Mera pričakovanih zadetkov v nogometu in njena uporaba

Peček, Urh (author), Kejžar, Nataša (mentor)

V delu je obravnavana mera pričakovanih zadetkov v nogometni igri. Koncept in izračun pričakovanih zadetkov je predstavljen tako teoretično kot praktično. Opisane so spremenljivke, za katere menimo, da v nogometni igri vplivajo na vrednosti pričakovanih zadetkov. Analiziran je vpliv porazdelitve vrednosti pričakovanih zadetkov in njihova uporaba za kvantifikacijo uspešnosti igralca ali ekipe. Na podlagi pričakovanih zadetkov je izpeljana in praktično predstavljena mera pričakovanih točk. Predstavljena je metoda napovedovanja rezultatov nogometnih tekem, ki temelji na Poissonovi porazdelitvi in je posodobljena z upoštevanjem pričakovanih zadetkov. Na praktičnem primeru so primerjane metode z in brez upoštevanja pričakovanih zadetkov. Obravnavana tema se trenutno zelo hitro razvija. Večina zamisli je objavljena v polstrokovnih člankih na spletu. V pričujočem delu so prevedene v matematični oziroma statistični jezik ter urejeno in celostno predstavljene, dodane pa so tudi nekatere nove, avtorjeve zamisli. Vsem teoretično predstavljenim konceptom so dodani praktični primeri. Vse analize, simulacije in rezultati so pridobljeni s pomočjo računalniškega statističnega programa R. V sklopu tega so uporabljeni tudi nekateri specifični paketi, kot so regista, StatsBombR, ggsoccer, SBpitch, worldfootballR in soccermatics. Uporabljeni pristop se je izkazal kot učinkovit. V prihodnosti bi bilo smiselno razširiti analize na preučevanje dejavnikov, ki vplivajo na spremenljivke, iz katerih se izračuna vrednost xG. Lahko bi preučili tudi, kako se vrednosti xG razlikujejo med različnimi ravnmi tekmovanj, ali pa bi za napovedovanje rezultatov nogometnih tekem uporabili modele strojnega učenja, v katere bi vključili vrednost xG.

• Language: Slovenian
• Keywords: pričakovani zadetki, pričakovane točke, Monte Carlo simulacija, logistična regresija, Poissonova porazdelitev, model Dixon-Coles, nogomet
• Work type: Master's thesis/paper
• Organization: FE - Faculty of Electrical Engineering
• Year: 2022
• PID: 20.500.12556/RUL-141222
• COBISS.SI-ID: 124345091
• Publication date in RUL: 26.09.2022

PEČEK, Urh, 2022, Mera pričakovanih zadetkov v nogometu in njena uporaba [online]. Master’s thesis. [Accessed 11 April 2025]. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=141222

Secondary language

• Language: English
• Title: Measure of expected goals in football and its applications

Abstract

The measure of expected goals in a a football game is discussed in the work. The concept and calculation of expected goals is presented both theoretically and practically. The impact of the distribution of expected goals and their use to quantify player or team performance is described. On the basis of expected goals, the measure of expected points is derived and practically presented. A method for predicting the results of football games based on the Poisson distribution is presented and updated to take expected goals into account. A practical example compares methods with and without taking expected goals into account. The topic under discussion is currently rapidly developing. Most of the ideas are obtained in semi-professional articles online. In the present work, they are translated into mathematical or statistical language and presented in an orderly and comprehensive manner, and some new ideas of the author are also added. Practical examples are added to all theoretically presented concepts. All analyses, simulations and results are obtained with the help of the computer statistical program R. As part of this, some specific packages are used, such as regista, StatsBombR, ggsoccer, SBpitch, worldfootballR and soccermatics. The approach used has proven to be effective. We assessed which variables statistically significant and in what way affect the probability of a goal in a football game at the highest male professional level. In the future, it would be reasonable to extend the analyzes to the study of factors that influence the variables from which the xG value is calculated. We could look at how the xG values vary between different levels of competition. We could also predict the results of football games with some machine learning models and check the impact of the inclusion of the xG value on the quality of the predictions.

• Keywords: expected goals, expected points, Monte Carlo simulation, logistic regression, Poisson distribution, Dixon-Coles model, football