Today, mathematical models play an important role in soccer predictions. Bookmakers, tipsters and experts use these models to estimate a possible outcome of the soccer games and to provide different types of betting tips. For years, the most popular mathematical models were these based on Poisson probability distribution.

This article summarizes the advanced Poisson methods, which, unlike older ones, take into account the mutual dependency between the opponent teams.

The well known method of Maher (1982) introduced the Poisson model, which uses attack and defense skills and home ground advantage in soccer predictions. Maher’s model assumes the Poisson distributions of the opponents are independent. In other words, the number of goals to be scored by each team depends only on the skills of this team and doesn’t depend on the opponent’s skills.

However, it is clear that when a strong team plays against a weak one, there exists the effect of underestimating the opponent. And vice versa, a weak team usually plays better against a team stronger than itself. This mutual dependency between the opponents was taken into account in the latest publications and will be discussed in this article.

Mark J. Dixon and Cole (1997) were the first to introduce the correlation factor into the Poisson model for games where the number of goals scored by each team was one or zero. The correlation was high for draw cases and low for matches with one score difference. When a team scored more than one goal, the correlation was equal to zero. The latest improvement of the correlation method was achieved in the works of Lee (1999) and Dawson at al. (2007). They assumed that the number of goals scored in a soccer match comes from a bivariate Poisson distribution and not from independent univariate Poisson distributions like it has been assumed in previous methods. Technically, the bivariate Poisson distribution is defined and implemented using the advanced Copula method. This method allows defining bivariate Poisson distributions, which use either a positive or a negative correlation unlike the standard bivariate Poisson distribution that supports only negative correlation factors.

The improvement of this method compared to the older Poisson-related methods is in using the mutual dependency between the opponent teams for soccer predictions.

Still, the Poisson methods have another drawback: the model doesn’t consider the time-dependent changes in team skills. This issue will be discussed in the next article.