Slitherine

shall wrote:The statistical profiles are not binomial, and indeed it would be a Poisson profile if your comment was correct about rare occurances. You are assuming that the big army was winning and the small army doing no damage. 1 of the 5 200pt gap games had the smaller army winning and very close to getting an army rout (if it stays at 1 in 10 for a big bonus that would be good IMHO). 3 times out of 21 an army rout was achieved with 100 pt deficit, which is not bad ( 1in 5 perhaps?).

Si

I was thinking, for 200 point difference games only, that it was pretty much a binomial with the two outcomes being "no army routed" and "smaller army routed". Poisson is for continuous time, so it can't be that, although a binomial with one outcome having a very low probability and a large number of trials does approximate a Poisson. That wouldn't apply in the case I was envisaging, where both results were fairly probable. It was the third result ("large army routed") that I was treating as negligible (since in practice it didn't happen). With a sample of 5 you can only reject the hypothesis that the pobability of the large army getting routed is greater than 0.55 (using a 5% significance level). Assuming it was zero was an assumption on my part, although it would be the result you get from using a maximum likeihood approach on the data. FRom your descriptions of the games your estimate of a 1 in 10 looks realistic in practice. This is all for the 200 point deficit. With the 100 point deficit, the results came out at 1 in 7, so 1 in 5 is also realistic.

Time to stop this and get back to wargaming.

Indeed. All useful, but I think the results, and your thoughts when put back in context of the comp, leave me pretty comfortable.

If there were only 2 results I think you havea point, but I think there are actually 4 results that will all occur.

Si