  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.
