Together with Elmar Bittner,
Andreas Nußbaumer and
Wolfhard Janke from the
University of Leipzig I had a scientific look at the problem of scoring in football
league and cup games. In particular, we wondered, "how
scoring in football and the component of self-affirmation depend on cultural and
political circumstances.".
Considering the score distributions of the home and away teams, we found that one
has to take into account a component of positive feedback or
self-affirmation of the teams upon scoring a goal to model the observed
distribution of goals. Without this effect of the "football fever", in
particular matches with outlandishly high results should occur less often than
actually observed.
The above figure shows a scatter plot of the fitted parameters of our model for
some of the teams of the finals of the FIFA World Cup 2006, found from fits to the
data of the past world cups' qualification rounds. The horizontal axis shows the
initial scoring probability (the "skill component"), while the vertical axis
denotes the increase of the scoring probability upon scoring a goal (the "football
fever"). The results from different continents, shown in different colors, cannot
be directly compared since the qualification is played separately for each
continent. Most of the all-time favorites of the past world cups appear in the
upper right corner, resulting in overall large scoring success.
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