Factorized Point Process Intensities: A Spatial Analysis of Professional Basketball

TL;DR

This paper introduces a machine learning method using non-negative matrix factorization to analyze and categorize NBA players' shot selection patterns based on spatial data, enabling more precise comparisons and predictions.

Contribution

It presents a novel application of NMF for low-dimensional spatial modeling of NBA shot data, revealing interpretable player types and improving analysis accuracy.

Findings

Low-rank spatial decomposition captures player shooting habits

Discovered spatial representations align with intuitive player types

Method enhances modeling of shooting accuracy and behavior

Abstract

We develop a machine learning approach to represent and analyze the underlying spatial structure that governs shot selection among professional basketball players in the NBA. Typically, NBA players are discussed and compared in an heuristic, imprecise manner that relies on unmeasured intuitions about player behavior. This makes it difficult to draw comparisons between players and make accurate player specific predictions. Modeling shot attempt data as a point process, we create a low dimensional representation of offensive player types in the NBA. Using non-negative matrix factorization (NMF), an unsupervised dimensionality reduction technique, we show that a low-rank spatial decomposition summarizes the shooting habits of NBA players. The spatial representations discovered by the algorithm correspond to intuitive descriptions of NBA player types, and can be used to model other spatial effects, such as shooting accuracy.