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The Number That Finds Your Match: A Narrative Review of Skill Rating and Matchmaking from Elo's Chess to TrueSkill 2

Year: 2026
Type: review
Abstract: Skill rating and matchmaking---the mathematics that turns thousands of scattered players into fair pairings---moved from Elo's 1978 chess rating through Glickman's dynamic estimation, Herbrich and colleagues's Bayesian TrueSkill, and Coulom's whole-history rating to the game industry's architectures, the evolutionary optimization of fairness, and TrueSkill 2's team models. This article presents a narrative review of that arc's canonical line: Elo's 1978 The Rating of Chessplayers, Batchelder and Bershad's 1979 statistical theory, Glickman's 1999 dynamic estimation, Glickman and Jones's 1999 evaluation, Herbrich, Minka, and Graepel's 2006 TrueSkill, Feng, Brandt, and Saha's 2007 matchmaking architecture, Dangauthier and colleagues's 2008 TrueSkill through time, Coulom's 2008 whole-history rating, Menke and Martinez's 2008 MCMC model, Chen and colleagues's 2017 evolutionary matchmaking, Minka, Cleven, and Zaykov's 2018 TrueSkill 2, and Kovalchik's 2020 margin-of-victory extension. The review is organized around three themes: the chess foundations, in which the rating table's logistic update, the paired-comparison statistics, and the system's evaluation made the skill a number; the Bayesian era, in which the multiplayer extensions, the histories' re-estimation, and the posterior's sampling made the uncertainty a first-class citizen; and the game industry's systems, in which the architectures' scaling, the evolutionary fairness's optimization, and the margins' and teams' models carried the mathematics into the lobbies. It is concluded that skill rating is the fairness's information system---and that its arc is the number's evolution from the scalar's chess to the Bayesian's teams.
DOI: 10.5281/zenodo.22181920
Language: English
Open Access status: green
OpenAlex ID: W7204686308
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