Estimation of the batting ability of South African international one-day cricket players

Abstract

It is shown that the international method of estimating a batsman’s ability by the average number of runs per completed innings, i.e. the total number of runs divided by the number of out innings, follows from the assumption that the scores follow an exponential distribution. The more general gamma and Weibull distributions are better representatives of the scores and are more satisfactory because not out scores are treated in a more sensible way. Estimates are made for the South African international one-day players based on data up to the end of August 2000. It is found that Klusener is the best batsman with an estimated average markedly higher than that of Kirsten, although according to the usual method their averages are approximately the same. The Weibull distribution is recommended as a very suitable model.