Abstract 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.

中文翻译：

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预期假设完成概率

摘要使用国家橄榄球联盟（NFL）在其2019年大数据碗比赛中提供的高分辨率球员跟踪数据，我们引入了预期假设完成概率（EHCP），这是一种评估比赛的客观框架。EHCP的核心问题是“在给定的传球比赛中，四分卫是否将传球扔给了最有可能接住传球的接球手？” 为了回答这个问题，我们首先建立了贝叶斯非参数接球概率模型，该模型自动考虑输入之间的复杂相互作用，例如接收者的速度，与球的距离以及距离最近的防守者的距离。尽管从原理上讲，建立这样的模型很简单，但是使用它来推理假设通过是有挑战性的，因为与假设相对应的许多模型输入都必不可少。综上所述，如果将通行证而不是实际成为目标的接收者扔给他，则无法观察到没有目标的接收者与他最近的防御者有多近。为了克服这一基本困难，我们建议对无法观察到的输入进行估算，并对这些估算的模型预测取平均值，以得出EHCP。通过这种方式，EHCP可以通过考虑到有关缺少输入的不确定性的方式，跟踪比赛过程中每个接收者的完成概率如何演变。我们建议对不可观察的输入进行估算，并对这些估算对模型预测取平均值，以得出EHCP。通过这种方式，EHCP可以通过考虑到有关缺少输入的不确定性的方式，跟踪比赛过程中每个接收者的完成概率如何演变。我们建议对不可观察的输入进行估算，并在这些估算中对模型预测取平均值，以得出EHCP。通过这种方式，EHCP可以通过考虑到有关缺少输入的不确定性的方式，跟踪比赛过程中每个接收者的完成概率如何演变。