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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

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 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

Assessing and comparing player skill in online multiplayer gaming environments is essential for fair matchmaking and player engagement. Traditional ranking models like Elo and Glicko-2, designed for two-player games, are insufficient for…

Human-Computer Interaction · Computer Science 2024-01-12 Vivek Joshy

The inverse problem of determining parameters in a model by comparing some output of the model with observations is addressed. This is a description for what hat to be done to use the Gauss-Markov-Kalman filter for the Bayesian estimation…

Numerical Analysis · Mathematics 2016-11-29 Hermann G. Matthies , Alexander Litvinenko , Bojana V. Rosic , Elmar Zander

A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…

Artificial Intelligence · Computer Science 2018-11-14 Zhenyu A. Liao , Charupriya Sharma , James Cussens , Peter van Beek

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

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

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 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

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

We study the use of novel techniques arising in machine learning for inverse problems. Our approach replaces the complex forward model by a neural network, which is trained simultaneously in a one-shot sense when estimating the unknown…

Numerical Analysis · Mathematics 2020-09-15 Philipp A. Guth , Claudia Schillings , Simon Weissmann

In this work we develop a new algorithm for rating of teams (or players) in one-on-one games by exploiting the observed difference of the game-points (such as goals), also known as a margin of victory (MOV). Our objective is to obtain the…

Methodology · Statistics 2022-02-09 Leszek Szczecinski

A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…

Artificial Intelligence · Computer Science 2020-09-01 Zhenyu A. Liao , Charupriya Sharma , James Cussens , Peter van Beek

We summarise popular methods used for skill rating in competitive sports, along with their inferential paradigms and introduce new approaches based on sequential Monte Carlo and discrete hidden Markov models. We advocate for a state-space…

Applications · Statistics 2024-08-20 Samuel Duffield , Samuel Power , Lorenzo Rimella

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

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

Matchmaking systems are vital for creating fair matches in online multiplayer games, which directly affects players' satisfactions and game experience. Most of the matchmaking systems largely rely on precise estimation of players' game…

Machine Learning · Computer Science 2022-08-17 Chaoyun Zhang , Kai Wang , Hao Chen , Ge Fan , Yingjie Li , Lifang Wu , Bingchao Zheng

To take the esports scene to the next level, we introduce PandaSkill, a framework for assessing player performance and skill rating. Traditional rating systems like Elo and TrueSkill often overlook individual contributions and face…

Machine Learning · Computer Science 2025-01-23 Maxime De Bois , Flora Parmentier , Raphaël Puget , Matthew Tanti , Jordan Peltier
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