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Averages are a good measure of a batsman's calibre, but here's method which attempts to combine big scoring with consistency
April 28, 2006
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.
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.
|Aravinda de Silva||6361||42.98||46.34||0.93|
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.
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.
S Rajesh is stats editor of Cricinfo. For the stats, he was helped by Travis Basevi.Feeds: S Rajesh
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