On the ranking of Test match batsmen

Ranking sportsmen whose careers took place in different eras is often a contentious issue and the topic of much debate. We focus on cricket and examine what conclusions may be drawn about the ranking of test batsmen by using data on batting scores from the first test in 1877 onwards. The overlapping nature of playing careers is exploited to form a bridge from past to present so that all players can be compared simultaneously, rather than just relative to their contemporaries. The natural variation in runs scored by a batsman is modelled by an additive log-linear model with year, age and cricket-specific components used to extract the innate ability of an individual cricketer. Incomplete innings are handled via censoring and a zero-inflated component is incorporated in the model to allow for an excess of frailty at the start of an innings. The innings-by-innings variation of runs scored by each batsman leads to uncertainty in their ranking position. A Bayesian approach is used to fit the model and realizations from the posterior distribution are obtained by deploying a Markov chain Monte Carlo algorithm. Posterior summaries of innate player ability are then used to assess uncertainty in ranking position and this is contrasted with rankings determined via the posterior mean runs scored. Posterior predictive checks show that the model provides a reasonably accurate description of runs scored.