One of the most important tasks in sports analytics is the development of binary response models for head-to-head game outcomes to estimate team and player strength. We discuss commonly used probability models for game outcomes, including the Bradley–Terry and Thurstone–Mosteller models, as well as extensions to ties as a third outcome and to the inclusion of a home-field advantage. We consider dynamic extensions to these models to account for the evolution of competitor strengths over time. Full likelihood-based analyses of these time-varying models can be simplified into rating systems, such as the Elo and Glicko rating systems. We present other modern rating systems, including popular methods for online gaming, and novel systems that have been implemented for online chess and Go. The discussion of the analytic methods are accompanied by examples of where these approaches have been implemented for various gaming organizations, as well as a detailed application to National Basketball Association game outcomes.

中文翻译：

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用于正面交锋比赛的模型和评级系统


体育分析中最重要的任务之一是为头对头比赛结果开发二进制响应模型，以估计球队和球员的实力。我们讨论了比赛结果的常用概率模型，包括 Bradley-Terry 和 Thurstone-Mosteller 模型，以及将平局作为第三种结果的扩展，以及包括主场优势。我们考虑对这些模型进行动态扩展，以解释竞争对手实力随时间的变化。对这些时变模型的基于完全似然的分析可以简化为评级系统，例如 Elo 和 Glicko 评级系统。我们介绍了其他现代评级系统，包括流行的在线游戏方法，以及已为在线国际象棋和围棋实施的新型系统。对分析方法的讨论附有这些方法已针对各种游戏组织实施的示例，以及对美国国家篮球协会比赛结果的详细应用。