"On kinetic rating models"Wolfram, Marie-ThereseThe Elo rating system, originally proposed by Arpad Elo to rank chess players, has become one of the most popular rating systems in sports, economics and gaming nowadays. While its original formulation is based on a two-player zero-sum game, it has recently been adapted for team sports and more general settings. In this talk I will give an overview on kinetic Elo-type models, which were originally proposed by Jabin and Junca in 2016. Hereby players are characterised by their underlying non-observable strength and their official rating - ideally this rating should converge to the player's strength. Jabin and Junca were able to prove convergence under certain assumptions on the playing frequency. I will discuss the long time behavior for different generalisations of the Elo model - which include for example performance fluctuations of individual players or teams - by investigating the limiting Fokker-Planck equations. Ref: P-E. Jabin, S. Junca, A continuous model for ratings, SIAP 75(2), 2015 |
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