January 30, 2009

A consistency index for batsmen

A stats analysis to measure the consistency of Test batsmen

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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