Player attribution in American football remains an open problem due to the complex nature of twenty-two players interacting on the field, but the granularity of player tracking data provides ample opportunity for novel approaches. In this work, we introduce the first public framework to evaluate spatial and trajectory tracking data of players relative to a baseline distribution of "ghost" defenders. We demonstrate our framework in the context of modeling the nearest defender positioning at the moment of catch. In particular, we provide estimates of how much better or worse their observed positioning and trajectory compared to the expected play value of ghost defenders. Our framework leverages high-dimensional tracking data features through flexible random forests for conditional density estimation in two ways: (1) to model the distribution of receiver yards gained enabling the estimation of within-play expected value, and (2) to model the 2D spatial distribution of baseline ghost defenders. We present novel metrics for measuring player and team performance based on tracking data, and discuss challenges that remain in extending our framework to other aspects of American football.

翻译：美式橄榄球中的球员归因问题仍然是一个开放性问题，这是由于二十二名球员在场上互动的复杂性所致，但球员追踪数据的细粒度特性为新颖方法提供了充分的机会。在本研究中，我们首次提出了一个公开框架，用于评估球员相对于“幽灵”防守队员基线分布的空间与轨迹追踪数据。我们在模拟接球瞬间最近防守队员定位的背景下展示了该框架。具体而言，我们量化了观测到的防守队员定位和轨迹相较于幽灵防守队员期望比赛价值的优劣程度。该框架通过两种方式利用灵活随机森林对高维追踪数据特征进行条件密度估计：（1）建模接球手推进码数分布，从而实现对比赛内期望价值的估计；（2）建模基线幽灵防守队员的二维空间分布。我们提出了基于追踪数据衡量球员与球队表现的新指标，并讨论了将该框架扩展至美式橄榄球其他方面所面临的挑战。