Vjerojatnosne razdiobe u nogometu

master's thesis

• Title (english): Probability distributions in football
• Author: Filip Brkić
• Mentor: Franka Miriam Brückler (mentor)
• Committee member: Franka Miriam Brückler (predsjednik povjerenstva)
• Committee member: Zrinka Franušić (član povjerenstva)
• Committee member: Tomislav Berić (član povjerenstva)
• Committee member: Snježana Lubura Strunjak (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2021-03-05, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom su radu opisane neke osnovne primjene vjerojatnosnih razdioba u jednom od najpopularnijih sportova, nogometu. Rad je podijeljen u četiri poglavlja u kojima su opisane primjene binomne, Poissonove i normalne razdiobe. U prvom poglavlju su opisani i definirani osnovni pojmovi iz teorije vjerojatnosti. U drugom poglavlju se opisuje primjena binomne razdiobe na konkretne nogometne situacije, točnije na izračunavanje vjerojatnosti određenih rezultata utakmica uz pretpostavku poznavanja ukupnog broja pogodaka i prosječnih brojeva pogodaka koje su momčadi dale u nekom prethodnom razdoblju. U trećem poglavlju koristi se Poissonova razdioba za prognoziranje vjerojatnosti ishoda nogometne utakmice. U posljednjem poglavlju koristimo normalnu razdiobu za procjenu vjerojatnosti da je prvak neke lige stvarno bio najbolji.

Abstract (english)

In this thesis we describe some basic applications of probability distributions in one of the most popular sports, football (soccer). The thesis is divided in four chapters, giving applications of binomial, Poisson and normal distribution. In the first chapter fundamental probability concepts are described. In the second chapter we describe the application of the binomial distribution in concrete football situations, more precisely for calculating probabilities of specific results given a total number of goals scored and average numbers of goals of the teams in a chosen previous period. In the third chapter we use the Poisson distribution to estimate probabilities of outcomes of a football match. In the last chapter we use the normal distribution to estimate the probability that the league champion was truly the best team.

• Keywords: binomna razdioba; Poissonova razdioba; normalna razdioba; teorija vjerojatnosti
• Keywords (english): binomial distribution; Poisson distribution; normal distribution; probability concepts
• Language: croatian
• URN:NBN: urn:nbn:hr:217:541367
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2021-03-23 12:31:19