Bayesian survival analysis of batsmen in Test cricket

Abstract

Cricketing knowledge tells us batting is more difficult early in a player's innings but becomes easier as a player familiarizes themselves with the conditions. In this paper, we develop a Bayesian survival analysis method to predict the Test Match batting abilities for international cricketers. The model is applied in two stages, firstly to individual players, allowing us to quantify players' initial and equilibrium batting abilities, and the rate of transition between the two. This is followed by implementing the model using a hierarchical structure, providing us with more general inference concerning a selected group of opening batsmen from New Zealand. The results indicate most players begin their innings playing with between only a quarter and half of their potential batting ability. Using the hierarchical structure we are able to make predictions for the batting abilities of the next opening batsman to debut for New Zealand. Additionally, we compare and identify players who excel in the role of opening the batting, which has practical implications in terms of batting order and team selection policy.

Modelling Career Trajectories of Cricket Players Using Gaussian Processes

“…In this paper, we extend the Bayesian parametric model detailed in [16], such that we can not only measure and predict how player batting abilities fluctuate during an innings, but also between innings, over the course of entire playing careers. This allows us to treat batting form as continuous, rather than binary; instead of defining players as 'in' or 'out' of form, we can describe players as improving or deteriorating in terms of batting ability.…”

“…Therefore, the model contains the set of parameters θ = {µ 1 , {µ 2 t }, L, m, σ , }. The model structure with respect to parameters µ 1 , L, C and D follows the model specification detailed in [16], with the parameters assigned the following prior distributions. (1,5) log(µ 2 t ) ∼ Gaussian process(m, K(X i , X j ; σ , )) m ∼ Lognormal(log(25), 0.75 2 ) σ ∼ Exponential (10) ∼ Uniform(0, 100)…”

“…The authors use a Bayesian parametric model to estimate the hazard function, allowing for a smooth transition in estimated dismissal probabilities between scores, rather than the sudden, unrealistic jumps seen in [12] and to a lesser extent [5]. For the vast majority of past and present international Test players, [16] found overwhelming evidence to suggest that players perform with decreased batting abilities early in an innings and improve as they score runs, further supporting the notion of 'getting your eye in'.…”

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

“…Motivated by the concept of getting your eye in, Brewer (2008) and Stevenson and Brewer (2017) proposed an alternative means of measuring how a player’s batting ability varies during an innings. Unlike previous studies, a Bayesian parametric model was used to model the hazard function, allowing for a smooth transition in estimated dismissal probabilities between scores, which in the context of batting in cricket, are more realistic than the erratic jumps observed in Kimber and Hansford (1993) and to a lesser extent Cai et al.…”

Determining spatio-temporal metrics that distinguish play outcomes in field hockey

“…Nevo and Ritov (2013) used survival analysis to inform a time-dependent model to estimate the likelihood of a second goal when the time of the first goal is known. Stevenson & Brewer (2017) also show an example of using survival analysis to model the progress of batting ability through a cricket Test Match. Survival analysis has similarly been used to investigate the relationship between subsequent substitutions (Del Corral et al 2008).…”