  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.
