastair Cook England 0.81 34.24 42.09 36 66 2 2694
Maurice Tate England 0.82 20.96 25.49 39 52 5 1198
Rusi Surti India 0.83 23.72 28.70 26 48 4 1263
Jock Cameron South Africa 0.83 25.05 30.22 26 45 4 1239
George Gunn England 0.83 33.39 40.00 15 29 1 1120
Chandika Hathurusingha Sri Lanka 0.84 24.74 29.63 26 44 1 1274
Ian Redpath Australia 0.84 36.62 43.46 66 120 11 4737
Sid Barnes Australia 0.85 53.39 63.06 13 19 2 1072
Mark Richardson New Zealand 0.86 38.33 44.77 38 65 3 2776
Taufeeq Umar Pakistan 0.87 34.22 39.30 25 46 2 1729
Imran Farhat Pakistan 0.88 29.02 33.10 27 51 1 1655
Charles Kelleway Australia 0.88 32.83 37.42 26 42 4 1422
Dwayne Bravo West Indies 0.88 28.74 32.73 31 57 1 1833
Peter Richardson England 0.88 33.08 37.47 34 56 1 2061
Chetan Chauhan India 0.89 28.07 31.58 40 68 2 2084
Colin Bland South Africa 0.89 43.67 49.09 21 39 5 1669
Trevor Goddard South Africa 0.89 30.67 34.47 41 78 5 2516
Deryck Murray West Indies 0.89 20.40 22.91 62 96 9 1993
Mahendra Singh Dhoni India 0.89 32.20 36.14 35 56 6 1807
David Sheppard England 0.89 33.70 37.81 22 33 2 1172
Alan Davidson Australia 0.89 21.97 24.59 44 61 7 1328

At the other end, we also have some current players in the least consistent category, notably Sinclair, Taibu, and until recently, Atapattu, who mixed a dreadful sequence of low scores early in his career with some heavy scoring later on:

Table 2: Consistency Index: Least Consistent (Minimum 1000 runs)
Batsman Team CI SD Average Matches Innings Not out Runs
Matthew Sinclair New Zealand 1.62 52.70 32.55 32 54 5 1595
Vinoo Mankad India 1.51 47.57 31.48 44 72 5 2109
Jacques Rudolph South Africa 1.49 53.81 36.21 35 63 7 2028
Guy Whittal Zimbabwe 1.48 43.65 29.43 46 82 7 2207
Tatenda Taibu Zimbabwe 1.45 42.94 29.60 24 46 3 1273
Wasim Akram Pakistan 1.44 32.57 22.63 104 147 19 2898
Mohammad Ashraful Bangladesh 1.43 34.10 23.88 48 93 4 2125
Javagal Srinath India 1.43 20.31 14.21 67 92 21 1009
Wasim Jaffer India 1.42 48.30 34.11 31 58 1 1944
Vic Pollard New Zealand 1.41 34.35 24.35 32 59 7 1266
Dilip Sardesai India 1.40 55.10 39.24 30 55 4 2001
Sidath Wettimuny Sri Lanka 1.39 40.31 29.07 23 43 1 1221
Marvan Atapattu Sri Lanka 1.39 54.40 39.02 90 156 15 5502
Matthew Elliot Australia 1.38 46.20 33.49 21 36 1 1172
Madan Lal India 1.38 31.27 22.65 39 62 16 1042
Ridley Jacobs West Indies 1.37 38.70 28.32 65 112 21 2577
Tim Robinson England 1.36 49.34 36.39 29 49 5 1601
Bill Ponsford Australia 1.35 65.00 48.23 29 48 4 2122
John Bracewell New Zealand 1.35 27.56 20.43 41 60 11 1001
Jimmy Adams West Indies 1.35 55.72 41.26 54 90 17 3012

Now for the serious Test batsmen:

