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Real-time probability forecasts for binary outcomes are routine in sports, online experimentation, medicine, and finance. Retrospective narratives, however, often hinge on pathwise extremes: for example, a forecast that becomes "90%…

Applications · Statistics 2026-04-03 Jonathan Pipping-Gamón , Abraham J. Wyner

To score goals in football, a team needs to move forward on the pitch and there are various ways to do so. Depending on the game plan & philosophy; some teams prefer to play long balls from either wings or defense. Others, prefer to…

Machine Learning · Computer Science 2023-02-22 Hadi Sotudeh

Do NFL teams make rational decisions? What factors potentially affect the probability of wining a game in NFL? How can a team come back from a demoralizing interception? In this study we begin by examining the hypothesis of rational…

Applications · Statistics 2017-02-08 Konstantinos Pelechrinis , Evangelos Papalexakis

We show that the standard computational pipeline of probabilistic programming systems (PPSs) can be inefficient for estimating expectations and introduce the concept of expectation programming to address this. In expectation programming,…

Machine Learning · Computer Science 2022-06-22 Tim Reichelt , Adam Goliński , Luke Ong , Tom Rainforth

In an attempt to provide an answer to the increasing criticism against p-values and to bridge the gap between statistical inference and prediction modelling, we introduce the probability of improved prediction (PIP). In general, the PIP is…

Methodology · Statistics 2024-05-28 Olivier Thas , Stijn Jaspers

With the development of measurement technology, data on the movements of actual games in various sports can be obtained and used for planning and evaluating the tactics and strategy. Defense in team sports is generally difficult to be…

Artificial Intelligence · Computer Science 2022-05-10 Kosuke Toda , Masakiyo Teranishi , Keisuke Kushiro , Keisuke Fujii

The most important part of model selection and hyperparameter tuning is the evaluation of model performance. The most popular measures, such as AUC, F1, ACC for binary classification, or RMSE, MAD for regression, or cross-entropy for…

Machine Learning · Computer Science 2019-08-27 Alicja Gosiewska , Mateusz Bakala , Katarzyna Woznica , Maciej Zwolinski , Przemyslaw Biecek

This paper introduces the Expected Booking (xB) model, a novel metric designed to estimate the likelihood of a foul resulting in a yellow card in football. Through three iterative experiments, employing ensemble methods, the model…

Machine Learning · Computer Science 2024-01-18 Adnan Azmat , Su Su Yi

A popular quantitative approach to evaluating player performance in sports involves comparing an observed outcome to the expected outcome ignoring player involvement, which is estimated using statistical or machine learning methods. In…

Applications · Statistics 2026-05-22 Robert Bajons , Lucas Kook

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

In this paper, we propose two novel basketball metrics: ``expected points'' for team-based comparisons and ``expected points above average (EPAA)'' as a player-evaluation tool. Established within the Bayesian hierarchical model framework,…

Other Statistics · Statistics 2025-08-05 Benjamin Williams , Erin M. Schliep , Bailey Fosdick , Ryan Elmore

In most sports, especially football, most coaches and analysts search for key performance indicators using notational analysis. This method utilizes a statistical summary of events based on video footage and numerical records of goal…

Machine Learning · Computer Science 2022-07-26 Chenyao Li , Stylianos Kampakis , Philip Treleaven

Line-breaking passes (LBPs) are crucial tactical actions in football, allowing teams to penetrate defensive lines and access high-value spaces. In this study, we present an unsupervised, clustering-based framework for detecting and…

Machine Learning · Computer Science 2025-06-10 Oktay Karakuş , Hasan Arkadaş

The increasing availability of spatio-temporal tracking data has created new opportunities for analysing tactical behaviour in football. However, many existing approaches evaluate passes primarily through outcome-based metrics such as…

Machine Learning · Computer Science 2026-04-01 Oktay Karakuş , Hasan Arkadaş

In this article we revise the football's performance score called PlayeRank, designed and evaluated by Pappalardo et al.\ in 2019. First, we analyze the weights extracted from the Linear Support Vector Machine (SVM) that solves the…

Machine Learning · Computer Science 2024-10-29 Louise Schmidt , Cristian Lillo , Javier Bustos

Many existing interpretation methods are based on Partial Dependence (PD) functions that, for a pre-trained machine learning model, capture how a subset of the features affects the predictions by averaging over the remaining features.…

Machine Learning · Computer Science 2025-06-05 Jinyang Liu , Tessa Steensgaard , Marvin N. Wright , Niklas Pfister , Munir Hiabu

Selective Prediction is the task of rejecting inputs a model would predict incorrectly on. This involves a trade-off between input space coverage (how many data points are accepted) and model utility (how good is the performance on accepted…

How much is an on-ball screen worth? How much is a backdoor cut away from the ball worth? Basketball is one of a number of sports which, within the past decade, have seen an explosion in quantitative metrics and methods for evaluating…

Applications · Statistics 2019-02-22 Anthony Sicilia , Konstantinos Pelechrinis , Kirk Goldsberry

Sports analytics -- broadly defined as the pursuit of improvement in athletic performance through the analysis of data -- has expanded its footprint both in the professional sports industry and in academia over the past 30 years. In this…

Applications · Statistics 2023-01-11 Benjamin S. Baumer , Gregory J. Matthews , Quang Nguyen

In the National Basketball Association (NBA), teams must make choices about which players to acquire, how much to pay them, and other decisions that are fundamentally dependent on player effectiveness. Thus, there is great interest in…

Applications · Statistics 2013-01-17 Dapo Omidiran