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We provide practical, efficient, and nonparametric methods for auditing the fairness of deployed classification and regression models. Whereas previous work relies on a fixed-sample size, our methods are sequential and allow for the…

Machine Learning · Statistics 2025-05-19 Ben Chugg , Santiago Cortes-Gomez , Bryan Wilder , Aaditya Ramdas

Converting betting odds into accurate outcome probabilities is a fundamental challenge in order to use betting odds as a benchmark for sports forecasting and market efficiency analysis. In this study, we propose two methods to overcome the…

Machine Learning · Statistics 2026-04-21 Kaito Goto , Naoya Takeishi , Takehisa Yairi

We consider the game-theoretic scenario of testing the performance of Forecaster by Sceptic who gambles against the forecasts. Sceptic's current capital is interpreted as the amount of evidence he has found against Forecaster. Reporting the…

Statistics Theory · Mathematics 2010-11-23 A. Philip Dawid , Steven de Rooij , Glenn Shafer , Alexander Shen , Nikolai Vereshchagin , Vladimir Vovk

The world of empirical machine learning (ML) strongly relies on benchmarks in order to determine the relative effectiveness of different algorithms and methods. This paper proposes the notion of "a benchmark lottery" that describes the…

Machine Learning · Computer Science 2021-07-19 Mostafa Dehghani , Yi Tay , Alexey A. Gritsenko , Zhe Zhao , Neil Houlsby , Fernando Diaz , Donald Metzler , Oriol Vinyals

We generalize the momentum indicator idea taking into account the volume of transactions as a multiplicative factor. We compare returns obtained following strategies based on the classical or the generalized technical analysis, taking into…

Statistical Mechanics · Physics 2025-10-20 M. Ausloos , K. Ivanova

A team of association football players may be envisioned as a directed network with player nodes and weighted pass edges. Such a simplistic representation of an otherwise complex structure yields several benefits, but also permits the…

Social and Information Networks · Computer Science 2021-08-12 Vid Stropnik , Vuk Đuranović , Maruša Oražem

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 study statistics of the knockout tournament, where only the winner of a fixture progresses to the next. We assign a real number called competitiveness to each contestant and find that the resulting distribution of prize money follows a…

Physics and Society · Physics 2014-01-09 Seung Ki Baek , Il Gu Yi , Hye Jin Park , Beom Jun Kim

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

Data visualizations are standard tools for assessing and communicating risks. However, it is not always clear which designs are optimal or how encoding choices might influence risk perception and decision-making. In this paper, we report…

Human-Computer Interaction · Computer Science 2020-10-28 Melanie Bancilhon , Zhengliang Liu , Alvitta Ottley

Penalty shootouts play a crucial role in the knockout stage of major football tournaments. Their importance has substantially increased from the 2021/22 season, when the Union of European Football Associations (UEFA) scrapped the away goals…

General Economics · Economics 2026-04-09 László Csató , Dóra Gréta Petróczy

Consumers often face products sold as lotteries rather than fixed outcomes. A prominent case is the loot box in video games, where players pay for randomized rewards. We investigate how presentation formats shape consumer beliefs and…

General Economics · Economics 2025-11-04 Markus Dertwinkel-Kalt , Hans-Theo Normann , Jan-Niklas Tiede , Tobias Werner

This paper develops a general framework for stochastic modeling of goals and other events in football (soccer) matches. The events are modelled as Cox processes (doubly stochastic Poisson processes) where the event intensities may depend on…

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 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

Financial markets investors are involved in many games -- they must interact with other agents to achieve their goals. Among them are those directly connected with their activity on markets but one cannot neglect other aspects that…

Trading and Market Microstructure · Quantitative Finance 2008-12-02 Edward W. Piotrowski , Jan Sladkowski , Anna Szczypinska

Tennis is so popular that coaches and players are curious about factors other than skill, such as momentum. This article will try to define and quantify momentum, providing a basis for real-time analysis of tennis matches. Based on the…

Machine Learning · Computer Science 2026-03-25 Ruixin Peng , Ziqing Li

This paper studies the problem of robot performance evaluation, focusing on how to obtain accurate and efficient estimates of real-world behavior under severe constraints on physical experimentation. Such estimates are essential for…

Robotics · Computer Science 2026-04-28 Zaid Mahboob , Yujia Chen , Bowen Weng

Much of modern society is founded on orchestrating institutions that produce social goods by fostering motivated teams, pitting them against each other, and distributing the fruits of the arms races that ensue. However, even when the…

Physics and Society · Physics 2020-09-23 Adam Sawyer , Seth Frey

Recent techniques for analyzing sports precisely has stimulated various approaches to improve player performance and fan engagement. However, existing approaches are only able to evaluate offline performance since testing in real-time…

Machine Learning · Computer Science 2022-11-23 Li-Chun Huang , Nai-Zen Hseuh , Yen-Che Chien , Wei-Yao Wang , Kuang-Da Wang , Wen-Chih Peng