{"title":"Generalizing the Elo rating system for multiplayer games and races: why endurance is better than speed","authors":"B. Powell","doi":"10.1515/jqas-2023-0004","DOIUrl":null,"url":null,"abstract":"Abstract We introduce a non-standard generalization of the Elo rating system for competitions involving two or more participants. The new system can be understood as an online estimation algorithm for the parameters of a Plackett–Luce model which can be used to make probabilistic forecasts for the results of future competitions. The system’s distinguishing feature is the way it treats competitions as sequences of elimination-type rounds that sequentially identify the worst competitors rather than sequences of selection-type rounds that identify the best. The significance of this important modelling choice is discussed and its consequences are explored. Finally, our generalized Elo system’s predictive power is demonstrated using data from Formula One racing.","PeriodicalId":16925,"journal":{"name":"Journal of Quantitative Analysis in Sports","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Quantitative Analysis in Sports","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/jqas-2023-0004","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"SOCIAL SCIENCES, MATHEMATICAL METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract We introduce a non-standard generalization of the Elo rating system for competitions involving two or more participants. The new system can be understood as an online estimation algorithm for the parameters of a Plackett–Luce model which can be used to make probabilistic forecasts for the results of future competitions. The system’s distinguishing feature is the way it treats competitions as sequences of elimination-type rounds that sequentially identify the worst competitors rather than sequences of selection-type rounds that identify the best. The significance of this important modelling choice is discussed and its consequences are explored. Finally, our generalized Elo system’s predictive power is demonstrated using data from Formula One racing.
期刊介绍：
The Journal of Quantitative Analysis in Sports (JQAS), an official journal of the American Statistical Association, publishes timely, high-quality peer-reviewed research on the quantitative aspects of professional and amateur sports, including collegiate and Olympic competition. The scope of application reflects the increasing demand for novel methods to analyze and understand data in the growing field of sports analytics. Articles come from a wide variety of sports and diverse perspectives, and address topics such as game outcome models, measurement and evaluation of player performance, tournament structure, analysis of rules and adjudication, within-game strategy, analysis of sporting technologies, and player and team ranking methods. JQAS seeks to publish manuscripts that demonstrate original ways of approaching problems, develop cutting edge methods, and apply innovative thinking to solve difficult challenges in sports contexts. JQAS brings together researchers from various disciplines, including statistics, operations research, machine learning, scientific computing, econometrics, and sports management.
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