Table 3: Consistency Index: Most Consistent (Minimum 5000 runs)
Batsman Team CI SD Average Matches Innings Not Out Runs
Jack Hobbs England 0.92 52.33 56.95 61 102 7 5410
Don Bradman Australia 0.94 93.49 99.94 52 80 10 6996
Arjuna Ranatunga Sri Lanka 0.94 33.48 35.50 93 155 12 5105
John Wright New Zealand 0.97 36.58 37.83 82 148 7 5334
Mark Waugh Australia 0.97 40.58 41.82 128 209 17 8029
Graham Thorpe England 0.98 43.25 44.23 100 179 28 6744
Rohan Kanhai West Indies 0.98 46.58 47.53 79 137 6 6227
Clive Lloyd West Indies 0.99 46.44 46.68 110 175 14 7515
Denis Compton England 1.00 49.9 50.06 78 131 15 5807
Sourav Ganguly India 1.00 42.22 42.18 113 188 17 7212
Bill Lawry Australia 1.03 48.43 47.15 67 123 12 5234
Ken Barrington England 1.03 59.9 58.28 82 131 15 6806
Matthew Hayden Australia 1.04 52.77 50.74 103 184 14 8625
Ricky Ponting Australia 1.05 59.47 56.88 128 215 26 10750
Michael Slater Australia 1.05 45.09 42.84 74 131 7 5312
Doug Walters Australia 1.06 50.86 48.10 74 125 14 5357
Marcus Trescothick England 1.06 46.34 43.80 76 143 10 5825
Sunil Gavaskar India 1.06 54.42 51.12 125 214 16 10122
David Gower England 1.07 47.29 44.25 117 204 18 8231
Vivian Richards West Indies 1.07 53.69 50.24 121 182 12 8540
Michael Atherton England 1.07 40.41 37.70 115 212 7 7728
Len Hutton England 1.07 60.86 56.67 79 138 15 6971

The higher Consistency Indices show that it is much harder to maintain consistency over a longer career. It is interesting to observe that the two most consistent batsmen are two "old-timers", Hobbs and Bradman - class will out! And who would have thought that the most consistent Australian after Bradman in this category was Mark Waugh!

At the other end of the scale for this category, we find Waugh's twin brother prominently placed:

Table 4: Consistency Index: Least consistent (Min 5000 runs)
Player For CI SD Ave M I NO Runs
Marvan Atapattu SL 1.39 54.40 39.02 90 156 15 5502
Zaheer Abbas Pak 1.32 59.29 44.80 78 124 11 5062
Kumar Sangakkara SL 1.31 71.23 54.38 78 129 9 6525
Virender Sehwag Ind 1.27 64.81 51.06 66 114 4 5617
Steve Waugh Aus 1.26 64.16 51.06 168 260 46 10927
Shivnarine Chanderpaul WI 1.25 62.37 49.72 114 196 31 8203
Brian Lara WI 1.24 65.33 52.89 131 232 6 11953
Herschelle Gibbs SA 1.24 51.85 41.95 90 154 7 6167
Ian Botham Eng 1.24 41.69 33.55 102 161 6 5200
Sanath Jayasuriya SL 1.23 49.15 40.07 110 188 14 6973
VVS Laxman Ind 1.22 54.24 44.46 102 169 24 6446
Aravinda de Silva SL 1.21 52.21 42.98 93 159 11 6361
Mark Taylor Aus 1.19 51.55 43.50 104 186 13 7525
Wally Hammond Eng 1.19 69.46 58.46 85 140 16 7249
Jacques Kallis SA 1.19 64.91 54.58 128 216 33 9988
Mahela Jayawardene SL 1.18 61.73 52.36 100 164 12 7959
Carl Hooper WI 1.18 43.09 36.47 102 173 15 5762
Sachin Tendulkar Ind 1.1 64.28 54.28 156 256 27 12429
Rahul Dravid Ind 1.17 61.07 52.28 131 227 26 10509
Stephen Fleming NZ 1.17 47.05 40.07 111 189 10 7172

The case of Chanderpaul is interesting. Ten years ago, he was heading towards being one of the most consistent batsmen ever, with a CI of 0.82. Over the last decade, while he has been one the Windies few shining lights, there has also been much greater variation in his scoring.

This group also contains a few batsmen who play more aggressively than most: Sehwag, Jayasuriya and Botham are notable here. One would expect, naturally, their consistency to suffer as a result of their aggression.

Finally, a table just for the mega-stars, those who have scored 10000 Test runs, plus Kallis, who will surely join them the next time he goes to bat:

Table 5: Consistency Index: Top eight run-scorers
Player For CI SD Ave M I NO Runs
Ricky Ponting Aus 1.05 59.47 56.88 128 215 26 10750
Sunil Gavaskar Ind 1.06 54.42 51.12 125 214 16 10122
Allan Border Aus 1.08 54.45 50.37 156 265 44 11174
Rahul Dravid Ind 1.17 61.07 52.28 131 227 26 10509
Sachin Tendulkar Ind 1.18 64.28 54.28 156 256 27 12429
Jacques Kallis SA 1.19 64.91 54.58 128 216 33 9988
Brian Lara WI 1.24 65.33 52.89 131 232 6 11953
Steve Waugh Aus 1.26 64.16 51.06 168 260 46 10927

I for one was surprised to find the Aussie captain heading this list, and Tendulkar so far down the table. And perhaps Gavaskar was a better player than he is perhaps given credit for.

