title: Match Prediction Using Learned History Embeddings
abstract: Contemporary ranking systems that are based on win/loss history, such as Elo  or TrueSkill  represent each player using a scalar estimate of ability (plus variance, in the latter case). While easily interpretable, this approach has a number of shortcomings: (i) latent attributes of a player cannot be represented, and (ii) it cannot seamlessly incorporate contextual information (e.g. home-field advantage). In this work, we propose a simple Transformer-based approach for pairwise competitions that recursively operates on game histories, rather than modeling players directly. By characterizing each player entirely by its history, rather than an underlying scalar skill estimate, it is able to make accurate predictions even for new players with limited history. Additionally, it is able to model both transitive and non-transitive relations and can leverage contextual information. When restricted to the same information as Elo and Glicko, our approach significantly outperforms them on predicting the outcome of real-world Chess, Baseball and Ice Hockey games. %Further gains can be achieved when game meta-data is added.
  
authors: Maxwell Goldstein Leon Bottou Rob Fergus
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