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 player representation via player generation framework 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 participations. To model the play dynamics in sequential sports data, we design a Variational Recurrent Ladder Agent Encoder (VaRLAE). It learns a contextualized player representation with a hierarchy of latent variables that effectively prevents latent posterior collapse.

A promising approach to incorporating player information into sports statistics is deep agent representation.

A promising approach to incorporating player information into sports statistics is deep agent representation.

We appreciate the reviewers for reading our paper and their constructive comments. "I would have liked to have seen comparisons to more fundamental baselines that didn't make the same Reviewer 3: "socialGAN, SoPHie and other multi-agent representation learning approaches should be added..." Reviewer 4: "The paper mentions other approaches and it might be useful to see a comparison to other papers..." "The shot quality prediction is similar to the results reported in ""Quality vs Quantity"... Can the Reviewer 4: "It is unclear that the ladder aspect of the architecture is providing an improvement on this application." Prior work on ice hockey shot prediction does not take into account the identity of the shooter. For instance, the scoring chance is higher for a top player v.s., an average Table 1 shows the benefits of modelling shooter-specific effects. We can discuss the higher levels in the final version. I suspect they might look similar to V aRLAE" Our main contribution is the idea of Player representation through Player Generation (Section 3).

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 player representation via player generation framework where a variational encoder embeds player information with latent variables.

In this paper, I introduce RisingBALLER, the first publicly available approach that leverages a transformer model trained on football match data to learn matchspecific player representations. Drawing inspiration from advances in language modeling, RisingBALLER treats each football match as a unique sequence in which players serve as tokens, with their embeddings shaped by the specific context of the match. Through the use of masked player prediction (MPP) as a pre-training task, RisingBALLER learns foundational features for football player representations, similar to how language models learn semantic features for text representations. As a downstream task, I introduce next match statistics prediction (NMSP) to showcase the effectiveness of the learned player embeddings. The NMSP model surpasses a strong baseline commonly used for performance forecasting within the community. Furthermore, I conduct an in-depth analysis to demonstrate how RisingBALLER's learned embeddings can be used in various football analytics tasks, such as producing meaningful positional features that capture the essence and variety of player roles beyond rigid x,y coordinates, team cohesion estimation, and similar player retrieval for more effective data-driven scouting. More than a simple machine learning model, RisingBALLER is a comprehensive framework designed to transform football data analytics by learning high-level foundational features for players, taking into account the context of each match. It offers a deeper understanding of football players beyond individual statistics. In recent years, the field of machine learning has been revolutionized by the introduction of the transformer architecture [1], which initially gained prominence in natural language processing (NLP) with models like BERT [2], RoBERTa [3], and more recently, the widespread use of large language models (LLMs). These models, often trained on seemingly simple tasks such as next token prediction or masked token prediction, have demonstrated remarkable performance in learning high-level features that effectively represent each word and model language intricately. They are capable of learning nuanced representations of the multiple meanings a word can have depending on its context.

Understanding a player's performance in a basketball game requires an evaluation of the player in the context of their teammates and the opposing lineup. Here, we present NBA2Vec, a neural network model based on Word2Vec which extracts dense feature representations of each player by predicting play outcomes without the use of hand-crafted heuristics or aggregate statistical measures. Specifically, our model aimed to predict the outcome of a possession given both the offensive and defensive players on the court. By training on over 3.5 million plays involving 1551 distinct players, our model was able to achieve a 0.3 K-L divergence with respect to the empirical play-by-play distribution. The resulting embedding space is consistent with general classifications of player position and style, and the embedding dimensions correlated at a significant level with traditional box score metrics. Finally, we demonstrate that NBA2Vec accurately predicts the outcomes to various 2017 NBA Playoffs series, and shows potential in determining optimal lineup match-ups. Future applications of NBA2Vec embeddings to characterize players' style may revolutionize predictive models for player acquisition and coaching decisions that maximize team success.