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.

中文翻译：

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Rao-Blackwellizing射门得分百分比

摘要NBA的投篮技巧通常由投篮命中率（FG％）来衡量-射门总数中的接球数。通过计算每个球员的2分，3分和罚球命中率和失误，甚至可以计算出更高级的指标，而忽略了现在可用的时空数据（Kubatko等，2007）。在本文中，我们旨在通过引入一种基于铅球后投篮命中率的新估算器来更好地表征球员的射击技能。通过Rao-Blackwell定理，我们提出了一种镜头制作概率模型，该模型根据镜头轨迹信息来对概率估计进行条件调整，从而减小了新估计量相对于标准FG％的方差。我们通过使用光学跟踪数据来估算每次射击的三个因素来获得射击信息：入射角，射击深度，和左右准确性。接下来，我们将使用这些因素来为2014–2015赛季中所有投篮的投篮命中率建模，并使用这些概率为每位球员生成Rao-Blackwellized FG％估计量（RB-FG％）。我们证明，在预测三分球命中率和真实投篮命中率方面，RB-FG％优于原始FG％。总体而言，我们发现在空间轨迹信息上调节镜头的命中概率可以稳定FG％的推断，从而有可能在一个季节内比以前更早地估计射击统计数据。我们证明，在预测三分球命中率和真实投篮命中率方面，RB-FG％优于原始FG％。总体而言，我们发现在空间轨迹信息上调节镜头的命中概率可以稳定FG％的推断，从而有可能在一个季节内比以前更早地估计射击统计数据。我们证明，在预测三分球命中率和真实投篮命中率方面，RB-FG％优于原始FG％。总体而言，我们发现在空间轨迹信息上调节镜头的命中概率可以稳定FG％的推断，从而有可能在一个季节内比以前更早地估计射击统计数据。