Statistical model

Consider a game between team A and team B. In our model, the number of goals scored by country A are Poisson distributed with parameter (a number) L(A,B). This means that we expect that team A will score about L(A,B) goals in a match against team B. Here

L(A,B) = "Normal number of goals" x ("Strength of team A")/("Strength of team B").

"Normal number of goals" is a parameter (a number) which is interpreted as the average number of goals scored by one team in a match between to equally good teams. "Strength of team A" is a parameter (a number), which tells how good team A is, whereas "Strength of team B" tells how good team B is. The strenght of Germany is fixed to 100, and the strengths of all other counties are given relative to this.

Further, the number of goals scored by team B are Poisson distributed with parameter L(B,A), independent of the number of goals scored by team A.

This means that if team A has a higher strength than team B, we will expect that team A wins, because L(A,B) will be greater than L(B,A). However, it will still be a possibility for a draw, or that team B wins.

Of course, our simple model is not able to cover all important aspects of a football match. However, in the championship, few match results will be available for parameter estimation, so a simple model is needed to avoid overfitting. However, in a national league, with many games over a season, one may consider several extensions to our model. These include

- Home-team advantage
- Offense strength and defense strength
- That the strengths of the teams vary over the season
- Number of goals of each team are correlated

In the later years, several articles about this theme have been published in the statistical literature. A good introduction is Lee, A. (1997), "Modeling Scores in the Premier League: Is Manchester United Really the Best?", Chance, Vol 10, s. 15-19.

Parameter estimation

The parameters in the model are "Normal number of goals" and the strengths of each team. These parameters must be estimated before any probability calculations can be done. Before the start of the tournament, the estimation is based on evaluations from sports jounalists in the Norwegian newspaper Aftenposten and six prominent Norwegian football players and experts. The journalists and experts have guessed the results of several hundred hypothetical games, and these results are tranferred to number values of the parameters.

When the tournament starts, the real games are taken into account as well. The information value of the hypotethical games (the expert guesses) are weighted versus the real games, such that the hypothetical games are equally important the real games when all teams have played two matches. When all teams have played three or more matches, the real games are the most important part in the estimation of the parameters.

Estimating the parameters means to find the parameter values that fit the data (the match results) as good as possible. In our case, the parameters are estimated by maximising a modified Poisson likelihood. The difference from an ordinary Poisson likelihood is that it is robustified by downweighting large victories and by adding a penalty term that shrinks the individual strength parameters towards a common mean.

Estimated strength of all countries

The current estimate of "Normal number of goals" is 1.13.

The estimated strength values of each team is given in the table to the right (sorted), together with the FIFA ranking per May 7, 2008. The discrepancy between the strength and the FIFA ranking is due to the fact that the expert opinions differ somewhat from the FIFA-ranking. In addition, as the tournament makes progress, teams with good results will obtain high strength, even though they might have a low FIFA ranking.

Responsible for web-page: Magne Aldrin

The calculations are updated: June 26, 2008 23:44

Method

Strength and ranking

Country	Strength	FIFA ranking
Spain	117	1303
Netherlands	116	1111
Germany	106	1274
Italy	100	1424
Croatia	99	1017
Portugal	89	1094
France	87	1143
Russia	87	846
Turkey	76	877
Czech-Republic	76	1246
Sweden	75	799
Romania	73	1069
Switzerland	71	644
Poland	66	805
Greece	64	1133
Austria	62	341