Rao-Blackwellizing Field Goal Percentage in the NBA

• Activity Number: 435 - SPEED: Sports to Fire: Fascinating Applications of Statistics
• Type: Contributed
• Date/Time: Tuesday, July 31, 2018 : 3:05 PM to 3:50 PM
• Sponsor: Section on Statistics in Sports
• Author(s): Daniel Daly-Grafstein* and Luke Bornn
• Companies: Simon Fraser University and Sacramento Kings and Simon Fraser University
• Keywords: Basketball; Optical Tracking; Shot Trajectories; Bayesian Regression; Variance Reduction

Abstract

Shooting skill in the NBA is almost exclusively defined by field goal percentage (FG%) - the number of makes out of the total number of shots. Even more advanced metrics like true shooting percentage (TS%) rely on FG%, ignoring the spatiotemporal data now available. In this paper we attempt to reduce the variability in predicting player FG% by using optical tracking data and shot trajectory characteristics to model shot-make probabilities. Using tracking data, we model the trajectories of individual shots from the 2014-15 season via a Bayesian Regression. We use these trajectories to create a shot-make probability model based on each shot's depth, left-right accuracy, and entry angle estimated from our modeled trajectories. Next we present a justification for the reduction in error when predicting FG% using our shot-make probability model. By the Rao-Blackwell Theorem, we condition shot-make probabilities on shooting factor information, thereby reducing the variance of our new estimator relative to raw FG%. Finally, we show that our modeled Rao-Blackwellized estimator is better than the raw estimator at predicting future shooting metrics like FG% and TS%.