What Influences the Field Goal Attempts of Professional Players? - Analysis of Basketball Shot Charts via Log Gaussian Cox Processes with Spatially Varying Coefficients

Oct 13, 2026

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Basketball shot charts reveal spatiotemporal patterns in performance, showing where professional players attempt shots and whether they succeed. The study models shot locations and outcomes as a marked spatiotemporal point process, capturing spatially dependent structure across multiple games. A Bayesian log Gaussian Cox process is developed with a hierarchical log intensity built on Gaussian processes. Spatially varying covariates target spatial relative risk. Posterior inference uses an MCMC kernel-convolution approach, validated through simulation, then applied to NBA legends Stephen Curry, LeBron James, and Michael Jordan to improve shooting strategy under varying conditions.

LanguageEnglish

CategoryGeneral

FormatPDF

Pages35

Reading Time12 min

AccessFree to download

Abstract

Introduction

Background: sports analytics and basketball shot data

Prior work: spatial point processes and spatial regression

Motivating data sets and covariates

arXiv :2503 .02137v1 [ stat .ME] 4 Mar 2025 What Influences the Field Goal Attempts of Professional Players? Analysis of Basketball Shot Charts via Log Gaussian Cox Processes with Spatially Varying Coefficients Jiahao Cao, Qingpo Cai, Lance A. Waller, DeMarc A. Hickson, Guanyu Hu, and Jian Kang ∗ March 5, 2025 Abstract Basketball shot charts provide valuable information regarding local patterns of ingame performance to coaches, players, sports analysts, and statisticians. The spatial patterns of where shots were attempted and whether the shots were successful suggest options for offensive and defensive strategies as well as historical summaries of performance against particular teams and players. The data represent a marked spatiotemporal point process with locations representing locations of attempted shots and an associated mark representing the shot’s outcome (made/missed) . Here, we develop a Bayesian log Gaussian Cox process model allowing joint analysis of the spatial pattern of locations and outcomes of shots across multiple games. We build a hierarchical model for the log intensity function using Gaussian processes, and allow spatially varying effects for various game-specific covariates. We aim to model the spatial relative risk under different covariate values. For inference via posterior simulation, we design a Markov chain Monte Carlo (MCMC) algorithm based on a kernel convolution approach. We illustrate the proposed method using extensive simulation studies. A case study analyzing the shot data of NBA legends Stephen Curry, LeBron James, and Michael Jordan highlights the effectiveness of our approach in real-world scenarios and provides practical insights into optimizing shooting strategies by examining how different playing conditions, game locations, and opposing team strengths impact shooting efficiency. Keywords: Bayesian Computing, Spatial Point Process, Spatial Relative Risk, Sports Analytics ∗ Jiahao Cao and Qingpo Cai are joint first authors. Guanyu Hu and Jian Kang are joint corresponding authors 1 Introduction In recent years, there has been a growing interest in the quantitative analysis of sports data, reflecting the expanding role of analytics in shaping decisions within the sports industry. For instance, national polls rank teams in college football and influence selections for post-season bowl games and championship playoffs. The abundance of data related to various aspects of sports has not only impacted coaching strategies—ranging from optimizing salary caps to in-game decision-making—but also highlighted discrepancies between perceived and actual risks under different play conditions. Sports data have become a valuable resource in introductory statistics courses and have spurred the development of specialty conferences and publications. For example, the annual MIT Sloan Sports Analytics Conference (SSAC) provides a platform for industry professionals, researchers, students, and enthusiasts to explore the growing influence of analytics in sports. In basketball, particularly in the National Basketball Association (NBA), statistical methods (Sampaio and Janeira 2003, Kubatko et al. 2007, Nikolaidis 2015, Cervone et al. 2016) have long been utilized to inform game strategies. Coaches frequently analyze shot data for game preparation and in-game adjustments, with halftime analyses often featuring displays of shot locations and outcomes. While basic statistical techniques offer some insights, the complexity of shot data patterns presents an opportunity for more sophisticated analyses, driving advances in the rapidly evolving field of sports analytics (Albert et al. 2017) . An early approach to modeling basketball short chart data through spatial point processes appears in a technical report by Hickson et al. (2003), analyzing shot charts from Michael Jordan during the 2001–2002 NBA season at the Washington Wizards, following his second return from retirement to active play. Th

FAQs

What data structure does the model use for basketball shots?

Shots are treated as a marked spatiotemporal point process, where locations represent where shots are attempted and the mark represents made vs. missed outcomes.

How does the proposed Bayesian log Gaussian Cox process contribute to the analysis?

It enables joint modeling of the spatial pattern of shot locations and shot outcomes across multiple games, using a hierarchical log intensity constructed with Gaussian processes and spatially varying effects for game-specific covariates.

How is inference performed in the proposed method?

Posterior simulation is carried out using an MCMC algorithm based on a kernel convolution approach.

Oct 13, 2026

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