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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

If the final position of a team is already secured independently of the outcomes of the remaining games in a round-robin tournament, it might play with little enthusiasm. This is detrimental to attendance and can inspire collusion and…

Physics and Society · Physics 2023-02-03 László Csató

Estimating win probability is one of the classic modeling tasks of sports analytics. Many widely used win probability estimators use machine learning to fit the relationship between a binary win/loss outcome variable and certain game-state…

Methodology · Statistics 2025-08-21 Ryan S. Brill , Ronald Yurko , Abraham J. Wyner

We investigate the relation between the number of passes made by a football team and the number of goals. We analyze the 380 matches of a complete season of the Spanish national league "LaLiga" (2018/2019). We observe how the number of…

Physics and Society · Physics 2020-07-23 D. R. Antequera , D. Garrido , I. Echegoyen , R. Lopez del Campo , R. Resta Serra , J. M. Buldu

Expected goals (xG) models estimate the probability that a shot results in a goal from its context (e.g., location, pressure), but they operate only on observed shots. We propose xG+, a possession-level framework that first estimates the…

Applications · Statistics 2026-01-27 Jonathan Pipping-Gamón , Tianshu Feng , R. Paul Sabin

This study explores the relationship between the performance of a football team and the topological parameters of temporal passing networks. To achieve this, we propose a method to identify moments of high and low team performance based on…

Physics and Society · Physics 2025-06-13 Andres Chacoma

This paper considers the use of observed and predicted match statistics as inputs to forecasts of the outcomes of football matches. It is shown that, were it possible to know the match statistics in advance, highly informative forecasts of…

Applications · Statistics 2020-01-27 Edward Wheatcroft

The sequence of moves in a dynamic team tournament may distort the ex-ante winning probabilities and harm efficiency. This paper compares seven soccer penalty shootout rules that determine the kicking order, from a theoretical perspective.…

Computer Science and Game Theory · Computer Science 2023-02-24 László Csató , Dóra Gréta Petróczy

Using a simple game-theoretical model of contests, we compare the effort exerted by rugby teams under three different point systems used in tournaments around the world. The scoring systems under consideration are NB, +4 and 3+. We state…

Physics and Society · Physics 2019-12-16 Federico Fioravanti , Fernando Delbianco , Alejandro Neme , Fernando Tohmé

This paper presents some useful mathematical results involved in football table prediction. In addition, some empirical results indicate that an alternative methodology for football table prediction may produce high quality forecasts with…

Applications · Statistics 2018-05-24 Kjetil Haugen , Brynjulf Owren

Score matching is an approach to learning probability distributions parametrized up to a constant of proportionality (e.g. Energy-Based Models). The idea is to fit the score of the distribution, rather than the likelihood, thus avoiding the…

Machine Learning · Computer Science 2024-01-31 Yilong Qin , Andrej Risteski

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

We present a new approach for identifying situations and behaviours, which we call "moves", from soccer games in the 2D simulation league. Being able to identify key situations and behaviours are useful capabilities for analysing soccer…

Machine Learning · Computer Science 2018-09-13 Olivia Michael , Oliver Obst , Falk Schmidsberger , Frieder Stolzenburg

When $n$ teams play in a football league with home and away matches against every opponent there are $M = n \cdot (n-1)$ matches. There are 3 possible match results: a victory is awarded 3 points, a draw 1 point and 0 points for a defeat.…

General Mathematics · Mathematics 2025-03-20 Rüdiger Jehn , Kester Habermann , Misha Lavrov

This paper introduces an approach to predicting the next event in a soccer match, a challenge bearing remarkable similarities to the problem faced by Large Language Models (LLMs). Unlike other methods that severely limit event dynamics in…

Machine Learning · Computer Science 2024-04-29 Tiago Mendes-Neves , Luís Meireles , João Mendes-Moreira

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

In the sports of soccer, hockey and basketball the most commonly used statistics for player performance assessment are divided into two categories: offensive statistics and defensive statistics. However, qualitative assessments of…

Applications · Statistics 2017-04-04 Shael Brown

In this paper, we examine team ball sports to investigate how the likelihood of weaker teams winning against stronger ones, referred to as underdog achievement, is influenced by inherent randomness factors that affect match outcomes in such…

Applications · Statistics 2024-04-11 Luis Nunes Vicente , Thaksheel Alleck , Tommaso Giovannelli , Roman Mitchell , Ori Remen

Contemporary statistical publications rely on simulation to evaluate performance of new methods and compare them with established methods. In the context of meta-analysis of log-odds-ratios, we investigate how the ways in which simulations…

Methodology · Statistics 2020-07-06 Elena Kulinskaya , David C. Hoaglin , Ilyas Bakbergenuly

Pressing is a fundamental defensive strategy in football, characterized by applying pressure on the ball owning team to regain possession. Despite its significance, existing metrics for measuring pressing often lack precision or…

Applications · Statistics 2025-07-01 Joris Bekkers