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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

We compare conversion rates of association football (soccer) penalties during regulation or extra time with those during shootouts. Our data consists of roughly 50,000 penalties from the eleven~most recent seasons in European men's football…

Applications · Statistics 2024-12-17 Silvan Vollmer , David Schoch , Ulrik Brandes

This report is devoted to the forecast of the UEFA EURO 2020, Europe's continental football championship, taking place across Europe in June/July 2021. We present the simulation results for this tournament, where the simulations are based…

Applications · Statistics 2021-06-10 Lorenz A. Gilch

I present a double-elimination format for the 48-team FIFA World Cup that solves many of the concerns raised about the considered formats with mixed round-robin with groups of 3 or 4 teams and single-elimination strategies. Using a…

Computer Science and Game Theory · Computer Science 2023-01-11 César Rennó-Costa

As Aumann stated, cooperation and non-cooperation are different ways of viewing the same game, with the main difference being whether players can reach a binding cooperative agreement. In the real world, many games often coexist competition…

Computer Science and Game Theory · Computer Science 2025-11-25 Xiang Shuwen , Luo Enquan , Yang Yanlong

We provide, to the best of our knowledge, the first computational study of extensive-form adversarial team games. These games are sequential, zero-sum games in which a team of players, sharing the same utility function, faces an adversary.…

Artificial Intelligence · Computer Science 2017-11-21 Andrea Celli , Nicola Gatti

Penalty shootout in soccer is recognized to be unfair because the team kicking first in all rounds enjoys a significant advantage. The so-called Catch-Up Rule has been suggested recently to solve this problem but is shown here not to be…

Computer Science and Game Theory · Computer Science 2021-06-15 László Csató

This study explores strategic considerations in professional golf's Match Play format, challenging the conventional focus on individual performance. Leveraging PGA Tour data, we investigate the impact of factoring in an adversary's…

Optimization and Control · Mathematics 2024-04-05 Nishad Wajge , Gautier Stauffer

Round robin tournaments are omnipresent in sport competitions and beyond. We propose two new integer programming formulations for scheduling a round robin tournament, one of which we call the matching formulation. We analytically compare…

Optimization and Control · Mathematics 2022-10-18 Jasper van Doornmalen , Christopher Hojny , Roel Lambers , Frits C. R. Spieksma

We introduce a new measure to capture fairness of a schedule in a single round robin (SRR) tournament when participants are ranked by strength. To prevent distortion of the outcome of an SRR tournament as well as to guarantee equal…

Combinatorics · Mathematics 2025-02-07 Sten Wessel , Cor Hurkens , Frits Spieksma

The incomplete round robin sports tournament format, where each team plays the same number of games but faces only a subset of the other teams, is becoming increasingly popular in both youth and professional competitions. In contrast to…

Optimization and Control · Mathematics 2026-05-12 Karel Devriesere , David Van Bulck , Dries Goossens

A \emph{fair competition}, based on the concept of envy-freeness, is a non-eliminating competition where each contestant (team or individual player) may not play against all other contestants, but the total difficulty for each contestant is…

Data Structures and Algorithms · Computer Science 2021-02-09 Siddharth Gupta , Meirav Zehavi

Single-elimination (SE) tournaments are a popular format used in competitive environments and decision making. Algorithms for SE tournament manipulation have been an active topic of research in recent years. In this paper, we initiate the…

Data Structures and Algorithms · Computer Science 2024-02-12 Sushmita Gupta , M. S. Ramanujan , Peter Strulo

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

Competition and cooperation are inherent features of any multi-echelon supply chain. The interactions among the agents across the same echelon and that across various echelons influence the percolation of market demand across echelons. The…

Theoretical Economics · Economics 2024-01-11 Gurkirat Wadhwa , Tushar Shankar Walunj , Veeraruna Kavitha

Scheduling a sports tournament is a complex optimization problem, which requires a large number of hard constraints to satisfy. Despite the availability of several such constraints in the literature, there remains a gap since most of the…

Numerical Analysis · Mathematics 2021-06-18 Syed Rameez Naqvi , Adnan Ahmad , S. M. Riazul Islam , Tallha Akram , M. Abdullah-Al-Wadud , Atif Alamri

We consider the unconstrained traveling tournament problem, a sports timetabling problem that minimizes traveling of teams. Since its introduction about 20 years ago, most research was devoted to modeling and reformulation approaches. In…

Discrete Mathematics · Computer Science 2022-09-08 Marije Siemann , Matthias Walter

In international football (soccer), two-legged knockout ties, with each team playing at home in one leg and the final outcome decided on aggregate, are common. Many players, managers and followers seem to believe in the `second-leg home…

Methodology · Statistics 2017-01-27 Gery Geenens , Thomas Cuddihy

We present a systematic approach to the prediction of soccer matches. First, we show that the information about chances for goals is by far more informative than about the actual results. Second, we present a multivariate regression…

Data Analysis, Statistics and Probability · Physics 2012-07-20 Andreas Heuer , Oliver Rubner

We study how increasing competition, by making prizes more unequal, affects effort in contests. In a finite type-space environment, we characterize the equilibrium, analyze the effect of competition under linear costs, and identify…

Theoretical Economics · Economics 2025-02-13 Andrzej Baranski , Sumit Goel
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