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Single-elimination tournaments are the standard paradigm both for the main tennis professional associations. Schedules are generated by allocating first seeded and then unseeded players with seeds prevented from encountering each other…

Physics and Society · Physics 2020-10-23 Federico Della Croce , Gabriele Dragotto , Rosario Scatamacchia

Machine learning has become a common approach to predicting the outcomes of soccer matches, and the body of literature in this domain has grown substantially in the past decade and a half. This chapter discusses available datasets, the…

Machine Learning · Computer Science 2024-03-13 Rory Bunker , Calvin Yeung , Keisuke Fujii

This paper proposes a multiple-membership generalized linear mixed model for ranking college football teams using only their win/loss records. The model results in an intractable, high-dimensional integral due to the random effects…

Applications · Statistics 2014-04-01 Andrew T. Karl

While discounted payoff games and classic games that reduce to them, like parity and mean-payoff games, are symmetric, their solutions are not. We have taken a fresh view on the constraints that optimal solutions need to satisfy, and…

Data Structures and Algorithms · Computer Science 2023-10-03 Daniele Dell'Erba , Arthur Dumas , Sven Schewe

While discounted payoff games and classic games that reduce to them, like parity and mean-payoff games, are symmetric, their solutions are not. We have taken a fresh view on the properties that optimal solutions need to have, and devised a…

Data Structures and Algorithms · Computer Science 2026-03-11 Daniele Dell'Erba , Arthur Dumas , Sven Schewe

When facing a heavily-favored opponent, an underdog must be willing to assume greater-than-average risk. In statistical language, one would say that an underdog must be willing to adopt a strategy whose outcome has a larger-than-average…

Physics and Society · Physics 2011-11-04 Brian Skinner

Tournament-based compensation schemes with forced distributions represent a widely adopted class of relative performance evaluation mechanisms in technology and corporate environments. These systems mandate within-team ranking and fixed…

General Economics · Economics 2025-12-09 Jeremy McEntire

We investigated the temporal distribution of goals in soccer using event-level data from 3,433 matches across 21 leagues and competitions. Contrary to the prevailing notion of randomness, we found that the probability of a goal being scored…

The Swiss-system is an increasingly popular competition format as it provides a favourable trade-off between the number of matches and ranking accuracy. However, there is no empirical study on the potential unfairness of Swiss-system chess…

General Economics · Economics 2026-02-27 László Csató , Alex Krumer

Discrimination via algorithmic decision making has received considerable attention. Prior work largely focuses on defining conditions for fairness, but does not define satisfactory measures of algorithmic unfairness. In this paper, we focus…

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

Every sport needs rules. Tournament design refers to the rules that determine how a tournament, a series of games between a number of competitors, is organized. This study aims to provide an overview of the tournament design literature from…

Physics and Society · Physics 2025-05-20 Karel Devriesere , László Csató , Dries Goossens

The paper presents a plus-minus rating for use in association football (soccer). We first describe the standard plus-minus methodology as used in basketball and ice-hockey and then adapt it for use in soccer. The usual goal-differential…

Applications · Statistics 2017-06-16 Tarak Kharrat , Javier López Peña , Ian McHale

In a distributed game we imagine a team Player engaging a team Opponent in a distributed fashion. Such games and their strategies have been formalised in concurrent games based on event structures. However there are limitations in founding…

Logic in Computer Science · Computer Science 2016-07-14 Marc de Visme , Glynn Winskel

The group draw of a sports tournament requires assigning teams to groups of (almost) the same size. The most important criteria for a draw procedure are balance, randomness, and transparency, which could not be satisfied simultaneously if…

Physics and Society · Physics 2026-05-25 László Csató

We consider the following sports scheduling problem. Consider $2n$ teams in a sport league. Each pair of teams must play exactly one match in $2n-1$ days. That is, $n$ games are held simultaneously in a day. We want to make a schedule which…

Combinatorics · Mathematics 2008-09-24 Kenji Kashiwabara

Analyzing football score data with statistical techniques, we investigate how the highly co-operative nature of the game is reflected in averaged properties such as the distributions of scored goals for the home and away teams. It turns out…

Physics and Society · Physics 2009-11-13 Elmar Bittner , Andreas Nussbaumer , Wolfhard Janke , Martin Weigel

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

In this work, we extended a stochastic model for football leagues based on the team's potential [R. da Silva et al. Comput. Phys. Commun. \textbf{184} 661--670 (2013)] for making predictions instead of only performing a successful…

Physics and Society · Physics 2022-06-08 Eduardo V. Stock , Roberto da Silva , Henrique A. Fernandes

We study uncoordinated matching markets with additional local constraints that capture, e.g., restricted information, visibility, or externalities in markets. Each agent is a node in a fixed matching network and strives to be matched to…

Computer Science and Game Theory · Computer Science 2014-09-16 Martin Hoefer , Lisa Wagner