On the Ranking of Test Match Batsmen

Abstract

Summary 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.

Finding Your Feet: A Gaussian Process Model for Estimating the Abilities of Batsmen in Test Cricket

“…The Gaussian process model rewards players who are able to get their eye in and remain on a not out out score, while the ICC ratings simply provide not out innings with a ‘bonus’ that we suspect is too low. In this sense, we agree with Boys and Philipson (2019), that the ICC rating system does not appropriately adjust for not out scores in a manner that takes account of player ability.…”

“…Similar to the approach used in Boys and Philipson (2019), the model output also allows us to quantify a player’s batting ability, in terms of a batting average, at their ‘lowest’ and ‘highest’ points of their career to date. We are also able to predict the number of runs we expect them to score in their next career innings.…”

“…The approach taken in Boys and Philipson (2019) overcomes these issues with the ICC ratings. In this study, the authors fit a Poisson random effects model to estimate the age at which individual players would reach their peak batting ability.…”

“…A preliminary version of this model was presented in Stevenson and Brewer (2018). Similar to Boys and Philipson (2019), the model estimates a player’s ability in terms of an expected number of runs to be scored in an innings and provides a more accurate quantification of an individual’s ability at any point of their career than traditional cricket metrics, such as the batting average. This allows us to treat batting form as continuous rather than binary; instead of defining players as being in or out of form, we can describe them as improving or deteriorating in terms of ability.…”

Age-related changes in the performance of bowlers in Test match cricket

“…No consideration of individual performance in cricket is complete without a discussion of rankings. Such discussions are often complicated by the need to draw comparisons across different eras, 72 however, the multivariate methods used in this study provide one such means of ranking Test match bowlers after having statistically controlled for temporal changes in the quality of the team and the opposition, alongside other confounding variables. If anything, the inclusion of a group-level 'random' effect of the Test playing nation in interaction with the decade will slightly devalue players from the best-performing teams through time.…”