# A Bayesian marked spatial point processes model for basketball shot chart

## TL;DR

This paper introduces a Bayesian joint model for analyzing basketball shot charts, capturing the relationship between shot success rate and shot locations, and applies it to NBA players to uncover patterns and groupings.

## Contribution

It develops a novel Bayesian marked spatial point process model that jointly models shot intensity and success, with a comprehensive application to NBA player data.

## Key findings

- Shot success rate is positively associated with shot intensity for most players.
- The model effectively captures spatial variation in shot success and intensity.
- Players can be clustered based on their shot patterns and success rates.

## Abstract

The success rate of a basketball shot may be higher at locations where a player makes more shots. For a marked spatial point process, this means that the mark and the intensity are associated. We propose a Bayesian joint model for the mark and the intensity of marked point processes, where the intensity is incorporated in the mark model as a covariate. Inferences are done with a Markov chain Monte Carlo algorithm. Two Bayesian model comparison criteria, the Deviance Information Criterion and the Logarithm of the Pseudo-Marginal Likelihood, were used to assess the model. The performances of the proposed methods were examined in extensive simulation studies. The proposed methods were applied to the shot charts of four players (Curry, Harden, Durant, and James) in the 2017--2018 regular season of the National Basketball Association to analyze their shot intensity in the field and the field goal percentage in detail. Application to the top 50 most frequent shooters in the season suggests that the field goal percentage and the shot intensity are positively associated for a majority of the players. The fitted parameters were used as inputs in a secondary analysis to cluster the players into different groups.