Modelling Career Trajectories of Cricket Players Using Gaussian Processes

Abstract

In the sport of cricket, variations in a player's batting ability can usually be measured on one of two scales. Short-term changes in ability that are observed during a single innings, and long-term changes that are witnessed between matches, over entire playing careers. To measure long-term variations, we derive a Bayesian parametric model that uses a Gaussian process to measure and predict how the batting abilities of international cricketers fluctuate between innings. The model is fitted using nested sampling given its high dimensionality and for ease of model comparison. Generally speaking, the results support an anecdotal description of a typical sporting career. Young players tend to begin their careers with some raw ability, which improves over time as a result of coaching, experience and other external circumstances. Eventually, players reach the peak of their career, after which ability tends to decline. The model provides more accurate quantifications of current and future player batting abilities than traditional cricketing statistics, such as the batting average. The results allow us to identify which players are improving or deteriorating in terms of batting ability, which has practical implications in terms of player comparison, talent identification and team selection policy.

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

“…The derivation of the model likelihood for a single innings follows the method detailed in Brewer (2008) and Stevenson and Brewer (2017, 2018). If X ∈ {0, 1, 2, 3,…} is the number of runs a batsman scores in a particular innings, we define a hazard function , H ( x ) ∈ [0,1], as the probability a batsman gets out on score x , that is, H ( x ) = P ( X = x | X ≥ x ).…”

“…A number of covariance functions are available to choose from, depending on how much we wish to allow player ability to fluctuate between innings. A common choice is the squared exponential covariance function, which was the choice of covariance function in Stevenson and Brewer (2018). However, we have since determined that the squared exponential function does not allow for enough short‐term variation in ability between innings since it implies smooth functions with high prior probability.…”

“…Our proposed model builds on those detailed in Stevenson and Brewer (2017), such that we can not only measure and predict how a player’s batting abilities fluctuate in the short‐term, during an innings, but also in the long‐term, between innings, over the course of entire playing careers. 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.…”

Comparative analysis of top Test batsmen before and after 20th century

“…With thisa new model of batting average was developed which suggested that Geometric distributions come into play and in which number of not outs also play a vital role.Inthe context of geometric distributions, batting consistency is also which mattered a lot while evaluating player performance (12) . Moreover, to measure batsmen performance and consistency a new gaussian model was developed, which measured fluctuations between the innings played by a batsman in different matches (13) . On the same lines, gaussian model which takes cricket statistics into consideration, was developed which was used to assess batsmen performance in the longest form of cricket i.e.…”

Classification of All-Rounders in the Game of ODI Cricket: Machine Learning Approach

“…In an attempt to rank all-rounders in test cricket, Tan and Ramachandran (2010) utilized both batting and bowling statistics to devise a mathematical formula. In another study, Stevenson and Brewer (2019) derived a Bayesian parametric model to predict how international cricketers' abilities change between innings in a game. Furthermore, Christie (2012) researched physical requirements of fast bowlers and stated the necessity of physiological demands to evaluate bowlers' performances.…”