Gents, I have to qualify this by saying that this question is partially driven to win an argument… but here goes.
I super enjoyed the dive into data on the podcast. The analytical question I wanted to answer was “what is the likelihood that a 3 shot group demonstrates a gun/load’s true dispersion?” I think you talked about a 5 shot group being like either less than a 50% confidence interval.
Rephrased: what are the odds a single 3-shot group is representive of a 20 shot group?
DB - I’d add a few more questions that popped up while I was listening to the podcast.
When Jim says (3) five-shot groups gets you within X% of the right answer - that’s based on the assumption that (4) or (5) five-shot groups is the right answer.
Since he’s seen the final group variance getting consistently larger (what I think I heard), I suggest to me that maybe 20 shots isn’t going to give you the answer (although it might be so close that no one cares). I’d be interested to see what happens (and I’d only do this with maybe two already tested guns). (Now, this is easy for me to suggest, but it’s not my ammo or my time… so)
A Test Case: Take 2 already tested guns with known loads.
Gun A - shoot (10) five-shot groups over 2 days.
Gun B - shoot (10) five-shot groups over 10 days.
Gun A - shoot (10) five-shot groups, clean between each group.
Gun B - shoot (10) five-shot groups over 10 days, clean daily.
That should tell us if 20 is the magic number for “correct” or so close it’s not worth expanding. It should also give us some idea (probably requiring further testing) as to what (or really what isn’t) the reason for the last group being pretty consistently larger than the first group.
Why is the variance from the first group to the last group always expanding? Is it fatigue? Maybe it’s cleaning? Maybe it’s changing conditions over the time spent? Maybe it’s something else?
I don’t think we’re going to get an answer from looking at data that wasn’t meant to test that. I’m also not convinced that there aren’t too many variables and that we won’t find out why.
Good question. We didn’t mark groups at the three-shot point so unfortunately I don’t know the chance of a 3-shot being within 10% of the final answer.
However, the data I’ve seen says a 5-shot group is on average 25% larger than a 3-shot group. You may be able to figure something out from there.
Good point on the assumption of 20 shots being the answer and you’re totally right. Hornady did some 100 shot groups and found that 20-shots had only a TINY error compared to 100 shots. But there is still a difference even though it’s very small.
We’re adding another four 5-shots being groups to some of the guns and so far we’ve never seen it move the overall average hardly.
I’m definitely interested in seeing how the groups change in different weather conditions and as cleaning gets pushed off and barrels wear.
Great points.
“5-shot group is on average 25% smaller than a 5-shot group.”
I assume you meant to say 3-shot group is on average…?
Yes, 3 shot. Sorry.
What you seem to be asking is the reliability or confidence level that a single 3-shot group accurately represents the normal curve describing the ammo’s precision. (a) First consider: What sort of curve could you graph with just three points; how accurately would it represent the universe that is that ammo? (b) Taking a basic look statistically: A sample of 3 gives you only about a 1-in-12 chance of estimating SD within ±10%. A sample size of 3 provides essentially no reliable information about the true standard deviation of a normal universe. Using a 3-shot group (or even a 5-shot group) doesn’t really tell you much. If you fired just one more shot, it could hit exactly on point of aim or 2 inches away…you really can’t predict based on a single 3- (or 5-) shot group.
PS - averaging is also not great. (i) the center of each group is not likely to be in the same spot relative to point of aim. (ii) an average necessarily excludes half the potential outcomes. (iii) really, you should overlay multiple groups and then (as Jim does) look at mean radius rather than simply considering extreme spread. Mean radius <0.3 is really good, 0.3-0.7 is generally acceptable for hunting, >0.7 is poor.
Hornady has several videos/podcosts on the subject. If you watch them all, it’s a bit long and maybe a little tedious…I recommend watching, if you watch, at 1.65x speed. in any case: Hornady Podcast (group size) ep. 50 & ep. 52 and (mean radius) ep 99 …and maybe (hit probability) ep 129. Bottom line (and to avoid hours of Hornady podcast) they generally recommends 20 shots as being sufficient with 35 being ideal ($$$! + time). You’d have to shoot multiple groups and then overlay them accurately to get the aggregate group, which can be plugged into a (free) app (ep 67) to calculate mean radius & scope adjustments as well as extreme spread.
To me, 3 v 5 v 20, depends on how far the proverbial “rabbit hole” you want to go down. I had a custom builder that would have his client show up at a private range and shoot 1 shot…for several days. He was looking solely for cold bore shots. He would compare different days targets. The old “one shot, one kill” with not so much consideration for follow up shots. The wildcard is if the shooter is doing his/her job. It was a 300 Dakota built for a friend of mine. That rifle was dead on at 200 yards cold bore and held 1/2 MOA for the next 15 rounds or so. I was reloading for this friend and didnt want to spend more time on his ammo than mine so I limited batches for him. 
Point is, what’s the intended purpose for the rifle? Hunting v competition is a big difference.
Personally, I do 5 shot and then verify with a 10 shot on a later date given same/similar conditions. I learned a long time ago that I can burn out a barrel by going too far down rabbit holes. It works as long as I do my part shooting. Me doing my part is key as for a while I deemed myself as “king of the 4 out of 5 group” then I stopped letting things mess with my calm.