Measuring batting consistency and comparing batting greats in test cricket: innovative applications of statistical tools

Abstract

This paper examines the intriguing problem of comparing great batsmen in test cricket across different eras. Traditional method of calculating a batsman抯 batting average may be justified under the assumption that runs scored in various complete and incomplete innings by a batsman form a random sample from an exponential or a geometric distribution. This assumption, however, leads to undesirably having batting inconsistency or standard deviation uniquely determined by the batting mean. To correct this drawback, we propose use of the Weibull distribution model. First, the Weibull model is seen to provide a far superior fit to the test cricket data of our study. Second, the maximum likelihood estimate (MLE) of the batting standard deviation is found to provide a very sensible estimate of batting inconsistency. Third, the resulting MLE of the batting mean in case of Bradman turns out to be 109.42 instead of 99.94. Fourth, we define player longevity as a third criterion and introduce an index for quality-runs scored as a function of opposition strength and another measure for diversity of opponent teams encountered by a player. Fifth, the Mahalanobis distance is used for overall ranking of a select group of batting greats on the basis of various combinations of these five criteria, without assigning any subjective weights to them. Finally, multivariate statistical outlier detection technique affirms two players as truly outstanding桞radman for his batting average and quality of runs scored, and Tendulkar for his longevity and opposition diversity he faced. The proposed techniques used here may easily be applied in sports management for ranking players available for procurement and in investment management for rating various financial assets.