Rao-Blackwellizing Field Goal Percentage

TL;DR

This paper introduces a new shot-make probability estimator for NBA players that uses spatiotemporal tracking data and Rao-Blackwellization to reduce variance and improve the accuracy of shooting skill measurement.

Contribution

It proposes a novel Rao-Blackwellized estimator for field goal percentage that incorporates shot trajectory data to better assess player shooting skill.

Findings

RB-FG% outperforms raw FG% in predicting 3-point and true-shooting percentages.

Conditioning on shot trajectory data stabilizes shooting skill inference.

Potential to estimate shooting statistics earlier in the season.

Abstract

Shooting skill in the NBA is typically measured by field goal percentage (FG%) - the number of makes out of the total number of shots. Even more advanced metrics like true shooting percentage are calculated by counting each player's 2-point, 3-point, and free throw makes and misses, ignoring the spatiotemporal data now available (Kubatko et al. 2007). In this paper we aim to better characterize player shooting skill by introducing a new estimator based on post-shot release shot-make probabilities. Via the Rao-Blackwell theorem, we propose a shot-make probability model that conditions probability estimates on shot trajectory information, thereby reducing the variance of the new estimator relative to standard FG%. We obtain shooting information by using optical tracking data to estimate three factors for each shot: entry angle, shot depth, and left-right accuracy. Next we use these factors to model shot-make probabilities for all shots in the 2014-15 season, and use these probabilities to produce a Rao-Blackwellized FG% estimator (RB-FG%) for each player. We demonstrate that RB-FG% is better than raw FG% at predicting 3-point shooting and true-shooting percentages. Overall, we find that conditioning shot-make probabilities on spatial trajectory information stabilizes inference of FG%, creating the potential to estimate shooting statistics earlier in a season than was previously possible.