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Competitive balance in a football league is extremely important from the perspective of economic growth of the industry. Many researchers have earlier proposed different measures of competitive balance, which are primarily adapted from the…

Applications · Statistics 2021-02-19 Soudeep Deb

This note proposes a penalty criterion for assessing correct score forecasting in a soccer match. The penalty is based on hierarchical priorities for such a forecast i.e., i) Win, Draw and Loss exact prediction and ii) normalized Euclidian…

Applications · Statistics 2018-06-06 Jean-Louis Foulley , Gilles Celeux

Performance prediction or forecasting sporting outcomes involves a great deal of insight into the particular area one is dealing with, and a considerable amount of intuition about the factors that bear on such outcomes and performances. The…

In this paper, we present a novel approach for optimising long-term tactical and strategic decision-making in football (soccer) by encapsulating events in a league environment across a given time frame. We model the teams' objectives for a…

Artificial Intelligence · Computer Science 2021-02-19 Ryan Beal , Georgios Chalkiadakis , Timothy J. Norman , Sarvapali D. Ramchurn

In-game win probability models, which provide a sports team's likelihood of winning at each point in a game based on historical observations, are becoming increasingly popular. In baseball, basketball and American football, they have become…

Machine Learning · Computer Science 2021-08-16 Pieter Robberechts , Jan Van Haaren , Jesse Davis

We introduce a class of extensive form games where players might not be able to foresee the possible consequences of their decisions and form a model of their opponents which they exploit to achieve a more profitable outcome. We improve…

Artificial Intelligence · Computer Science 2016-05-31 Paolo Turrini

A knowledgeable observer of a game of football (soccer) can make a subjective evaluation of the quality of passes made between players during the game. We investigate the problem of producing an automated system to make the same evaluation…

Machine Learning · Computer Science 2017-08-22 Michael Horton , Joachim Gudmundsson , Sanjay Chawla , Joël Estephan

Probability forecasts are intended to account for the uncertainties inherent in forecasting. It is suggested that from an end-user's point of view probability is not necessarily sufficient to reflect uncertainties that are not simply the…

Statistics Theory · Mathematics 2015-01-22 Kevin Judd

Accurately predicting the outcome of sporting events has been a goal for many groups who seek to maximize profit. What makes this challenging is that the outcome of an event can be influenced by many factors that dynamically change across…

Applications · Statistics 2017-10-23 Erik J. Schlicht

Although the data-driven analysis of football players' performance has been developed for years, most research only focuses on the on-ball event including shots and passes, while the off-ball movement remains a little-explored area in this…

Machine Learning · Computer Science 2023-09-06 Yisheng Pei , Varuna De Silva , Mike Caine

An open problem posed by the first author is the complexity to decide whether a sequence of nonnegative integer numbers can be the final score of a football tournament. In this paper we propose polynomial time approximate and exponential…

Discrete Mathematics · Computer Science 2012-07-27 A. Iványi , J. E. Schoenfield

Football (soccer) is a sport that is characterised by complex game play, where players perform a variety of actions, such as passes, shots, tackles, fouls, in order to score goals, and ultimately win matches. Accurately forecasting the…

Machine Learning · Computer Science 2025-11-25 Michael Horton , Patrick Lucey

Forecast of football outcomes in terms of Home Win, Draw and Away Win relies largely on ex ante probability elicitation of these events and ex post verification of them via computation of probability scoring rules (Brier, Ranked…

Applications · Statistics 2024-08-09 Jean-Louis Foulley

We provide a comprehensive examination of the predictive performance of panel forecasting methods based on individual, pooling, fixed effects, and empirical Bayes estimation, and propose optimal weights for forecast combination schemes. We…

Econometrics · Economics 2026-01-30 M. Hashem Pesaran , Andreas Pick , Allan Timmermann

This paper gives game-theoretic versions of several results on "merging of opinions" obtained in measure-theoretic probability and algorithmic randomness theory. An advantage of the game-theoretic versions over the measure-theoretic results…

Probability · Mathematics 2007-05-23 Vladimir Vovk

Continuous-time assessments of game outcomes in sports have become increasingly common in the last decade. In American football, only discrete-time estimates of play value were possible, since the most advanced public football datasets were…

The English Premier League is well-known for being not only one of the most popular professional sports leagues in the world, but also one of the toughest competitions to predict. The first purpose of this research was to verify the…

Applications · Statistics 2022-01-05 Quang Nguyen

A myriad of different data are generated to characterize a soccer match. Here we discuss which performance indicators are particularly helpful to forecast the future results of a team via an estimation of the underlying team strengths with…

Physics and Society · Physics 2020-03-10 Andreas Heuer

The goal of this thesis is to investigate the potential of predictive modelling for football injuries. This work was conducted in close collaboration with Tottenham Hotspurs FC (THFC), the PGA European tour and the participation of…

Applications · Statistics 2016-09-27 Stylianos Kampakis

Transfers in professional football (soccer) are risky investments because of the large transfer fees and high risks involved. Although data-driven models can be used to improve transfer decisions, existing models focus on describing…

Applications · Statistics 2025-09-29 Koen W. van Arem , Floris Goes-Smit , Jakob Söhl