This is daunting to me with a barrel that gets very hot so quickly but I wont rule it out - do you truly suggest this for such a thin barrel rather than for something like an F class or heavy barreled rifle?
Yes, take your time a shoot it over a time period that allows the barrel to remain at a decent temp. One shot every 3-7 minutes. My pencil barrel 30-06 takes longer to shoot groups than my 300 RUM because of the barrel, but in the end the hour it'll take is worth it if it helps you avoid taking the entire rifle apart chasing a mechanical issue. And you can also overlay groups - don't change anything (specifically scope settings), and you can draw the holes of several targets together onto a fresh target to aggregate a 10-shoot group without actually having to shoot ten consecutive shots.
What you're trying to do is see if the "two together" are consistently landing compared to other "two together" groups, or if those two shot groups are orbiting around your point-of-aim (POA). If the two-shot groups are consistently grouping and the outlier single shots are grouping together, it's most likely something mechanical - a loose screw or cracked bedding or scope problem, etc. But if the clusters are moving in relation to POA, what you're seeing in the 10-shot group is the true group size.
This is an overlay where apparent "fliers" are actually within the mean radius of the overall aggregate group. There's no problem here, the rifle is just a 1" gun in reality, and not a .25" gun like Group 1 makes it look. Anything less than 10 shots is statistically irrelevant, and only provides negative confirmation that that particular load's aggregate group "can't be any better" than the spread, but does not give confidence that the rifle is capable of that small of a group size consistently.
To expand on the negative confirmation thing - when testing a new barrel tuner, a common method is to shoot just two shots at each setting (even though I just said less than 10 is statistically invalid). As the groups close - you shoot more at the better settings. Across the top row you see the two shot groups close then open again. You can rule out the settings where the two shots aren't touching, and then start shooting more (5-10 shot strings) at the initially more promising settings so that you don't waste rounds on groups that you know aren't going to be better than those first two shots. (please don't think I'm saying to do this test on a hunting rifle, this is a benchrest/ competition method I'm using to illustrate my point).
This is what ES is to velocity, but in the context of group statistics. Normally ES is a weak indicator because it ignores every data point in the population other than the highest and lowest, so it's based on the least possible amount of information. It can't give any confidence about what
will happen in the future (predicting the next shot), but if it shows a range that is too wide you can rule out that load as not being capable of placing the next shot correctly. If you need to be able to hit 4" at 400 yards every time, then a load that puts the first two shots 8" apart at 400 yards obviously isn't going to cut it.
On the predictive side then, if it shoots the first two shots 3" apart, there's still a large likelihood that Shots 3-5 aren't going to fall into the middle of those two, and the group will be larger than 4". So you have to shoot more shots to be sure. If the load printed a 4" group at 400 yards for 5 shots.... there's about a 34% chance it'll be under 4" next time. If the load printed a 1" group at 400 yards for 5 shots.... 90% chance it'll be under 4" next time. (roughly, based on terrible napkin math looking at a z-table
)
Source of pic/ great read on group sizes:
This article is going to dive into the most effective ways to quantify the precision of a rifle and...
precisionrifleblog.com
(Random aside - an "acceptable range" for ES could easily be anything from 30FPS to 300FPS, depending on application and range. There is no broad-based maximum acceptable ES, just like there's no maximum acceptable group size - all that matters is that the rifle does what you need it to. That might mean chasing a .25" group at 100 yards, that might mean accepting an 8" group at 400 yards. Define the goal first, that will drive what you really need to chase in terms of muzzle velocity and group size statistics.)