Traditional NBA player evaluation metrics are based on scoring differential or some pace-adjusted linear combination of box score statistics like points, rebounds, assists, etc. These measures treat performances with the outcome of the game still in question (e.g. tie score with five minutes left) in exactly the same way as they treat performances with the outcome virtually decided (e.g. when one team leads by 30 points with one minute left). Because they ignore the context in which players perform, these measures can result in misleading estimates of how players help their teams win. We instead use a win probability framework for evaluating the impact NBA players have on their teams’ chances of winning. We propose a Bayesian linear regression model to estimate an individual player’s impact, after controlling for the other players on the court. We introduce several posterior summaries to derive rank-orderings of players within their team and across the league. This allows us to identify highly paid players with low impact relative to their teammates, as well as players whose high impact is not captured by existing metrics.
Since the advent of high-resolution pitch tracking data (PITCHf/x), many in the sabermetrics community have attempted to quantify a Major League Baseball catcher’s ability to “frame” a pitch (i.e. increase the chance that a pitch is a called as a strike). Especially in the last 3 years, there has been an explosion of interest in the “art of pitch framing” in the popular press as well as signs that teams are considering framing when making roster decisions. We introduce a Bayesian hierarchical model to estimate each umpire’s probability of calling a strike, adjusting for the pitch participants, pitch location, and contextual information like the count. Using our model, we can estimate each catcher’s effect on an umpire’s chance of calling a strike. We are then able translate these estimated effects into average runs saved across a season. We also introduce a new metric, analogous to Jensen, Shirley, and Wyner’s Spatially Aggregate Fielding Evaluation metric, which provides a more honest assessment of the impact of framing.
Using high-resolution player tracking data made available by the National Football League (NFL) for their 2019 Big Data Bowl competition, we introduce the Expected Hypothetical Completion Probability (EHCP), a objective framework for evaluating plays. At the heart of EHCP is the question “on a given passing play, did the quarterback throw the pass to the receiver who was most likely to catch it?” To answer this question, we first built a Bayesian non-parametric catch probability model that automatically accounts for complex interactions between inputs like the receiver’s speed and distances to the ball and nearest defender. While building such a model is, in principle, straightforward, using it to reason about a hypothetical pass is challenging because many of the model inputs corresponding to a hypothetical are necessarily unobserved. To wit, it is impossible to observe how close an un-targeted receiver would be to his nearest defender had the pass been thrown to him instead of the receiver who was actually targeted. To overcome this fundamental difficulty, we propose imputing the unobservable inputs and averaging our model predictions across these imputations to derive EHCP. In this way, EHCP can track how the completion probability evolves for each receiver over the course of a play in a way that accounts for the uncertainty about missing inputs.