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Consider two forecasters, each making a single prediction for a sequence of events over time. We ask a relatively basic question: how might we compare these forecasters, either online or post-hoc, while avoiding unverifiable assumptions on…

Methodology · Statistics 2023-11-10 Yo Joong Choe , Aaditya Ramdas

League competition is investigated using random processes and scaling techniques. In our model, a weak team can upset a strong team with a fixed probability. Teams play an equal number of head-to-head matches and the team with the largest…

Physics and Society · Physics 2007-08-13 E. Ben-Naim , N. W. Hengartner

Despite growing interest in quantifying and modeling the scoring dynamics within professional sports games, relative little is known about what patterns or principles, if any, cut across different sports. Using a comprehensive data set of…

Applications · Statistics 2014-03-24 Sears Merritt , Aaron Clauset

There seems to be an upper limit to predicting the outcome of matches in (semi-)professional sports. Recent work has proposed that this is due to chance and attempts have been made to simulate the distribution of win percentages to identify…

Applications · Statistics 2015-08-21 Albrecht Zimmermann

We present a framework that gives a deep insight into the link between physical and technical-tactical aspects of soccer and it allows associating physical performance with value generation thanks to a top-down approach. First, we estimate…

Machine Learning · Statistics 2022-04-06 Sergio Llana , Borja Burriel , Pau Madrero , Javier Fernández

We propose a new mathematical model for the decision-making of players in football (soccer) and the efficiency of the game style. Our approach is based on $4$-networks, which is a mathematical concept that we introduce. The decision of…

General Mathematics · Mathematics 2024-01-31 Brahim Boudine

We compare various extensions of the Bradley-Terry model and a hierarchical Poisson log-linear model in terms of their performance in predicting the outcome of soccer matches (win, draw, or loss). The parameters of the Bradley-Terry…

Penalties are fraught and game-changing moments in soccer games that teams explicitly prepare for. Consequently, there has been substantial interest in analyzing them in order to provide advice to practitioners. From a data science…

Machine Learning · Computer Science 2025-06-02 Lotte Bransen , Tim Janssen , Jesse Davis

Injuries have a great impact on professional soccer, due to their large influence on team performance and the considerable costs of rehabilitation for players. Existing studies in the literature provide just a preliminary understanding of…

Machine Learning · Statistics 2018-11-06 Alessio Rossi , Luca Pappalardo , Paolo Cintia , Marcello Iaia , Javier Fernandez , Daniel Medina

We present an extensive statistical analysis of the results of all sports competitions in five major sports leagues in England and the United States. We characterize the parity among teams by the variance in the winning fraction from…

Physics and Society · Physics 2007-05-23 E. Ben-Naim , F. Vazquez , S. Redner

We consider the task of determining the number of chances a soccer team creates, along with the composite nature of each chance-the players involved and the locations on the pitch of the assist and the chance. We propose an interpretable…

Applications · Statistics 2018-02-26 Gavin A. Whitaker , Ricardo Silva , Daniel Edwards

Predicting the results of soccer matches is of great interest. This is not only due to the popularity of the sport and the joy of private "betting rounds", but also due to the large sports betting market. Where previously expert knowledge…

Applications · Statistics 2025-07-09 Mirko Fischer , Andreas Heuer

Probabilistic properties of tennis scoring systems are examined and compared with best-of-K systems. A model, where each player has his/her own probability of winning his/her service point and which remains invariant for the duration of the…

Probability · Mathematics 2026-03-04 Edsel A. Pena , Dip Das , Yuexuan Wu

Evaluating the individual movements for teammates in soccer players is crucial for assessing teamwork, scouting, and fan engagement. It has been said that players in a 90-min game do not have the ball for about 87 minutes on average.…

Artificial Intelligence · Computer Science 2022-07-28 Masakiyo Teranishi , Kazushi Tsutsui , Kazuya Takeda , Keisuke Fujii

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

In this paper, we describe an approach to rank sport players based on their efficiency. Although is extremely useful to analyze the performance of team games there is no unanimity on the use of a single index to perform such a ranking. We…

Optimization and Control · Mathematics 2018-02-21 Víctor Blanco , Román Salmerón , Samuel Gómez-Haro

In a soccer game, the information provided by detecting and tracking brings crucial clues to further analyze and understand some tactical aspects of the game, including individual and team actions. State-of-the-art tracking algorithms…

Computer Vision and Pattern Recognition · Computer Science 2020-11-23 Samuel Hurault , Coloma Ballester , Gloria Haro

In this paper, we study collective interaction dynamics emerging in the game of football-soccer. To do so, we surveyed a database containing body-sensors traces measured during three professional football matches, where we observed…

Physics and Society · Physics 2021-08-18 A. Chacoma , N. Almeira , J. I. Perotti , O. V. Billoni

Existing match classification models in the tournament design literature have two major limitations: a contestant is considered indifferent only if uncertain future results do never affect its prize, and competitive matches are not…

Physics and Society · Physics 2026-01-29 László Csató , András Gyimesi

Game Theory concepts have been successfully applied in a wide variety of domains over the past decade. Sports and games are one of the popular areas of game theory application owing to its merits and benefits in solving complex scenarios.…

Computer Science and Game Theory · Computer Science 2021-05-26 Ambareesh Ravi , Atharva Gokhale , Anchit Nagwekar