We summarise popular methods used for skill rating in competitive sports, along with their inferential paradigms and introduce new approaches based on sequential Monte Carlo and discrete hidden Markov models. We advocate for a state-space model perspective, wherein players' skills are represented as time-varying, and match results serve as observed quantities. We explore the steps to construct the model and the three stages of inference: filtering, smoothing and parameter estimation. We examine the challenges of scaling up to numerous players and matches, highlighting the main approximations and reductions which facilitate statistical and computational efficiency. We additionally compare approaches in a realistic experimental pipeline that can be easily reproduced and extended with our open-source Python package, https://github.com/SamDuffield/abile.

翻译：我们总结了竞技体育中用于技能评级的常用方法及其推理范式，并介绍了基于序贯蒙特卡洛和离散隐马尔可夫模型的新方法。我们倡导采用状态空间模型视角，其中运动员的技能被表示为时变参数，比赛结果作为观测变量。我们探讨了模型构建的步骤以及推理的三个阶段：滤波、平滑与参数估计。我们研究了扩展到大量运动员和比赛时面临的挑战，重点阐述了实现统计与计算效率的主要近似方法和降维策略。此外，我们在一个可轻松复现且可扩展的现实实验流程中对各方法进行了比较，该流程基于我们的开源Python包https://github.com/SamDuffield/abile实现。