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Competitor rating systems for head-to-head games are typically used to measure playing strength from game outcomes. Ratings computed from these systems are often used to select top competitors for elite events, for pairing players of…

Methodology · Statistics 2025-07-14 Mark E. Glickman

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

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

This paper introduces a score-driven rating system, a generalization of the classical Elo rating system that employs the score, i.e. the gradient of the log-likelihood, as the updating mechanism for player and team ratings. The proposed…

Machine Learning · Computer Science 2026-04-13 Vladimír Holý , Michal Černý

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

Competition is a primary driver of player satisfaction and engagement in multiplayer online games. Traditional matchmaking systems aim at creating matches involving teams of similar aggregated individual skill levels, such as Elo score or…

Social and Information Networks · Computer Science 2020-06-25 Sofia M Nikolakaki , Ogheneovo Dibie , Ahmad Beirami , Nicholas Peterson , Navid Aghdaie , Kazi Zaman

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

In this work, we deal with the problem of rating in sports, where the skills of the players/teams are inferred from the observed outcomes of the games. Our focus is on the online rating algorithms which estimate the skills after each new…

Machine Learning · Statistics 2021-04-30 Leszek Szczecinski , Raphaëlle Tihon

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

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

Rating systems play a crucial role in evaluating player skill across competitive environments. The Elo rating system, originally designed for deterministic and information-complete games such as chess, has been widely adopted and modified…

Computer Science and Game Theory · Computer Science 2025-12-23 Avirup Chakraborty , Shirsa Maitra , Tathagata Banerjee , Diganta Mukherjee , Tridib Mukherjee

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

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

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

The Elo rating system is a popular and widely adopted method for measuring the relative skill levels of players or teams in various sports and competitions. It assigns players numerical ratings and dynamically updates them based on game…

Probability · Mathematics 2026-01-28 Roberto Cortez , Hagop Tossounian

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

Evaluation has traditionally focused on ranking candidates for a specific skill. Modern generalist models, such as Large Language Models (LLMs), decidedly outpace this paradigm. Open-ended evaluation systems, where candidate models are…

Computer Science and Game Theory · Computer Science 2025-05-09 Siqi Liu , Ian Gemp , Luke Marris , Georgios Piliouras , Nicolas Heess , Marc Lanctot

Online competitive games have become increasingly popular. To ensure an exciting and competitive environment, these games routinely attempt to match players with similar skill levels. Matching players is often accomplished through a rating…

Information Retrieval · Computer Science 2020-08-18 Arman Dehpanah , Muheeb Faizan Ghori , Jonathan Gemmell , Bamshad Mobasher

We introduce a novel system of matching and scoring players in tournaments, called Multi-Tier Tournaments, illustrated by chess and based on the following rules: 1. Players are divided into skill-based tiers, based on their Elo ratings. 2.…

Theoretical Economics · Economics 2024-07-22 Steven J. Brams , Mehmet S. Ismail

Elo rating systems measure the approximate skill of each competitor in a game or sport. A competitor's rating increases when they win and decreases when they lose. Increasing one's rating can be difficult work; one must hone their skills…

Combinatorics · Mathematics 2024-04-16 Rikhav Shah
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