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The integrity of a sport can be seriously undermined if its rules punish winning as this creates incentives for strategic manipulation. Therefore, a sports tournament can be called unfair if the overall win probabilities are not ordered…

Applications · Statistics 2021-02-15 László Csató

A strong structural regularity of classes is found in soccer teams ranked by the Union of European Football Associations (UEFA) for the time interval 2009-2014. It concerns 424 to 453 teams according to the 5 competition seasons. The…

Applications · Statistics 2018-02-14 Marcel Ausloos

Classification of matches played in the last rounds of sports competitions is a well-established tool for evaluating tournament designs. Both deterministic and probabilistic approaches are available for this purpose. Our paper offers the…

Physics and Society · Physics 2026-05-26 László Csató , András Gyimesi

This article presents a Bayesian implementation of a cumulative probit model to forecast the outcomes of the UEFA Champions League matches. The argument of the normal CDF involves a cut-off point, a home vs away playing effect and the…

Applications · Statistics 2015-02-16 Jean-Louis Foulley

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

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

Tournament organisers supposedly design rules such that a team cannot be strictly better off by exerting a lower effort. However, the European qualification tournaments for recent FIFA soccer World Cups are known to violate this…

Physics and Society · Physics 2020-05-28 László Csató

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

We argue for the application of bibliometric indices to quantify the long-term uncertainty of outcome in sports. The Euclidean index is proposed to reward quality over quantity, while the rectangle index can be an appropriate measure of…

Applications · Statistics 2024-12-10 László Csató , Dóra Gréta Petróczy

The paper analyses how draw constraints influence the outcome of a knockout tournament. The research question is inspired by European club football competitions, where the organiser generally imposes an association constraint in the first…

Physics and Society · Physics 2023-02-24 László Csató

The group stage of a sports tournament is often made more appealing by introducing additional constraints in the group draw that promote an attractive and balanced group composition. For example, the number of intra-regional group matches…

Applications · Statistics 2026-02-25 László Csató , Martin Becker , Karel Devriesere , Dries Goossens

The Union of European Football Associations (UEFA) distributes commercial revenue from its club competitions according to a complex mechanism. Coefficient-based amounts are paid such that the participating teams are ranked on the basis of…

Physics and Society · Physics 2023-03-22 László Csató

We analysed the distribution of the number of goals scored in each of the 51 football matches played in the UEFA EURO 2020 final phase as well as the waiting times between scores (also considering censored times). We found that the Poisson…

Applications · Statistics 2022-03-16 Giulia Fedrizzi , Luisa Canal , Rocco Micciolo

The selection of an appropriate competition format is critical for both the success and credibility of any competition, both real and simulated. In this paper, the automated parallelism offered by the RoboCupSoccer 2D simulation league is…

Multiagent Systems · Computer Science 2014-06-27 David Budden , Peter Wang , Oliver Obst , Mikhail Prokopenko

The chances to win a football match can be significantly increased if the right tactic is chosen and the behavior of the opposite team is well anticipated. For this reason, every professional football club employs a team of game analysts.…

Machine Learning · Computer Science 2019-10-02 Eric Müller-Budack , Jonas Theiner , Robert Rein , Ralph Ewerth

FIFA World Cup is one of the most watched sporting event in the world and its popularity continue to increase. While currently 32 teams participate in this event, starting with 2026 the number of participants will increase to 48. As a…

Physics and Society · Physics 2018-10-23 Traian Marius Truta

In this work we develop an innovative hierarchical clustering method to divide a sample of undirected weighted networks into groups. The methodology consists of two phases: the first phase is aimed at putting the single networks in a…

Applications · Statistics 2021-03-31 Jacopo Diquigiovanni , Bruno Scarpa

A paper published in a leading journal of management science has recently analysed the mechanism used for the UEFA Champions League Round of 16 draw. Since the authors have not been familiar with the related sports analytics literature,…

Physics and Society · Physics 2023-02-07 László Csató

Problem definition: Professional sports leagues may be suspended due to various reasons such as the recent COVID-19 pandemic. A critical question the league must address when re-opening is how to appropriately select a subset of the…

Optimization and Control · Mathematics 2024-04-02 Ali Hassanzadeh , Mojtaba Hosseini , John G. Turner

We use European football performance data to select teams to form the proposed European football Super League, using only unsupervised techniques. We first used random forest regression to select important variables predicting goal…

Applications · Statistics 2021-04-21 A. J. Bond , C. B. Beggs