I hope the browsers of this site find this a worthwhile exercise. I would value their comments.

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Keywords: Stats, Trivia

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Posted by Harsh Thakor on (February 1, 2010, 11:57 GMT)

Jack Hobbs deserves his ranking considering his brilliant consistency,scoring over half his first class Centuries after the age of 40.

I was impressed with the choice of Rohan Kanhai, ,who to me was the most consummate batsmen of all,scoring a fifty every 3 innings.Clive Lloyd was a more consistent batsman after gaining captaincy,being a champion in a crisis.

Overall,I feel Geoff Boycott,should have atleast been in the top dozen for his remarkable consistency all over the world,including the Carribean .

Rahul Dravid should have atleast made the top dozen,considering his overseas record,while Steve Waugh and Javed Miandad were the best batsman in their day in a crisis-the ultimate batsman to bat for your life.I would place them above Mark Waugh.

To me Gavaskar and Hutton should have been ranked much higher as well as Sachin Tendulkar.Imagine Sachin retaining a 55+average after crossing 13000 test runs!Gavaskar faced the best bowling of all and broke batting records.

Posted by Harsh Thakor on (January 29, 2010, 12:15 GMT)

I find it hard to understand the omission of Javed Miandad,Everton Weekes,George Headley and Geoff Boycott.

No opener was more difficult to dismiss than Boycott who very rarely lost his form and dispalyed consistency all over the world,particularly in the West Indies,standing up against the graet battery of pacemen.

Javed Miandad was brilliantly consistent at home and in his peak was more conistent than any Pakistani batsman away like in 1987-1988 in England,India and West Indies.He was neck to neck with Allan Border when the chips were down-perhaps the best batsman in a crisis.

Everton Weekes in his era played more like Sir Don than any batsman at one stage scoring 5 consecutive hundreds!His test scores at his peak were like a Black Bradman batting.

Mark Waugh ,no doubt a class act on his day and posessing talent in the Lara class was nowhere as consistent as his brother Steve.

George Headley was an epitome of consistency-Imagine Bradman was called the White Headley!

Posted by Harsh Thakor on (January 29, 2010, 12:00 GMT)

Jack Hobbs deservingly wins his place because of his outstanding consistency.No batsman displayed such consistency in such a long period-Imagine scoring more than half of his first-class centuries after the first World War!Another deserving selection is Rohan Kanhai,perhaps the most complete batsman of all,who has often not been given his true worth.Clive Lloyd,considering the great consistency he displayed after becong skipper deserves his ranking.Considering they opened the batting Len Hutton and Gavaskar should have even been ranked ahead,close to Sir Jack Hobbs. However it is ridiculous that batsman like Rahul Dravid and Steve Waugh are ranked so low in consistency.Both batsman were champions in a crisis and rarely were out of form.Sachin Tendulkar,should atleast have made the top dozen.Imagine retaining a 54+average crossing 13000 runs!Infact Brian Lara,in comparison suffered from bouts of loss of form. Modern day greats played much more cricket than yesteryear players.

Posted by shaphysics on (March 6, 2009, 21:07 GMT)

I like the spirit of the analysis. However, the CL number proposed here is meaningless.If we were to come up with a number indepepndent of pitch and weather conditions then I would consider suggestions by TomC and Koos van Zyl above as serious suggestions. Personally average only plays role defining whether batsman is recognized specialist or not. I could settle for a simpler critereasuch as shown below:

consistency index = [number of times a batsman crosses a scorde of 40] / [total innings played]

I am ssunming tht a recognized btsman should at least cross a score of 40 to be considered s a recognized batsman.

