Home Forums Reloading Big Game Rifles Group statistics

I was thinking about Bryan's statement on that podcast that group size SD tends to be about 30% of the mean group size, in his experience, so I ran some simulations based on my model. I modelled a rifle/load that averages 0.915 MOA for 5-shot groups and one that averages 0.306 MOA. I used 100,000 shots total, but explored what happens if those 100,000 shots are divided up into 3-,4-,5-,7-,10-,20-,35-, and 50-shot groups. Then I looked at the average group size, and the group size SD, in addition to the kurtosis and skewness of the mean shot separation within a given group (average distance between a pair of shots for every possible combination of shots within a group), for all the groups in each data set. Some interesting trends emerged.

Just using visual inspection, the group size SD seems to have an exponential dependence on the number of shots in each group, asymptotically approaching 11% (where SD is 11% of the group size mean), and the skewness follows a similar trend. Kurtosis doesn't seem to have a strong correlation with the number of shots in each group. Interestingly, these trends seem to hold true regardless of the level of precision of the rifle/load, whether 0.915 or 0.306 MOA on average. So to Bryan's point, it seems that SD is about 25-37% of mean group size for 3-5-shot groups, but drops to 11-20% for 7-shot groups or larger. That gives us a good idea of how much dispersion we can expect from shot to shot, whether we have a 1 MOA rifle/load or something approaching BR standards at 0.3 MOA.

0.915 MOA rifle/load


0.306 MOA rifle/load