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Football is a very result-driven industry, with goals being rarer than in most sports, so having further parameters to judge the performance of teams and individuals is key. Expected Goals (xG) allow further insight than just a scoreline.…

Machine Learning · Computer Science 2023-09-04 James H. Hewitt , Oktay Karakuş

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

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

This study employs Bayesian methodologies to explore the influence of player or positional factors in predicting the probability of a shot resulting in a goal, measured by the expected goals (xG) metric. Utilising publicly available data…

Applications · Statistics 2025-01-14 Alexander Scholtes , Oktay Karakuş

Analysis of the popular expected goals (xG) metric in soccer has determined that a (slightly) smaller number of high-quality attempts will likely yield more goals than a slew of low-quality ones. This observation has driven a change in…

Artificial Intelligence · Computer Science 2023-02-17 Maaike Van Roy , Pieter Robberechts , Wen-Chi Yang , Luc De Raedt , Jesse Davis

The expected goal provides a more representative measure of the team and player performance which also suit the low-scoring nature of football instead of score in modern football. The score of a match involves randomness and often may not…

Machine Learning · Computer Science 2023-02-14 Mustafa Cavus , Przemysław Biecek

This study develops a hierarchical Bayesian framework that integrates expert domain knowledge to quantify player-specific effects in expected goals (xG) estimation, addressing a limitation of standard models that treat all players as…

Signal Processing · Electrical Eng. & Systems 2025-12-01 Mikayil Mahmudlu , Oktay Karakuş , Hasan Arkadaş

Probabilistic modeling is an effective tool for evaluating team performance and predicting outcomes in sports. However, an important question that hasn't been fully explored is whether these models can reliably reflect actual performance…

Methodology · Statistics 2026-02-18 Sheikh Badar Ud Din Tahir , Leonardo Egidi , Nicola Torelli

In recent years, many different approaches have been proposed to quantify the performances of soccer players. Since player performances are challenging to quantify directly due to the low-scoring nature of soccer, most approaches estimate…

Machine Learning · Computer Science 2021-05-31 Jan Van Haaren

Measuring soccer shooting skill is a challenging analytics problem due to the scarcity and highly contextual nature of scoring events. The introduction of more advanced data surrounding soccer shots has given rise to model-based metrics…

Applications · Statistics 2024-01-08 Ethan Baron , Nathan Sandholtz , Devin Pleuler , Timothy C. Y. Chan

The expected goal models have gained popularity, but their interpretability is often limited, especially when trained using black-box methods. Explainable artificial intelligence tools have emerged to enhance model transparency and extract…

Machine Learning · Computer Science 2023-08-31 Mustafa Cavus , Adrian Stando , Przemyslaw Biecek

The recent growth in data availability in football has increased the risk of incorrect use of data-driven models, making guidelines on their validation and application necessary. The Expected Threat (xT) model is an accessible option for…

Applications · Statistics 2026-04-28 Koen van Arem , Jakob Söhl , Mirjam Bruinsma , Geurt Jongbloed

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

This paper proposes a novel framework to assess individual player contributions in football, explicitly accounting for the cooperative nature of shot-ending offensive actions. By incorporating team interaction into player evaluation, it…

Applications · Statistics 2026-05-05 Mattia Cefis , Rodolfo Metulini , Maurizio Carpita

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

Complex interactions between two opposing agents frequently occur in domains of machine learning, game theory, and other application domains. Quantitatively analyzing the strategies involved can provide an objective basis for…

Machine Learning · Computer Science 2023-07-28 Calvin C. K. Yeung , Keisuke Fujii

Scientifically evaluating soccer players represents a challenging Machine Learning problem. Unfortunately, most existing answers have very opaque algorithm training procedures; relevant data are scarcely accessible and almost impossible to…

Machine Learning · Computer Science 2021-01-15 Paul Garnier , Théophane Gregoir

This study outlines a light gradient boosted model aimed at predicting shot outcomes in the NHL. The model uses the NHL's spatiotemporal data to account for both the skill of shooters and goaltenders. This approach involves isolating and…

Other Computer Science · Computer Science 2025-11-18 J. T. P. Noel

Football forecasting models traditionally rate teams on past match results, that is based on the number of goals scored. Goals, however, involve a high element of chance and thus past results often do not reflect the performances of the…

Applications · Statistics 2021-01-07 Edward Wheatcroft , Ewelina Sienkiewicz

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
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