Modelling football

Method

It is important to state that Ffogger and Ffogger Pro use a purely mathematical method for modelling football results. The method is not based on historical data and it does not use parameters which are fitted to any kind of reference data. Ffogger and Ffogger Pro solely rely on Poisson statistics, i.e., a statistical method which is applicable in scenarios with a small number of events (=goals in the context of football).

Both programs use the average values of home and away goals to calculate the probabilities of the different outcomes. Since all probabilities within a market add up to 1, the odds of this outcome are the reciprocal of its probability. For example, the odds of the match finishing with a result of 3-2 are odds(3-2) = 1 / probability(3-2). (NB: Whenever the very low probability of a result would lead to odds larger than 1000, for the sake of convenience our programs will show odds of 999. Nevertheless, the probability of this result remains unchanged and will be used with its unchanged value in subsequent calculations.) These odds are therefore the fair odds for a bet on said outcome.

However, it is known that Poisson statistics underestimates the probability of draws, especially the 0-0. For this reason we improve the method to a bivariate Poisson statistic by the introduction of interdependent (=shared) goals. The interdependent goal average means that this portion of the team goal averages is not independent anymore: If the home team scores this average, than the away team does so as well. In other words, either both teams score this average or none does. The interdependent goal average can be understood as a reflection of the nature of the match: In a free-flowing match, both sides will score more easily (and thus higher) than in a defensive-minded match or under bad conditions. In real life, team goals are not (fully) independent, but also (partly) depend on the amount of goals the opposition scores.

In general terms, the interdependent goal average increases the probability of scores in which the goal difference reflects the difference of the expected goal averages. Since in most cases the home and away goal average differ by less than 1 goal, the use of interdependent goals increases the probability of the draw; the probability of a 0-0 is always increased.

Example: Premier League 2012/13 season

The 2012/13 season of the Premier League saw 380 matches (166 home wins, 108 draws, 106 away wins) with 592 home goals and 471 away goals, which is equal to 1.558 average home goals and 1.239 average away goals. Using these averages as input, Ffogger calculates odds of 2.24, 4.01 and 3.30 for the home win, draw and away win, respectively; after taking the reciprocal of these values and multiplying with the number of games, we get the number of home wins, draws and away wins our method expects for the whole season. The similarity of the calculated and the actual numbers, especially of the respective percentages, is very satisfying (see table). You can easily see how the inclusion of the interdependent goal average λ improves this agreement.

λ Home Win Draw Away Win
Ffogger 0.0
170 (45%)
95 (25%)
115 (30%)
0.1
169 (44%)
99 (26%)
112 (30%)
0.2
168 (44%)
104 (27%)
109 (29%)
0.3
166 (44%)
109 (29%)
105 (28%)
Actual
166 (44%)
108 (28%)
106 (28%)

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