Learning Agent Representations for Ice Hockey

Team sports is a new application domain for agent modeling with high real-world impact. A fundamental challenge for modeling professional players is their large number (over 1K), which includes many bench players with sparse participation in a game season. The diversity and sparsity of player observations make it difficult to extend previous agent representation models to the sports domain. This paper develops a new approach for agent representations, based on a Markov game model, that is tailored towards applications in professional ice hockey. We introduce a novel framewwork player representation via player generation, where a variational encoder embeds player information with latent variables. The encoder learns a context-specific shared prior to induce a shrinkage effect for the posterior player representations, allowing it to share statistical information across players with different participation rates. To capture the complex play dynamics in sequential sports data, we design a Variational Recurrent Ladder Agent Encoder (VaRLAE). This architecture provides a contextualized player representation with a hierarchy of latent variables that effectively prevents latent posterior collapse. We validate our player representations in three major sports analytics tasks. Our experimental results, based on a large dataset that contains over 4.5M events, show state-of-theart performance for our VarLAE on facilitating 1) identifying the acting player, 2) estimating expected goals, and 3) predicting the final score difference.