Football fever: goal distributions and non-Gaussian statistics
Analyzing football score data with statistical techniques, we investigate how the not purely random, but highly co-operative nature of the game is reflected in averaged properties such as the probability distributions of scored goals for the home and away teams. As it turns out, especially the tails of the distributions are not well described by the Poissonian or binomial model resulting from the assumption of uncorrelated random events. [...]
In other words, contrary to previous studies, but agreeing with popular belief, the probability of a team scoring in a game is not the same through out the game. That is, factors such as "being on fire", support from the crowd and other psychological factors carry a considerable impact in the outcome of the game, and there seem to be a correlation between scoring before and scoring again.
This particular study says that they developed some models that assume non-Gaussian distribution (not like a bell-curve) that seem to work very well for many leagues but not for the World Cup. More precise time-resolved scoring data would be necessary to make more detailed studies.
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