  Analyzing football score data with statistical techniques, we investigate how
the highly co-operative nature of the game is reflected in averaged properties
such as the distributions of scored goals for the home and away teams. It turns
out that in particular the tails of the distributions are not well described by
independent Bernoulli trials, but rather well modeled by negative binomial or
generalized extreme value distributions. To understand this behavior from first
principles, we suggest to modify the Bernoulli random process to include a
simple component of self-affirmation which seems to describe the data
surprisingly well and allows to interpret the observed deviation from Gaussian
statistics. The phenomenological distributions used before can be understood as
special cases within this framework. We analyzed historical football score data
from many leagues in Europe as well as from international tournaments and found
the proposed models to be applicable rather universally. In particular, here we
compare men's and women's leagues and the separate German leagues during the
cold war times and find some remarkable differences.
