A truncated mean-parameterised Conway-Maxwell-Poisson model for the analysis of Test match bowlers

Assessing the relative merits of sportsmen and women whose careers took place far apart in time via a suitable statistical model is a complex task as any comparison is compromised by fundamental changes to the sport and society and often handicapped by the popularity of inappropriate traditional metrics. In this work we focus on cricket and the ranking of Test match bowlers using bowling data from the first Test in 1877 onwards. A truncated, mean-parameterised Conway-Maxwell-Poisson model is developed to handle the under- and overdispersed nature of the data, which are in the form of small counts, and to extract the innate ability of individual bowlers. Inferences are made using a Bayesian approach by deploying a Markov Chain Monte Carlo algorithm to obtain parameter estimates and confidence intervals. The model offers a good fit and indicates that the commonly used bowling average is a flawed measure.