Bayesian group learning for shot selection of professional basketball players

Abstract

In this paper, we develop a group learning approach to analyze the underlying heterogeneity structure of shot selection among professional basketball players in the NBA. We propose a mixture of finite mixtures (MFM) model to capture the heterogeneity of shot selection among different players based on the Log Gaussian Cox process (LGCP). Our proposed method can simultaneously estimate the number of groups and group configurations. An efficient Markov Chain Monte Carlo (MCMC) algorithm is developed for our proposed model. Simulation studies have been conducted to demonstrate its performance. Finally, our proposed learning approach is further illustrated in analyzing shot charts of selected players in the NBA's 2017-2018 regular season. KEYWORDSbasketball shot charts, heterogeneity pursuit, log gaussian cox process, mixture of finite mixtures, nonparameteric bayesian INTRODUCTIONIn basketball data analytics, one primary problem of research interest is to study how players choose the locations to make shots. Shot charts, which are graphical representations of players' shot location selections, provide important summary of information for basketball coaches as well as teams' data analysts, as no good defense strategies can be made without understanding the shot selection habits of players in the rival teams.Shot selection data have been discussed from different statistical perspectives. Reich, Hodges, Carlin, and Reich (2006) developed a spatially varying coefficients model for shot-chart data, where the court is divided into small regions and the probability of making a shot in these zones is modeled using the multinomial logit approach. Recognizing the random nature of shot location selection, Miller et al. (2014) analyzed the underlying spatial structure among professional basketball players based on spatial point processes. Franks, Miller, Bornn, and Goldsberry (2015) combined spatial and spatio-temporal processes, matrix factorization techniques, and hierarchical regression models for characterizing the spatial structure of locations for shot attempts. In spatial point processes, locations for points are assumed random and are regarded as realizations of a process governed by an underlying intensity. Spatial point processes are well discussed in many statistical literatures, such as the Poisson process (Geyer, 1998), the Gibbs process (Goulard, Särkkä, & Grabarnik, 1996), and the Log Gaussian Cox process (LGCP Møller, Syversveen, & Waagepetersen, 1998). In addition, they have been applied to different areas, such as ecological studies (Jiao, Hu, & Yan, 2020;Thurman, Fu,

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