Growing up, the standard for hunting rifles was a 3-shot group. Because most hunting barrels start to heat up after that and wonky things happen, and, hunting rifles usually never saw more than 3 shots the entire season in my family. One shot a week before hunting season to verify zero, one shot to kill your deer, and one shot to kill your elk. A box of cartridges lasts years, lol.
Group size is definitely not Normally Distributed. A three-shot group is a very weak predictor of the size of your next three-shot group. A rifle that has a long term average of 1" five-shot groups will routinely print five-shot groups as small as 1/2" and as large as 1 1/2" with no change at all in the rifle, ammunition, or shooting technique. The worst sewer pipe barrel you can find will eventually produce a 1/2" group, if you shoot enough of them. The average of three five-shot groups will get you a rifle's long term average five-shot group size within plus or minus 25%.
Without question. But I think there’s a distinct skew (for good reason) which squishes the lower group size side probability towards the Mode, and tails the higher group size probability away from the Mode. I typed up at least 3 different walls of text here this morning explicating the failings of a Normal Distribution plot for defining group size probabilities, but I doubt folks are terribly interested in that level of detail. Turning over a new leaf... I’d be happy to explicate and debate with others if interested either in a separate thread or in PM, but won’t monopolize the thread just yet with these rabbit trails. But I will say this: a logical analysis of ammunition manufacturing or reloading processes, empirical observations from firing a great number of groups, and colloquial vernacular for rifle precision really don’t line up with the principles of Normal Distribution statistics.
This has not been my experience. Normal distribution statistics would support it, but it absolutely isn’t aligned with what I have seen in my own shooting or that of others in competition and instructed courses.
The statistics of group size are particularly troublesome. You can't use the usual tests of dispersion, since, unlike tests of means and medians, they are very sensitive to non-normality. Also, it takes a lot of data to get a precise estimate, many more data than when testing means, and there other problems beyond these. When the going gets tough, the tough resort to simulation. So my solution was a set of 20,000 rows of 7 pairs of X,Y coordinate points, from a normally distributed random number generator. If you assume that the process is free from fliers, i.e., no barrel rubs, no shooter flinch, then this is a good model for 20,000 groups of up to 7 shots per group. It was then a fairly easy task to have the spreadsheet compute the distance between the two shots farthest apart for 3, 4, 5, and 7 shot groups. Sorting these groups in descending order then allowed me to find what percentage fall within any given interval. That is the source of my statement about 1/2" to 1 1/2" groups five-shot groups. After I published my work, I was pleased to find that Creighton Audette had investigated the same question a few decades earlier, and that our results agreed very well.
It depends on what you are trying to do, sight in, finding cold bore zero. Testing the accuracy potential of your rifle or shooting competition. I use usually 3 shots if they group well for sight in. More if not going well. If preparing for a match, I might shoot a dozen 5 shot groups or more. The more you shoot the more things happen. It is harder to be consistent for both you and the rifle as more shots are fired. You said bragging rights. I agree that several groups of 5 shots is realistic. a cherry picked 3 shot group is just kidding yourself.
After sighting in my .308 hunting rifle with a new scope, I let it cool completely and shot these two rounds at 2X at 100 rounds. I'm happy. Now, if this was a target rifle..............not so much.
The only reason a three shot group exists is it is the fewest number of shots required to establish a "point-of-aim", and the Army is cheap. The "shoot three rounds and move the sights" goes way back.... Unfortunately, that was never intended to establish the rifles "precision", just the rough point of aim.
All I know for certain is that one should only post photos or talk about decent groups... Unless you’re trying to explain how you can get 10 shot groups at 100 yards, with a 9mm to go from this, To this, With no other change than the projectile. Or something that simply won’t ever work. Of maybe enlighten performance from start to falling off the end. That said a 24 shot group all in the minute of squirrel head is a good indicator that I can make the shot that needs to be made.
I would never be surprised to find that synthetic data created by a Normal Distribution RNG would follow a Normal Distribution probability profile. We have cliche’s for such things, “you are what you eat,” “garbage in, garbage out,” “the simulation is only as good as the assumptions”... If it’s built with a Normal Distribution probability, even compounded with a multivariate matrix - all following Normal distributions, the model could never be anything but a Normal Distribution probability model. I know I’m not the only guy putting rounds downrange, many folks do a lot more than I, but I more than most rifle owners, and I can say I have not lived in a world where a “1moa average” rifle prints as many 1/2moa groups as it does 1.5moa groups.
You have mis-stated my conclusion. I did not say that a 1 MOA rifle will print as many 1/2" groups as it does 1 1/2" groups. I also did not say that group size is Normally Distributed. In fact, I took care to state that it is not. That is why an analytical approach is difficult. Then there is the problem that Audette came to the same conclusion as mine, but his result was based on physical tests.
"I honestly care less about how many shots are in the group as I do about how many groups the rifle will repeat the same group size." +1. I shoot three shot group with my centerfires. They are basically hunting rifles and the first shot will always be a cold bore shot and then two for follow up in case of misses. Yeah, I'll admit to missing but just very infrequently. The rifle then gets set aside to cool down while I shoot something else or more something elses depending on the temperature at the time I'm shooting. When cool I do another three shot group and so on until I believe the rifle and load I'm shooting is performing to what I want .If not I go home and make tweaks and start over. Eventually I'll determine if the rifle is a shooter or trade goods.
Years ago I had a little Steyr stalking rifle made by some gunsmith in Austria based on a M95 Steyr Mannlicher action. Beautiful lightweight gun around 6 to 6 1/2 lbs. in 8x50R. It had a pencil barrel with a full rib.( It kicked hard enough that you really didn't want to shoot more than a couple of rounds at a time.) Anyway, that thin barrel with the soldered on rib was quite usable for the first two rounds, Then, when it heated up, the third round could be thrown as much as 6 inches off at a 100 yds. You could almost see the warp in the barrel.
Billfold groups or "if I do my part" won't cut it when the rubber hits the road. That's then the wind is blowing, the clock is ticking and you're shoulder to shoulder with scores of other top shooters who came from across the country to beat you. The event is Light Varmint Rifle (10.5 lbs including scope) stage of a major benchrest tournament. Your score is the aggregate of five 5-shot groups at 100 yards fired over the course of several hours. During which the wind, light and temperature, plus the resolve of other shooters, have changed for the worse. These five groups averaged .1441" breaking a World Record that had stood for 15 years. That was 7 years ago and the record has been broken twice since then.