Nowadays, soccer gamblers are using mathematical models to estimate an outcomes of the soccer game and provide different tips for betting. Poisson probability distribution is most popular model for years.
This article focuses on the Poisson methods, which are under the account of mutual dependency among the opponent teams.
Maher introduces the Poisson model. This model tells that the goal scoring is depend only on the skills of the team not on the skills of the opponent team.
However, the assumption like the strong team playing against the weakest team, and the stronger one will won, this is like underestimating the opponent. Sometimes, weakest team play better against the strongest one.
Mark J. Dixon and Cole are the one who introduce the correlation factor in the Poisson model for games. But the correlation was high for draw matches and low for matches with one score difference. The improvement of the correlation method was done by Lee and Dawson at al. They define that the goals scored in a match are assumed from bivariate Poisson distribution but not from the univariate Poisson distribution. The bivariate Poisson distribution is defined using advanced Copula method, which use either positive or negative correlation links not like the previous method which supports only negative correlation factors.
The improvement of bivariate method as compared to the univariate Poisson method is in using the depend upon the opponent team.
Poisson method has drawback, that the model doesn't judge the time-management in team skills.
Mathematical model are used in some cases. Bivariate Poisson model is the improved and the trusted one model.