Cricket averages have for long been a point of contention. They place, for instance, Michael Bevan (53.58) above Sachin Tendulkar (44.05) in one-dayers. Now, two Indian actuaries, who assess risk for insurance companies, have devised a method to better calculate averages and will soon take their finding to the International Cricket Council (ICC).
Their findings have appeared in a paper published in a recent issue of Actuary, a journal for actuaries as the name indicates, and have been reported in the latest issue of The Economist.
Sanchit Maini, who recently moved to BNP Paribas in Paris, and Sumit Narayanan thought the prevalent method of calculating averages—dividing total runs by total innings in which the batsman was out—did not take into account the number of balls the player faced in unbeaten (not-out) innings. This led to inflated averages for lower-order batsmen, who come in to bat late in the innings and, because there are fewer overs left to play, are not-out more frequently than top-order batters.
“We’d look at Michael Bevan’s average and think that he was good, but not that good,” says Narayanan, a consultant at Watson Wyatt, Singapore. Narayanan follows the game closely: “What did you expect? I’m Indian”, he says.
“It just so happened that I was reading about ‘exposure to risk’. It struck us that if we could determine the exposure to risk of a batsman, we could use that to calculate averages,” adds Narayanan. Exposure to risk is a fundamental principle of actuarial science, and looks at the amount of risk a person is exposed to.
The article in Actuary notes that each innings of a player contributes to his exposure, “and the fact that a batsman ends up being not out at the end of the innings does not indicate that the exposure was zero, since the player has had the opportunity to score runs in that innings.”
According to the new method, if a not-out batsman has played fewer balls than his own average (number of balls faced on an average in his career) up till that game, it is not counted as a not-out. For instance, if a cricketer has played 10 innings, facing an average of 41 balls in each innings, and remained not-out in four, but faced at least 41 balls in only one of these four innings, then he is counted as having been out in three of his ‘not-out’ innings. His average will fall because his score in this 10 innings will now be divided by nine (the number of innings in which he is considered out), and not six as it would have otherwise been.
The effect of this is dramatic. Bevan, who was not-out 67 times in 196 innings, sees his average fall from 53.58 to 38.7. Tendulkar’s average reduces by 3.8 to 40.2.
Of the seven batsmen worst affected by the new methodology, five are Australians, including two in the current team, Michael Clarke and Andrew Symonds.
Revealingly, when the inflation has been accounted for among the batsmen used as examples in the study, Vivian Richards comes out on top, followed by Tendulkar and Ricky Ponting.
Not for Tests
The method is less suited to Tests because this format of the game, unlike the one-day version, is played over a significant amount of time. “Tests would not have such a bigger variant in results because you play for a longer time and are not-out less often,” says Narayanan.
“We actually did this a long time ago,” says Maini. “We came out with the method during the last World Cup, but never did any stats. We couldn’t get the data, but knew intuitively what the method should be. Then when this World Cup came around, we just thought we should get it out there.”
BATTING AVERAGES A FLAWED FORMULA? (Graphic)