In a bid to combine numeracy with sports coverage, The Observer presents the Poisson distribution as a headline on its front page today. Supposedly, it has something to do with predicting the number of goals a team will score in the World Cup. The Poisson distribution is
P(n) = λn e-λ/n!
This gives the probability, P(n), that a team will score n goals in a given game, if the average number of goals they are expected to score is λ. Unfortunately, that’s the easy part; the hard part is figuring out that expected number, λ. We don’t just want to know the average number that, say, England scores in all the games it has ever played, but the average in circumstances like the World Cup: against Brazil and not, for example, Belarus (OK, that’s a bad example…).
I was pleased to note that the article said that the company making these predictions, “Decision Technology,” uses “maximum likelihood estimation”, which is strongly related to the Bayesian Probability theory I wrote about a few weeks ago.
(Aside: I really wish MathML was more standard so I could put equations in here more easily, although I know that Jacques Distler has been pretty successful at it.)