The resulting distribution depends on how we define “group size,” though for practical purposes, both definitions (maximum separation between any two shots in a group, and the mean separation between all pairs of shots in the group) result in distributions that very closely approximate a Normal (Gaussian) distribution. In terms of accurately predicting real-world behaviour, the simulation suggests that the CLT is closely approximated. If you want an accurate model, calculate the mean separation between shots (or the mean radius, which is essentially the same but uses a fixed point of reference) for each group, and expect your calculations to approximately follow a Normal distribution.
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.
Gotchya, that makes sense. Earlier in the thread when you mentioned "the mean distance between pairs of shots in a group" I didn't entirely get what that meant. It's the mean separation between all the pairs of shots in the group. I can see how that's similar to mean radius in that they're both accounting for every shot in the group rather than just the two furthest shots. I just downloaded OnTarget to play around with it a little bit. Like I mentioned earlier, I know statistics isn't my strong suit but sometimes digging into a subject with something that's interesting is a good way to learn more about it.
