Statistics Lesson with Cricket

Interesting article from The Economist on cricket's maths;

CRICKET is a game dominated by statistics. The ultimate measure of a batsman's worth is his average: the total number of runs he has scored divided by the number of times he has been out. In the case of Sir Donald Bradman, Australia's most famous batsman, this reached near perfection: a fraction under 100 runs per innings over a 20-year international career.

But batting averages can be distorted by a quirk—innings in which the batsman is not out are included in the total but excluded from the divisor. Occasionally, this can produce bizarre results. During the 1953 season for example, a complete duffer called Bill Johnston also managed an average of 100, thanks to being dismissed just once in 17 innings.

Now two actuaries have diverted their attention from falling mortality rates to devise a system that eliminates this perversity. Sanchit Maini and Sumit Narayanan base their idea on the number of balls faced in an innings. If a batsman comes in and survives one ball unvanquished, only for the team's innings to end, it says little either way about his scoring ability. If he bats for a long time, though, it does. So Mr Maini and Mr Narayanan propose, in the latest edition of the Actuary, that a not-out innings should sometimes count in the divisor—thus reducing a batsman's average compared with the traditional method of calculation—but only if the number of balls he faced in that innings is greater than the average for his career.

When averages for one-day international matches are recalculated using this system, batsmen from the top of the order, such as Brian Lara, a recently retired West Indian genius, barely suffer. Such men normally bat early, in order to give them the opportunity to score the maximum number of runs, and also to tire out the bowlers so that weaker batsmen who come in later on still have a chance. They rarely survive the whole innings without being dismissed. The biggest reductions in average are suffered by those who start batting near the end of an innings and are thus more likely to remain when it closes. English cricket fans will be delighted to learn that in the group of one-day batsmen examined by Mr Maini and Mr Narayanan, five of the seven to suffer most are Australian. Now if only actuaries can find a way to revise away England's 5-0 winter defeat by the colonials...

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