Rao-Blackwellizing Field Goal Percentage
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Shooting skill in the NBA is typically measured by field goal percentage (FG 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 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 player. We demonstrate that RB-FG shooting and true-shooting percentages. Overall, we find that conditioning shot-make probabilities on spatial trajectory information stabilizes inference of FG season than was previously possible.
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