| Today, mathematical models play an important role in | | | | for games where the number of goals scored by |
| soccer predictions. Bookmakers, tipsters and experts | | | | each team was one or zero. The correlation was high |
| use these models to estimate a possible outcome of | | | | for draw cases and low for matches with one score |
| the soccer games and to provide different types of | | | | difference. When a team scored more than one goal, |
| betting tips. For years, the most popular mathematical | | | | the correlation was equal to zero. The latest |
| models were these based on Poisson probability | | | | improvement of the correlation method was achieved |
| distribution. | | | | in the works of Lee (1999) and Dawson at al. (2007). |
| This article summarizes the advanced Poisson | | | | They assumed that the number of goals scored in a |
| methods, which, unlike older ones, take into account the | | | | soccer match comes from a bivariate Poisson |
| mutual dependency between the opponent teams. | | | | distribution and not from independent univariate Poisson |
| The well known method of Maher (1982) introduced | | | | distributions like it has been assumed in previous |
| the Poisson model, which uses attack and defense | | | | methods. Technically, the bivariate Poisson distribution is |
| skills and home ground advantage in soccer | | | | defined and implemented using the advanced Copula |
| predictions. Maher's model assumes the Poisson | | | | method. This method allows defining bivariate Poisson |
| distributions of the opponents are independent. In other | | | | distributions, which use either a positive or a negative |
| words, the number of goals to be scored by each | | | | correlation unlike the standard bivariate Poisson |
| team depends only on the skills of this team and | | | | distribution that supports only negative correlation |
| doesn't depend on the opponent's skills. | | | | factors. |
| However, it is clear that when a strong team plays | | | | The improvement of this method compared to the |
| against a weak one, there exists the effect of | | | | older Poisson-related methods is in using the mutual |
| underestimating the opponent. And vice versa, a weak | | | | dependency between the opponent teams for soccer |
| team usually plays better against a team stronger than | | | | predictions. |
| itself. This mutual dependency between the opponents | | | | Still, the Poisson methods have another drawback: the |
| was taken into account in the latest publications and | | | | model doesn't consider the time-dependent changes in |
| will be discussed in this article. | | | | team skills. This issue will be discussed in the next |
| Mark J. Dixon and Cole (1997) were the first to | | | | article. |
| introduce the correlation factor into the Poisson model | | | | |