Analysis of professional basketball field goal attempts via a Bayesian matrix clustering approach

Abstract

We propose a Bayesian nonparametric matrix clustering approach to analyze the latent heterogeneity structure in the shot selection data collected from professional basketball players in the National Basketball Association (NBA). The proposed method adopts a mixture of finite mixtures framework and fully utilizes the spatial information via a mixture of matrix normal distribution representation. We propose an efficient Markov chain Monte Carlo algorithm for posterior sampling that allows simultaneous inference on both the number of clusters and the cluster configurations. We also establish large sample convergence properties for the posterior distribution. The excellent empirical performance of the proposed method is demonstrated via simulation studies and an application to shot chart data from selected players in the 2017 18 NBA regular season.