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Randomness has a big effect on football results. To a good approximation, a football match can be simulated using a large number of time slices, in each of which each team has a given probability of scoring a goal. The effect is that the number of goals each team scores in a match is a sample from a Poisson distribution. It's characteristic of a Poisson distribution that the variance is equal to the mean, so that for sports, like football, with low mean scores, the standard deviation is large. For example, in a match in which on average team A is expected to beat team B 2-1, team A will in practice win about 60% of the time, and team B will win about 18% of the time.
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Sep 22, 2011