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ESPNcricinfo's stats editor S Rajesh looks at the stories behind the stats

The Friday column

The most consistent and prolific batsman of all

Averages are a good measure of a batsman's calibre, but here's method which attempts to combine big scoring with consistency

S Rajesh

April 28, 2006

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Jacques Kallis: scores big, and scores all the time © Getty Images

When comparing different batsmen, the statistic that is invariably brought out is the batting average. It is a fair enough indicator of a batsman's ability too, for it suggests the number of runs he scores per dismissal - Brian Lara makes 53 runs per dismissal to Ramnaresh Sarwan's 40, hence Lara is clearly a superior batsman, even without giving him extra points for grace, elegance, and all other factors which can't be measured in statistical terms. The method is also easy to calculate and understand, another criterion so essential for widespread acceptance.

While the efficacy of averages is inarguable, it has its limitations. For instance, it doesn't tell us the consistency levels of a player: a batsman who scores 0, 200, 25 has exactly the same average - 75 - as one who makes 70, 80, 75, though it's obvious which one of the two has been more consistent.

Enter a statistical tool called the standard deviation. As the name suggests, this method indicates how much a sequence of numbers deviates from its average. (For those interested in how standard deviation is calculated, click here, but broadly, it culls out the difference between each entry and the mean of the sequence, and then averages it out.) In the two run-sequences given earlier, for example, the second one has a standard deviation of just 4.08, while for the first, it's a whopping 88.98.

You'd obviously want greater consistency from a batsman, but check this sequence out: 16, 15, 17, 20, 22, 14, 18. Mr X is obviously extremely consistent - the standard deviation is only 2.61 - but at an average of 17.43, he isn't doing much to help the cause of his team. (Marvan Atapattu was consistency personified in his first six innings, but Sri Lanka will surely take his current version over his earlier one.)

A meaningful stat, then, is one which combines batting averages - for that is an indication of the sheer volume of runs he scores each time he bats - with a consistency index which measures how much he deviates from his average score. For the purpose of this exercise, the batting average has been divided by the standard deviation to arrive at an index. Intuitively, it's a fair measure, for it offers a batsman with a higher average more leeway to be inconsistent: Don Bradman, for instance, had a standard deviation of nearly 87, easily the highest among all batsmen with at least 3000 runs, but that's offset by a staggering average of 99.94.

One limitation of the method is that all not-out innings have also been considered when calculating the standard deviation, though strictly speaking, an innings of, say, 4 not out should not count against a batsman's consistency. However, such instances are relatively few for most batsmen and hence don't affect the numbers significantly.

The table below lists the ones with the most favourable batting index for players with at least 5000 Test runs, and it's interesting to see the ones who make the cut. On top of the ranking is Jacques Kallis, the batting machine from South Africa. The batsmen in the top ten are all those who, not surprisingly, are well known for their consistency, along with their run-scoring ability.

Highest batting index (Qual: 5000 Test runs)
Batsman Runs Average SD Batting index
(Average/ SD)
Jacques Kallis 7940 56.31 44.54 1.26
Allan Border 11,174 50.56 40.49 1.25
Ken Barrington 6806 58.67 47.36 1.24
Jack Hobbs 5410 56.95 46.68 1.22
Arjuna Ranatunga 5105 35.70 29.44 1.21
Graham Thorpe 6744 44.66 37.22 1.20
Shivnarine Chanderpaul 6230 44.82 38.27 1.17
Don Bradman 6996 99.94 86.65 1.15
Geoff Boycott 8114 47.73 41.57 1.15
Steve Waugh 10,927 51.06 44.51 1.15

Steve Waugh just about manages to squeeze into the list, but what might be just a little more startling is that Mark Waugh, supposedly the more flamboyant and inconsistent of the two, follows him very closely in 11th place, with an index of 1.14, marginally ahead of the likes of Ricky Ponting (1.13), Rahul Dravid (1.12), Adam Gilchrist and Sourav Ganguly (both 1.10). Two other modern giants follow close behind - Inzamam-ul-Haq manages an index of 1.07, while Sachin Tendulkar has 1.03, both slightly better than two stalwarts from the 1980s, Sunil Gavaskar and Viv Richards (both 1.02, rounded off to the second decimal).

Of the 66 players who make the 5000-run cut, 46 of them have a batting index greater than 1. So which are the great names whose consistency isn't so great? Topping that chart is a player who was briefly mentioned earlier in the piece: Atapattu has six double-centuries, and yet averages 38.90, and the inconsistency those numbers suggest duly comes through, with an index of just 0.77. Lara, with his tendency to alternate between the sublime and the ordinary, is among the top five as well.

Lowest batting index (Qual: 5000 Test runs)
Batsman Runs Average SD Batting index
(Average/ SD)
Marvan Atapattu 5330 38.91 50.40 0.77
Zaheer Abbas 5062 44.80 54.00 0.83
Sanath Jayasuriya 6613 41.59 48.85 0.85
Brian Lara 11,294 53.02 62.24 0.85
Ian Botham 5200 33.55 36.68 0.91
Herschelle Gibbs 5599 44.79 48.73 0.92
Aravinda de Silva 6361 42.98 46.34 0.93
Graham Gooch 8900 42.58 45.69 0.93
Martin Crowe 5444 45.37 48.03 0.94
Stephen Fleming 6200 38.75 40.85 0.95

Let's now lower the bar to 3000 runs and look for consistency alone. How many would have guessed that Shaun Pollock would have had the lowest standard deviation among this group? In fact, the top six are all lower middle order batsmen who have consistently bailed their teams out in crises. Their averages aren't so impressive, but the standard deviations indicate just how consistently they have performed.

The six most consistent ones (Qual: 3000 Test runs)
Batsman Runs Average SD
Shaun Pollock 3406 31.25 23.44
Rodney Marsh 3633 26.52 25.91
Richard Hadlee 3124 27.17 26.31
Mark Boucher 3357 29.97 26.65
Ian Healy 4356 27.40 26.69
Jeff Dujon 3322 31.94 29.01

And for who have been clamouring about Tendulkar's inconsistency of late, here's confirmation: as against a career index of 1.03, over the last four years the corresponding figure has fallen to 0.87. Among batsmen with at least 2000 runs since 2002, this is among the lowest.

Lowest batting index since 2002 (Qual: 2000 Test runs)
Batsman Runs Average SD Batting index
Stephen Fleming 2302 41.11 53.56 0.77
Marvan Atapattu 2292 40.93 50.32 0.81
Brian Lara 4073 58.19 70.90 0.85
Virender Sehwag 3474 52.64 63.81 0.82
Kumar Sangakkara 3059 47.80 55.82 0.86
Chris Gayle 3132 42.32 46.16 0.86
Sachin Tendulkar 3050 50.00 57.18 0.87
Graeme Smith 3735 49.14 54.85 0.90

S Rajesh is stats editor of Cricinfo. For the stats, he was helped by Travis Basevi.

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S Rajesh Stats editor Every week the Numbers Game takes a look at the story behind the stats, with an original slant on facts and figures. The column is edited by S Rajesh, ESPNcricinfo's stats editor in Bangalore. He did an MBA in marketing, and then worked for a year in advertising, before deciding to chuck it in favour of a job which would combine the pleasures of watching cricket and writing about it. The intense office cricket matches were an added bonus.

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