If we go back to the original question.... it's about getting an accurate velocity average, to meet the rules of a competition. So, part of that is not only the average, but what sorts of extreme spreads that different loads are giving. Lower extreme spread, less change of showing up for competition and not making the minimum threshold.

That's a situation where "more is better" for sure. If you want to get an idea of statistical validity of small sample sizes, look up Student's T-test.

I was going to comment regarding t-Statistics, but you beat me to it. People who know "a little" statistics believe that "2-sigma" includes a 95% confidence interval, but (as someone else posted) 30 shots are considered a minimum for the 2-sigma rule to equate to 95% confidence. The actual distribution is, as you say, the t-Distribution, which gradually approaches the standard normal distribution for a "large number of shots." What is "large?" Well, statisticians consider 30 shots to be "close enough." If you have N shots, the confidence coefficient can be found from "t-tables" for N-1 degrees of freedom (df). Instead of "2" (actually 1.96 for the standard normal distribution), this coefficient increases with decreasing N (reflecting less "knowledge" of the real population being sampled). For N=7 shots (df=6), the confidence coefficient (t_alpha) is 2.447, while for N=5 (df=4), the confidence coefficient is 2.776. To construct a 95% confidence interval, you calculate the mean (m) and sample standard deviation (s, using N-1 weighting), and then you can conclude with 95% confidence that the "true" mean is inside the interval m +/- s x t_alpha. With decreasing N, t_alpha increases, so you have a larger confidence interval.