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Bayesian approach for K-football league using Poisson distribution
Journal of the Korean Data & Information Science Society 2024;35:309-20
Published online May 31, 2024;
© 2024 Korean Data and Information Science Society.

Yoon Sanghoo1 · Baek Namjin2 · Seo Yun Am3

1Department of Statistics, Chonnam National University
2Department of Statistics, Daegu University
3Department of Data Science, Jeju National University
Correspondence to: 1 Associate Professor, Department of Statistics , Chonnam National University, Gwangju, 61186, Korea.
2 Under graduate student, Department of Statistics , Daegu University, Daegu, 38453, Korea.
3 Assistant Professor, Department of Data Science, Jeju National University, Jeju, 63423, Korea. E-mail:
Received April 21, 2024; Revised May 8, 2024; Accepted May 10, 2024.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
In sports, statistics play a crucial role in determining game performance and outcome. Football is the most popular sport globally, played by kicking a ball into the opponent’s net to score points and decide the outcome. This study analyzes K-League football matches from 2023 using the Poisson distribution (PD). In football, the number of goals scored follows a PD, making it ideal for analyzing goal frequency. However, since goals in football involve two components - goals scored and goals conceded - a bivariate PD (or double PD) can be applied for a more comprehensive analysis. The Skellam distribution, which focuses on the probability distribution of goal difference, was also considered. Extending the probability distribution to a dynamic model, we can simulate the variation in goal difference throughout a football match. This study employed a dynamic bivariate PD and a dynamic double PD to analyze the round-by-round changes in K-League matches during 2023. The Markov chain for the Bayesian model was set to 4, and the number of iterations was set to 1,000. The analysis using Bayesian likelihood ratio testing revealed that the Skellam distribution provided the best fit for K-League football in 2023.
Keywords : Bivariate Poisson distribution, double Poisson distribution, football statistics, K-League, Skellam distribution