Posted by shaphysics on (March 6, 2009, 21:07 GMT)

I like the spirit of the analysis. However, the CL number proposed here is meaningless.If we were to come up with a number indepepndent of pitch and weather conditions then I would consider suggestions by TomC and Koos van Zyl above as serious suggestions. Personally average only plays role defining whether batsman is recognized specialist or not. I could settle for a simpler critereasuch as shown below:

consistency index = [number of times a batsman crosses a scorde of 40] / [total innings played]

I am ssunming tht a recognized btsman should at least cross a score of 40 to be considered s a recognized batsman.

Posted by Andrew on (February 26, 2009, 22:51 GMT)

Mark "Audi" Waugh ranked consistent despite the Sri Lanka debacle, but Attapattu has not been able to shrug off his horror start. Presumably he's middling consistency once he actually got going.

This tends to punish batsmen for going on with big scores - MEWaugh never made the massive scores that drag down Bradman to only 2nd place.

Maybe too technical, but how would a "semi-variance" measure go, penalising only for downside scores below the average?

Posted by Jeremy Gilling on (February 17, 2009, 3:09 GMT)

Two surprising omissions from the least consistent (1000 run minimum) table are Ken Rutherford (NZ) and Bill Edrich (England), both of whom had Atapattu-like horror starts to their careers.

Ric's comment: Edrich had an index of 1.18, reasonably high, and Rutherford only 1.06. The latter scored quite consistently in the second half of his career, and with only 3 centuries, had little at the top end to stretch his standard deviation.

Posted by Tom on (February 7, 2009, 17:07 GMT)

Doug Walters on the list of consistent batsmen surprised me; and as much as I loved to watch Doug bat, consistency was not one of the traits he was known for. Therefore, I think some of the criticism regarding exactly what is being measured here needs a look at.

Posted by keyur on (February 3, 2009, 5:50 GMT)

good analysis but i have a few queries regarding it. firstly, i believe notout innings must be excluded. even if a batsman made a unbeaten innings of 50 last time,he does not start his next innings on 50 but on a fresh zero the batting conditions and opposition bowling also vary. further this method punishes those who have streak of notouts & hence notouts should be excluded.admittedly leaving notouts will reduce the avg. as well but as we are measuring consistency it shouldn't make a difference. secondly as has been noted in the very first comment, the CI tends to rise with the no. of innings played or no. of dissmissals. i believe it is easier to maintain consistency over say 50 innings or dismissals than over 200. so to correct this error the consistency index as obtained by you should be further divided by square root of the no. of dissmissals. (i think this is how variance is measured in stats) this will allow fair comparison of all players irrespective of no. of innings played

Ric's comment: I did actually do it ignoring incompleted innings - Hobbs was still top of the 5000+ group, but Bradman dropped, Clive Lloyd was second - Laird dropped to 3rd in the 1000+ group, David Hookes was top - Tendulkar and Gavskar came down to equal Ponting, Lara was still high in the 10000+ group, Kallis was even lower. But I question the validity of doing this - whole slabs of players' careers are ignored, and anyway, does not the common old batting average measure the runs scored between dismissals, rather than in each innings? Given that, I still reckon the way I presented it is the best methodology. Thanks for your input, Keyur!

Posted by Ambuj Saxena on (February 2, 2009, 23:41 GMT)

Interesting analysis, though I do not agree with the procedure. If I were to analyze consistency, I would have used the following formula:

C(X)=Percent of times a batsman scores less than X% of his average.

As you might have noticed, this formula allows for a lot of different standards of consistency measurements. For example, one can measure the C(50) consistency of all batsman, which would be calculating the percent of times each batsman scores less than half of his average. I have not been able to figure out what will be a good value of X for the most objective analysis and I believe this will remain subjective. What I like most about this formula is that it doesn't punish the batsman for scoring big in a few innings. It also doesn't punish the batsman within a few runs of his average, and is universal enough to compare most batsman in a single statistics pool.

Can you please do an analysis based on this formula and share the results.

Ric's comment: I've quickly used your method to determine the percentage of scores below 50% of the Test averages of Ranatunga (consistent in my analysis) and Attapattu (inconsistent), two player who had similar overall averages and aggregates. Ranatunga had 39% of his scores below 50% of his average, while Atapattu had 53%. I suppose this means (on the basis of a very small sample!) that both methods are going to produce more or less the same outcome. With my method though, every single score counts, whereas with yours, all scores below 50% of the average carry the same weight (eg, a duck carries the same weight as a score of 18) while those above it are not taken into account at all. I think your method if applied to all players would produce an interesting point of discussion, but I'm not sure it is as effective in determining overall consistency. Thanks for your input.

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