Originally Posted by Jordan Smith
Originally Posted by denton
Originally Posted by Jordan Smith
Originally Posted by denton
Originally Posted by Jordan Smith
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. grin

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).

While you are at it, you might try running 3, 4 and 7 shot groups. That will let you compare average group sizes for different numbers of shots. I published my results a few years ago, and it would be cool to have the results duplicated.

The stats for group size are nasty. I couldn't see any way to do it except by simulation, as you have done. When the going gets tough, the tough resort to simulation.
Haha, very true.

Where are your results published?

I'm already seeing some interesting results and will comment more later.

Varmint Hunter

Things are simpler if you simply worry about how far each shot is from the center of the group, but that is more complex than anyone is going to do in the field. For groups with 5 shots, group size has practically all the statistical strength of standard deviation.

Be not weary in well doing.