  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.
