# SOCCER SEASON SIMULATION WITH FIXED MATCHES

## Authors

• Oleg Chertov National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"; Faculty of Applied Mathematics; Department of Applied Mathematics, ave. 37 Beresteyskyi str., Kyiv, Ukraine, 03056, Ukraine
• Ivan Zhuk National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"; Faculty of Applied Mathematics; Department of Applied Mathematics, ave. 37 Beresteyskyi str., Kyiv, Ukraine, 03056, Ukraine

## Keywords:

football season, team grouping, Poisson distribution, goal difference histogram, type of match result

## Abstract

Background. Football is a huge industry comparable to traditional economic sectors. In numerical terms, it is tens of billions of dollars. But one of the most important problems that this industry faces is match fixing (matches with a fixed result).

The most effective way to prevent this threat is a multilateral approach combined with measures aimed at expanding the potential of law enforcement agencies and sports organizations. One of the components of this approach is the use of mathematical methods for identifying suspicious match-fixing results.

Objective. The purpose of the paper is to develop an algorithm for modelling fixed matches related to earnings on bets, which is used to form matches which results are different from the expected ones and can be considered as anomalous.

Methods. Calculation of probabilities of scoring goals by teams during the game based on real data of the season; development of a simulation model of a football season without fixed matches and its analysis by means of statistical modelling; development of an algorithm for modelling fixed matches related to earnings on bets and its analysis.

Results. A simulation model of a football season has been developed, which allows, using probability distributions of the number of goals scored by teams during home or away games obtained on real data, simulating the results of matches, taking into account the strength of the teams and the game type, as well as to simulate the situations of a “fixed” match, replacing the current results. In terms of the overall distributions of match result types and goal differences of all matches, the simulated season is similar to the real season. According to the Kolmogorov-Smirnov test, the difference between the given distributions at the significance level of 0.001 is statistically insignificant.

Conclusions. The developed simulation model of a football season can be used to study the effectiveness of methods for detecting fixed matches and their comparative analysis.

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