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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

Qualifications for several world championships in sports are organised such that distinct sets of teams play in their own tournament for a predetermined number of slots. Inspired by a recent work studying the problem with the tools from the…

General Economics · Economics 2025-01-07 László Csató , László Marcell Kiss , Zsombor Szádoczki

League competition is investigated using random processes and scaling techniques. In our model, a weak team can upset a strong team with a fixed probability. Teams play an equal number of head-to-head matches and the team with the largest…

Physics and Society · Physics 2007-08-13 E. Ben-Naim , N. W. Hengartner

In this paper we show a new technique to analyze families of rankings. In particular we focus on sports rankings and, more precisely, on soccer leagues. We consider that two teams compete when they change their relative positions in…

Physics and Society · Physics 2015-06-16 Regino Criado , Esther Garcia , Francisco Pedroche , Miguel Romance

Elite football is believed to have evolved in recent years, yet systematic evidence for the pace and form of that change remains sparse. Drawing on event-level records for 13,018 matches across ten top-tier men's and women's leagues in…

We undertake extensive analysis of English Premier League data over the period 2009/10 to 2017/18 to identify and rank key factors affecting the economic and footballing performances of the teams. Alternative end-of-season league tables are…

Other Statistics · Statistics 2024-08-12 Amit K Chattopadhyay , A. Abdul , Sudhir Jain

In this work, a machine learning approach is developed for predicting the outcomes of football matches. The novelty of this research lies in the utilisation of the Kelly Index to first classify matches into categories where each one denotes…

Machine Learning · Computer Science 2022-11-30 Yiming Ren , Teo Susnjak

Predicting the results of sport matches and competitions is an arising research field, benefiting from the growing amount of available data and the novel data analytics techniques. Excellent forecasts can be achieved by advanced machine…

Applications · Statistics 2015-11-20 Giuseppe Jurman

Since March 2020, the environment surrounding football has changed dramatically because of the COVID-19 pandemic. After a few months' break, re-scheduled matches were held behind closed doors without spectators. The main objective of this…

Applications · Statistics 2021-03-09 Eiji Konaka

The usual FIFA World Cup-TM group stage format is eight groups of four teams for a total of 32 teams. The top two teams from each group advance to the next round, resulting in a 16-team knockout stage. The next edition of the World Cup will…

Physics and Society · Physics 2023-08-08 Jose A. Troyano

We propose utilizing match-level suspense and surprise - which capture the entertainment utility created by competitive balance and outcome uncertainty for sports spectators - as alternative policy targets for league organizers and…

General Economics · Economics 2025-06-27 Raphael Flepp , Tim Pawlowski , Travis Richardson

In this manuscript, we concentrate on a specific type of covariates, which we call statistically enhanced, for modeling tennis matches for men at Grand slam tournaments. Our goal is to assess whether these enhanced covariates have the…

Applications · Statistics 2025-02-27 Nourah Buhamra , Andreas Groll

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

Algorithmic fairness plays an important role in machine learning and imposing fairness constraints during learning is a common approach. However, many datasets are imbalanced in certain label classes (e.g. "healthy") and sensitive subgroups…

Machine Learning · Computer Science 2022-06-08 Zhun Deng , Jiayao Zhang , Linjun Zhang , Ting Ye , Yates Coley , Weijie J. Su , James Zou

A match played in a sports tournament can be called stakeless if at least one team is indifferent to its outcome because it already has qualified or has been eliminated. Such a game threatens fairness since teams may not exert full effort…

Optimization and Control · Mathematics 2026-04-02 László Csató , András Gyimesi

This paper assesses the convergence of the EU-28 countries towards their common goal of 20% in the renewable energy share indicator by year 2020. The potential presence of clubs of convergence towards different steady state equilibria is…

Econometrics · Economics 2024-02-02 María José Presno , Manuel Landajo

In this paper, a new continuous scoring system for soccer is proposed, based on the proportion of time that a team is winning, losing or tied. Several simulations are made applying this technique to complete seasons of different leagues. As…

Applications · Statistics 2018-03-22 Manuel Cruz , Sandra Ramos , Miguel Pinho

The draw of some knockout tournaments requires finding a perfect matching in a balanced bipartite graph. The problem becomes challenging with draw constraints: the two draw procedures used in sports are known to be non-uniformly distributed…

Physics and Society · Physics 2025-04-17 László Csató

In this paper are used historical statistical data to track the evolution of the game in the European-wide top-tier level professional basketball club competition (until 2017-2018 season) and also are answered questions by analyzing them.…

Applications · Statistics 2023-05-23 Christos Katris

In recent years excessive monetization of football and professionalism among the players has been argued to have affected the quality of the match in different ways. On the one hand, playing football has become a high-income profession and…

Physics and Society · Physics 2023-01-05 Victor Martins Maimone , Taha Yasseri