Two thoughts: 1) this is a somewhat bizarre exercise. It seems like it's more relevant to work out the probability that the better team wins, for empirically r

Two thoughts: 1) this is a somewhat bizarre exercise. It seems like it's more relevant to work out the probability that the better team wins, for empirically relevant values of what the author's calling "expectation value" --- i.e., give team A an expected scoring rate of (say), 2.0 goals per 90 minutes and give team B a rate of 1.9 goals per 90 minutes, then see how likely each team is to win. (R code, based on 10,000 simulations because I'm lazy and don't feel like working out the probabilities by hand: > mean(rpois(10000, 2) - rpois(10000, 1.9) > 0) [1] 0.42 > mean(rpois(10000, 2) - rpois(10000, 1.9) < 0) [1] 0.38 > mean(rpois(10000, 2) - rpois(10000, 1.9) == 0) [1] 0.20 In words: the better team wins 42% of the time, the worse team 38%, and they tie 20%;) The numbers 2.0 and 1.9 were made up, and the disadvantage of this approach is that you're required to get some data and estimate reasonable values of each team's scoring rate, or make them up. I should note here that OP has to do the same thing; the line "We can turn the Poisson distribution around, and ask: if a team scores N points, what is the probability (or more technically correct, the probability density) that the underlying expectation value is X?" is nonsense without a Bayesian interpretation, which requires a prior density (which is the equivalent of making up numbers like the 2.0 and the 1.9 I used above, and weighting them by how likely you believe they are). Note that I could put a dogmatic prior on 2.0 and 1.9---a point mass for each team at one of the points---which would make me believe that the "expectation values" are 2.0 and 1.9 regardless of the actual score. Clearly that would be a bad prior, but it's not clear that the implicit prior used in the article is a good one. 2) More important: teams sit on leads, so the probabilities aren't constant. A team that outclasses another team probably won't win by 19-0, because at 8-0 they'll focus less on scoring and more on playing defense and avoiding injury. The same concept applies less dramatically with a 4-1 win, a 3-2 win, etc. Modeling strategy is much harder, so I'm not going to provide R code :). But one effect is that a poisson process will probably predict too many extreme scores. That said, the OP's thesis is self-evidently true: "My thesis is that soccer is an amalgam of random processes whose net effect produces rare events—those more-or-less unpredictable events spread more-or-less uniformly in time." It's a game with about 3-5 goals scored in 90 minutes. They're rare!