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The Elo rating system is a highly successful ranking algorithm for games of skill where, by construction, one team wins and the other loses. A primary limitation of the original Elo algorithm is its inability to predict information beyond a…

Methodology · Statistics 2018-02-05 J. Scott Moreland , Matthew C. Superdock

In Natural Language Processing (NLP), the Elo rating system, originally designed for ranking players in dynamic games such as chess, is increasingly being used to evaluate Large Language Models (LLMs) through "A vs B" paired comparisons.…

Computation and Language · Computer Science 2023-11-30 Meriem Boubdir , Edward Kim , Beyza Ermis , Sara Hooker , Marzieh Fadaee

The Elo rating system, which was originally proposed by Arpad Elo for chess, has become one of the most important rating systems in sports, economics and gaming nowadays. Its original formulation is based on two-player zero-sum games, but…

Optimization and Control · Mathematics 2022-04-12 Düring Bertram , Fischer Michael , Wolfram Marie-Therese

Elo rating, widely used for skill assessment across diverse domains ranging from competitive games to large language models, is often understood as an incremental update algorithm for estimating a stationary Bradley-Terry (BT) model.…

Machine Learning · Computer Science 2025-02-18 Shange Tang , Yuanhao Wang , Chi Jin

This work is concerned with the rating of players/teams in face-to-face games with three possible outcomes: loss, win, and draw. This is one of the fundamental problems in sport analytics, where the very simple and popular, non-trivial…

Statistics Theory · Mathematics 2019-10-15 Leszek Szczecinski , Aymen Djebbi

The Elo rating system has been used world wide for individual sports and team sports, as exemplified by the European Go Federation (EGF), International Chess Federation (FIDE), International Federation of Association Football (FIFA), and…

Artificial Intelligence · Computer Science 2021-05-04 Ben Wise

This article discusses in detail the rating system that won the kaggle competition "Chess Ratings: Elo vs the rest of the world". The competition provided a historical dataset of outcomes for chess games, and aimed to discover whether novel…

Machine Learning · Computer Science 2015-03-17 Yannis Sismanis

This paper presents a data-driven statistical framework to quantify the role of skill in games, addressing the long-standing question of whether success in a game is predominantly driven by skill or chance. We analyze player level data from…

Computer Science and Game Theory · Computer Science 2025-05-28 Tathagata Banerjee , Anushka De , Subhamoy Maitra , Diganta Mukherjee

This study aims to provide a data-driven approach for empirically tuning and validating rating systems, focusing on the Elo system. Well-known rating frameworks, such as Elo, Glicko, TrueSkill systems, rely on parameters that are usually…

Applications · Statistics 2025-12-23 Shirsa Maitra , Tathagata Banerjee , Anushka De , Diganta Mukherjee , Tridib Mukherjee

Rating systems play an important role in competitive sports and games. They provide a measure of player skill, which incentivizes competitive performances and enables balanced match-ups. In this paper, we present a novel Bayesian rating…

Information Retrieval · Computer Science 2021-01-05 Aram Ebtekar , Paul Liu

The Elo system for rating chess players, also used in other games and sports, was adopted by the World Chess Federation over four decades ago. Although not without controversy, it is accepted as generally reliable and provides a method for…

Physics and Society · Physics 2011-03-31 Trevor Fenner , Mark Levene , George Loizou

This paper presents an Elo-based rating system for programming contests, specifically Topcoder's Single Round Matches (SRMs). We introduce a logarithmic rank-based performance metric that allows single-round, multi-player contest results to…

Multiagent Systems · Computer Science 2026-02-24 Fred Batty

The Elo rating system is widely adopted to evaluate the skills of (chess) game and sports players. Recently it has been also integrated into machine learning algorithms in evaluating the performance of computerised AI agents. However, an…

Machine Learning · Computer Science 2022-01-21 Xue Yan , Yali Du , Binxin Ru , Jun Wang , Haifeng Zhang , Xu Chen

Real-world competitive games, such as chess, go, or StarCraft II, rely on Elo models to measure the strength of their players. Since these games are not fully transitive, using Elo implicitly assumes they have a strong transitive component…

Computer Science and Game Theory · Computer Science 2023-03-08 Quentin Bertrand , Wojciech Marian Czarnecki , Gauthier Gidel

ELO rating system is proposed by Arpad Elo, a Hungarian-American physics professor. Originally, it was proposed for the ranking system of chess players, but it was soon adapted to many other zero-sum sports fields like football, baseball,…

Human-Computer Interaction · Computer Science 2023-10-24 Yuhan Song

This paper investigates the evaluation of learned multiagent strategies in the incomplete information setting, which plays a critical role in ranking and training of agents. Traditionally, researchers have relied on Elo ratings for this…

Multiagent Systems · Computer Science 2020-01-13 Mark Rowland , Shayegan Omidshafiei , Karl Tuyls , Julien Perolat , Michal Valko , Georgios Piliouras , Remi Munos

Assessing the skill level of players to predict the outcome and to rank the players in a longer series of games is of critical importance for tournament play. Besides weaknesses, like an observed continuous inflation, through a steadily…

Artificial Intelligence · Computer Science 2021-04-13 Stefan Edelkamp

The Elo algorithm, renowned for its simplicity, is widely used for rating in sports tournaments and other applications. However, despite its widespread use, a detailed understanding of the convergence characteristics of the Elo algorithm is…

Machine Learning · Computer Science 2023-11-28 Daniel Gomes de Pinho Zanco , Leszek Szczecinski , Eduardo Vinicius Kuhn , Rui Seara

It was recently observed that Elo ratings fail at preserving transitive relations among strategies and therefore cannot correctly extract the transitive component of a game. We provide a characterization of transitive games as a weak…

Computer Science and Game Theory · Computer Science 2024-03-07 Nelson Vadori , Rahul Savani

One of the main goals of online competitive games is increasing player engagement by ensuring fair matches. These games use rating systems for creating balanced match-ups. Rating systems leverage statistical estimation to rate players'…

Artificial Intelligence · Computer Science 2021-06-23 Arman Dehpanah , Muheeb Faizan Ghori , Jonathan Gemmell , Bamshad Mobasher
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