Rao-Blackwellizing field goal percentage

Daly-Grafstein Daniel () and Bornn Luke ()
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Daly-Grafstein Daniel: Department of Statistics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
Bornn Luke: Department of Statistics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada

Journal of Quantitative Analysis in Sports, 2019, vol. 15, issue 2, 85-95

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 2014–2015 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.

Keywords: basketball; bayesian regression; optical tracking; shot trajectories; variance reduction (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1515/jqas-2018-0064

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