Hmm, well, one way to look at it is, a collection of 2-shot groups is noisier than a single 10-shot group. Consider the "relative standard error" of our data. That is, the standard deviation of the estimate divided by its expected value, a measure of how much random noise is left in that estimate. If we run Monte Carlo simulations of shot groups from the same underlying accuracy, the RSE numbers come out like this for 10 shots:
For mean radius of all 10 shots: ~0.165 (100%)
ES for a single 10-shot group: ~0.195 (118%)
Average ES for five 2-shot groups: ~0.234 (142%)
So while you do have the average of five groups instead of just one, the 2-shot data contains more noise, so more uncertainty. Years ago, I used to subscribe to the 2-shot group theory, thinking that it solved that "you're throwing away 80% of shots" problem, until I learned this. That OnTarget software made it incredibly easy to get the mean radius, among the other things it also tells you, and once I found out about it I started considering the more sound numbers, such as that mean radius. Having less noise in your estimate of general performance, making it a tighter estimate, gives you a clearer picture. And considering all shots like you do with the mean radius reduces that noise by a non-trivial amount, along with giving you a better idea of what's going on with all shots, as depicted in the last example I gave with those two hypothetical/artificial group images. The one tiny clump with the one flyer on the complete other side of the bull is obviously showing much better performance than the one with all shots generally around the entire edge of the bull. They're both exactly 1.000", but all the other metrics more than clearly indicate that the tiny clump and flyer is much better than the "flower" result. Plus you just intuitively know the tiny clump and flyer is better when you look at the two examples together. I couldn't even try to convince anyone they were equal given how apparently false that is just by glancing at the two groups.
Regardless of method, increasing the sample size gives you a clearer picture. The amount of noise goes down more and more as you consider more and more shots. But the difference in clarity between the different methods still exists. Take 50 10-shot groups and compare it to the mean radius of 500 shots:
0.165 / sqrt(500) = 0.00738 (100%)
0.195 / sqrt(50) = 0.0276 (374%)
That noise difference isn't trivial. This indicates the 50 x 10-shot answer is a much worse estimator of general performance than the 500-shot mean radius. The overall noise level is smaller in both cases since we now have 500 shots instead of 10, but it is still 374% more noise for that one case! But, again, this should be more than apparent with a look at the flower vs. the small clump and flyer. The mean radius of the flower (0.419") vs. the mean radius of the small clump and flyer (0.080") confirms the gut feeling one gets when simply looking at both groups. But you don't get anything like the same kind of information from 1.000" vs. 1.000". Nobody that wants to win the match that day should choose the rifle that shot the flower. And when you actually dig into the numbers they show you which method contains less error, which method gives a clearer picture without having to actually see the target. So do you choose your rifle by 1.000" vs. 1.000" group size or 0.419" vs. 0.080" mean radius? I'll take the latter. The former is just a coin flip.
