I've never been much interested in prop bets, but maybe that will change...
Reading through the threads and elsewhere, I understand well the idea behind using the Poisson dist to model such bets. My question is, has anyone investigated/discussed the likelihood of over- or under-dispersion in different types of prop situations (ie., variance not equal to the mean, which is assumed in the Poisson). In which case, using the negative binomial dist instead would be a preferred alternative. Or is this not considered a relevant practical issue in prop betting?
Poisson is useful for a lot of props but certainly not all. Clearly the type of distribution you use is going to depend on the prop. For example, a total bases prop in baseball is quite clearly not poisson. It's up to you to find the distribution that best fits the prop you're looking at.