A Model-Based Approach to Shot Charts Estimation in Basketball

TL;DR

This paper introduces a model-based method for estimating and visualizing basketball shot charts that accounts for court boundaries, improving accuracy in shot density and success probability estimations.

Contribution

The authors develop a Gaussian mixture model approach that explicitly incorporates court boundaries, enhancing shot chart accuracy over traditional methods.

Findings

More accurate shot density estimations near court boundaries.

Effective probability estimates for successful shots from any location.

Application to NBA data demonstrates practical utility.

Abstract

Shot charts in basketball analytics provide an indispensable tool for evaluating players' shooting performance by visually representing the distribution of field goal attempts across different court locations. However, conventional methods often overlook the bounded nature of the basketball court, leading to inaccurate representations, particularly along the boundaries and corners. In this paper, we propose a novel model-based approach to shot chart estimation and visualization that explicitly considers the physical boundaries of the basketball court. By employing Gaussian mixtures for bounded data, our methodology allows to obtain more accurate estimation of shot density distributions for both made and missed shots. Bayes' rule is then applied to derive estimates for the probability of successful shooting from any given locations, and to identify the regions with the highest expected scores. To illustrate the efficacy of our proposal, we apply it to data from the 2022-23 NBA regular season, showing its usefulness through detailed analyses of shot patterns for two prominent players.