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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

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

As Large Language Models (LLMs) achieve breakthroughs in complex reasoning, Codeforces-based Elo ratings have emerged as a prominent metric for evaluating competitive programming capabilities. However, these ratings are often reported…

Software Engineering · Computer Science 2026-02-06 Shenyu Zheng , Ximing Dong , Xiaoshuang Liu , Gustavo Oliva , Chong Chun Yong , Dayi Lin , Boyuan Chen , Shaowei Wang , Ahmed E. Hassan

Arena-based evaluation is a fundamental yet significant evaluation paradigm for modern AI models, especially large language models (LLMs). Existing framework based on ELO rating system suffers from the inevitable instability problem due to…

Artificial Intelligence · Computer Science 2025-05-30 Zirui Liu , Jiatong Li , Yan Zhuang , Qi Liu , Shuanghong Shen , Jie Ouyang , Mingyue Cheng , Shijin Wang

New large language models (LLMs) are being released every day. Some perform significantly better or worse than expected given their parameter count. Therefore, there is a need for a method to independently evaluate models. The current best…

Artificial Intelligence · Computer Science 2025-09-30 Ashwin Ramaswamy , Nestor Demeure , Ermal Rrapaj

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

This work reconciles two perspectives on the Elo ranking that coexist in the literature: the practitioner's view as a heuristic feedback rule, and the statistician's view as online maximum likelihood estimation via stochastic gradient…

Methodology · Statistics 2026-04-07 Leszek Szczecinski

In competitive games, strength ratings like Elo are widely used to quantify player skill and support matchmaking by accounting for skill disparities better than simple win rate statistics. However, scalar ratings cannot handle complex…

Machine Learning · Computer Science 2025-02-07 Chiu-Chou Lin , I-Chen Wu

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 rating system is a simple and widely used method for calculating players' skills from paired comparisons data. Many have extended it in various ways. Yet the question of updating players' variances remains to be further explored. In…

Applications · Statistics 2023-10-17 Hsuan-Fu Hua , Ching-Ju Chang , Tse-Ching Lin , Ruby Chiu-Hsing Weng

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

The Elo rating system has been recognised as an effective method for modelling students and items within adaptive educational systems. The existing Elo-based models have the limiting assumption that items are only tagged with a single…

Computers and Society · Computer Science 2019-10-29 Solmaz Abdi , Hassan Khosravi , Shazia Sadiq , Dragan Gasevic

We suggest an improvement of the Elo rating system. Whereas Elo's theoretical background remains unaffected, we significantly change the way in which rating values are adjusted. It turns out that the modified system behaves much more…

Classical Analysis and ODEs · Mathematics 2018-01-17 Fabian Langholf

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

Accurate estimation of question difficulty and prediction of student performance play key roles in optimizing educational instruction and enhancing learning outcomes within digital learning platforms. The Elo rating system is widely…

Computers and Society · Computer Science 2024-03-14 Erva Nihan Kandemir , Jill-Jenn Vie , Adam Sanchez-Ayte , Olivier Palombi , Franck Ramus

The meteoric rise of online games has created a need for accurate skill rating systems for tracking improvement and fair matchmaking. Although many skill rating systems are deployed, with various theoretical foundations, less work has been…

Artificial Intelligence · Computer Science 2024-10-07 Mikel Bober-Irizar , Naunidh Dua , Max McGuinness

The TextClass Benchmark project is an ongoing, continuous benchmarking process that aims to provide a comprehensive, fair, and dynamic evaluation of LLMs and transformers for text classification tasks. This evaluation spans various domains…

Computation and Language · Computer Science 2024-12-10 Bastián González-Bustamante

Large language models perform surprisingly well on many zero-shot classification tasks, but are difficult to fairly compare to supervised classifiers due to the lack of a modifiable decision boundary. In this work, we propose and evaluate a…

Computation and Language · Computer Science 2025-11-25 WonJin Yoon , Ian Bulovic , Timothy A. Miller

Many environments assign several Elo ratings to the same agent: a chess player has classical, rapid, and blitz ratings; an online platform may rate by time control, mode, or format; an evaluator may rate performance across tasks or roles.…

Theoretical Economics · Economics 2026-05-12 Mehmet Mars Seven

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