A State-Space Perspective on Modelling and Inference for Online Skill Rating

In the quantitative analysis of competitive sports, a fundamental task is to estimate the skills of the different agents ('players') involved in a given competition based on the outcome of pairwise comparisons ('matches') between said players, often in an online setting. Skill estimation facilitates the prediction of various relevant outcomes of subsequent matches, which can then be applied towards high-level decision-making for the competition, including player seeding, fair team matching, and more. There are several established approaches to the task of skill estimation, including among others the Bradley-Terry model (Bradley and Terry, 1952), the Elo rating system (Elo, 1978), the Glicko rating system (Glickman, 1999), and TrueSkill (Herbrich et al., 2006) each with various levels of complexity and varying degrees of statistical motivation. Skill rating is of paramount importance in the world of competitive sports as it serves as a foundational tool for assessing and comparing the abilities of players and how they vary over time. By accurately quantifying skill levels, skill rating systems enable fair and balanced competition, inform strategic decision-making, and enhance the overall sporting level.