Simulating Defensive Trajectories in American Football for Predicting League Average Defensive Movements.

American football is an appealing field of research for the use of information technology. While much effort is made to analyze the offensive team in recent years, reasoning about defensive behavior is an emergent topic. As defensive performance and positioning largely contribute to the overall success of the whole team, this study introduces a method to simulate defensive trajectories. The simulation is evaluated by comparing the movements in individual plays to a simulated league average behavior. A data-driven ghosting approach is proposed. Deep neural networks are trained with a multi-agent imitation learning approach, using the tracking data of players of a whole National Football League (NFL) regular season. To evaluate the quality of the predicted movements, a formation-based pass completion probability model is introduced. With the implementation of a learnable order invariant model, based on insights of molecular dynamical machine learning, the accuracy of the model is increased to 81%. The trained pass completion probability model is used to evaluate the ghosted trajectories and serves as a metric to compare the true trajectory to the ghosted ones. Additionally, the study evaluates the ghosting approach with respect to different optimization methods and dataset augmentation. It is shown that a multi-agent imitation learning approach trained with a dataset aggregation method outperforms baseline approaches on the dataset. This network and evaluation scheme presents a new method for teams, sports analysts, and sports scientists to evaluate defensive plays in American football and lays the foundation for more sophisticated data-driven simulation methods.