A sports rating system is a method for assessing the ability of players or teams in competitive sports. This is especially useful in tournament-based sports where the scheduling of matches is irregular and decentralised. The first sports rating system to have rigorous statistical foundations was Elo. The system was adopted by the World Chess Federation (FIDE) in the 1970 and by the International Football Federation (FIFA) in 2018.In the last two decades more accurate rating systems were developed that extend Elo to the framework of Bayesian statistics, most notably Glicko by Mark Glickman, a Harvard Professor in Statistics, and Trueskill by Microsoft. The Bayesian framework allows us to introduce an additional parameter measuring the uncertainty in a player’s rating. This in turn endows the system with a more flexible learning rate that is adjusted to the uncertainty of each player.In this talk I will present some of the basic mathematical ideas that go in the construction of a modern sports rating system. I will discuss concepts such as the paired comparison models, the method of stochastic gradient descent, and the basic ideas of Bayesian statistics. I will present the Elo rating system and a related class of Bayesian rating systems that I have investigated recently. I will try to make the talk accessible to a wider audience. My focus will be on the explanation of the basic ideas and their application, while omitting most of the mathematical technicalities.
Dr. Evgeni Ovcharov is a mathematical statistician with Ph.D. from the University of Edinburgh, UK, and postdoctoral research work at Heidelberg University, Germany. Currently, he lives in Sofia, Bulgaria and works at the Bulgarian Academy of Sciences. His research interests focus on the development and application of machine learning algorithms in areas such as sports forecasting and financial time series forecasting. He also occasionally consults private companies who need to apply more sophisticated statistical and machine learning models.
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