Adam Slivinsky - Nonparametric NBA Shot Inference

Bayesian Nonparametric Mixture Modeling for NBA Shot Data

Post Date: 11/18/2024

In the last quarter of my undergraduate education, I took a course on Bayesian Nonparametrics, and to demonstrate what I learned, I implemented a project making inference on NBA shot chart data. This data is publicly available, and the goal is to estimate a player's shooting tendencies, in terms of where they are likely to shoot, and how likely they are to make a shot given its location. These two items are highly correlated: If a player makes a lot of shots from one location on the court, they are more likely to take shots from that area in the future. Ideally, any model making inference on this data can account for this dependence.

The model I used came from the paper Mixture Modeling for Marked Poisson Processes, by Athanasios Kottas and Matthew A. Taddy. The paper describes Bayesian Nonparametric models that are fitting to model marked point processes, and can incorporate the above-described dependence. We assume that shot charts follow a Non-homogeneous Marked Poisson Point Process (Parametric assumption here):

The intensity function, which for NBA shot chart data is a joint intensity for both shot locations and makes/misses, can be modeled nonparametrically with a Dirichlet Process mixture model:

A blocked Gibbs sampler is derived and implemented, and we arrive at posterior inference for any given set of shot locations and makes/misses. I applied this model to a few notable NBA player-seasons of data, which include all of a player's shot chart data from an individual season.

I decided to study Kobe Bryant's '05-'06 player-season data (The year he scored > 35 PPG over 80 GP), Steph Curry's '15-'16 unanimous-MVP player-season data, and Nikola Jokic's '21-'22 player-season data (Back-to-back MVP).

To show the inference on these player-seasons, I first show the shot chart data, along with the posterior intensity surface for how likely a player is to take a shot from every on-court location:

Next, I show a plot describing the posterior probability a shot is made given on-court location. Instead of just plotting the shot make probability, I instead multiply each shot make probability by 2 or 3, depending on if it was a 2pt or 3pt shot attempt. This allows us to derive the posterior expected points from any on-court location, which can then be compared to the league average points per possession. If the posterior expected points is higher than the league average, then we can infer this is an efficient shot location (ignoring all in-game factors). Below, any area in green represents shots taken from this area are above league average expected points, and any area in pink is below. The legend below, and the distinct outline of the 3pt line in the plots reflect this fact.

From here, differences between player tendencies can be examined and discussed using NBA intuition. This post is designed to attract interest towards this project, and show the success of the model towards interesting plots. A full discussion of posterior inference results can be found in the paper here (Also linked below).

The code implementing the blocked Gibbs sampler and generating posterior plots can be found here.

Bayesian Nonparametric Mixture Modeling for NBA Shot Data.pdf