Out of curiosity, I just coded up a similar simulation using 100,000 shots divided into 5-shot groups. The individual shot POI was modelled using a Gaussian distribution. The group size, when defined as the maximum distance between two shots in a group, looked as you described with a skewness of ~0.41. Interestingly, when group size is defined as the mean distance between pairs of shots in a group, the distribution is more normal with skewness of ~0.28.
Wow! Someone as curious as I am. Well, maybe more curious, since you took it to 100K, and I only did 20K.
Haha, well going from 20k to 100k was as simple as 3 key strokes, so I'm not sure it says much about the relative curiosity.
I'm seeing some very interesting results, however, and am now running a simulation using 1M shots for both 5-shot groups and 10-shot groups, using both definitions of group dispersion (distance between two furthest shots, and mean distance between all pairs of shots).
