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# A parametric deterministic model for estimating football trivariate outcome point

AUTHOR(S):

JOURNAL: Journal of Nigerian Statistical Association Vol.32, 2020
YEAR: 2020

## ABSTRACT

This study aimed at using a standardized bivariate Pearson family of distribution to generalize a bivariate function and also develop a Parametric Deterministic Model (PDM) that represents mathematical relationship between football matches having trivariate outcomes and the position of teams in the league table. The study established bivariate function as a useful generalization of the univariate Pareto (Type 1) distribution; it also evaluated the previous five-year performance of teams from four major leagues in Europe based on their end of season points(Pik). The Anderson-Darling goodness of fit test (AD-Test) was employed to measure how well the data fits specified theoretical distribution. Negative Binomial distribution is the model that provides the best fit for approximating the distribution of the over-dispersed estimated points associated with six top teams in each of the four leagues. The result revealed Ligue 1 is the most competitive among the four leagues while English Premier League (EPL) is rated the most competitive in the sub-leagues of six teams at the top of the table. The PDM accurately modelled the potential outcomes of series of football matches with the corresponding estimated points for the teams and also generated the league table for EPL using data of 2016/2017 football season.

## BIBLIOGRAPHY

Baio, G. Blangiardo, M. (2010). Bayesian Hierarchical Model for the Prediction of Football Results. Journal of Applied Statistics, 37(2), 253-264, DOI: 10.1080/02664760802684177.

Barry C.A. (1983). Pareto Distribution, International Cooperative Publ. House.

Bittner, A., Nussbaumer, A., Janke, W. and Weigel, M. (2007). Self –Affirmation Model for Football Goal Distributions, Europhysics Letters Association, arXiv:0705-2724v1.1-6. DOI: 10.1209/0295-5075/78/58002.

Broatch, J.E. and Karl, A.T. (2017). Multivariate Generalized Linear Mixed Models for Joint Estimation of Sporting Outcomes, Italian Journal of Applied Statistics, 30(2), 189-211.

Cattelan, M., Varin, C. and Firth, D. (2013). Dynamic Bradley – Terry Modeling of Sports Tournaments, Journal of the Royal Statistical Society, Series C, 62, 135-150.

Dixon, M. and Cole, S. (1997). Modeling Association Football Scores and Inefficiencies in the Football Betting Market, Journal of the Royal Statistical Society, Series C, 46, 265 – 280.

Eugene N., Lee, C and Famoye, F. (2002). Beta-Normal Distribution and its Applications, Communications in Statistics-Theory Methods, 31, 497-512.

Giovanni, A. and Luca, D.A. (2016). PARX Model for Football Match Predictions, Journal of Forecasting, DOI; 1002/for.2471.

Hill, I.D. (1974). Association Football and Statistical Inference, Applied Statistics, 23(2), 203-208.

Hughes, M. and Franks, I. (2005). Analysis of Passing Sequences, Shots and Goals in Soccer, Journal of the Royal Statistical Society, Series A, Vol. 134, DOI: 10.1080/02640410410001716779.

Johnson N.L (1949). Systems of Frequency Curves Generated by Translation, Biometrika, 36, 149-176.

Karlis, D. and Ntzoufras, I. (2003). Analysis of Sports Data Using Bivariate Poisson Models, Journal of the Royal Statistical Society, Series D, 52,381-393, DOI:10.1111/1467-9884.00366.

Karlis, D. and Ntzoufras, I. (2008). Bayesian Modeling of Football Outcomes: Using the Skellam’s Distribution for the Goals Difference, IMAJ Management Math, 20 (2), 133 – 145.

Maher, M.J. (1982). Modeling Association Football Scores, Statistica Neeerlandica, 36, 109 – 118, DOI:10.1111/j.1467-9574.1982.tb00782.x.

Marshall, A.N. and Olkin, I. (1997). A New Method of Adding Parameter to a Family of Distributions with Applications to the Exponential and Weibull Families, Biometrika, 84, 64 1-652.

Moroney, M.J. (1957). Facts from Figures, The Journal of the American Statistical Association, 52 (277), 623 – 629.

Pearson, K. (1895). Contribution to the Mathematical Theory of Evolution. II. Skew Variation in Homogeneous Material, Philos Trans. R. Soc. Lond. A, 186, 343-414.

Reep, C. and Benjamin, B. (1968). Skill and Chance in Association Football, Journal of the Royal Statistical Society, 131, 581-585.

Reep, C., Pollard, and Benjamin, B. (1971). Skill and Chance in Ball Games, Journal of the Royal Statistical Society A, 134, 623-629.

Siem J.K. and Rutger, L. (2015). A Dynamic Bivariate Poisson Model for Analyzing and Forecasting Match Results in the English Premier League, Journal of the Royal Statistical Society, Series A, 178 (1), 167-186, DOI:10.1111/rssa.12042.

Smith, M. (2014). How Big Data Gives Premier League Football Clubs and Edge, PM Sports.

Stuart A. and Ord K.J. (1994). Kendall’s Advanced Theory of Statistics, Distribution Theory, Vol. 1 Sixth Edition, Oxford University Press Inc., NY 10016.

VanUven, M.J. (1947). Extension of Pearson’s Probability Distribution to Two Variables, I-IV. Nedelandsche Akademie Van Wetenschappen, 50(1947), 191-196.

Wittwer J.W. (2014). Deterministic Model, A Dictionary of Ecology, encyclopedia.com 25. http://www.encyclopodia.com

Wittwer, J.W. (2004). Deterministic Model Example: Compound Interest, https://www.Vertex42.com.