Judging Accuracy: Analyzing Shot Groups (Take 2!)

Introduction
Shooters often talk only about their group size when discussing the accuracy of a group of shots, but group size is a relatively unimportant factor for understanding accuracy.  I have written about this subject previously but have heard from several people vociferously insisting that “group size is king,” and nothing else matters, so this article is intended to try to help folks like that understand.  I jokingly entitled my last article on this subject “No One Cares About Your Group Size,” and I’ll admit that was somewhat unfair (as I tried to make plain in the article) and only intended as a humorous way of making my point, but hopefully this article will make things clearer.  Group size isn’t entirely valueless—in general, a small group is, of course, better than a large one—but it would be more fair to say that group size is the least important gauge of accuracy because it fails to take into account two more important factors:  Mean Radial Deviation and the distance from the Mean Point of Impact to the Intended Mean Point of Impact, so let’s explore those two factors.

Mean Radial Deviation
Consider a group in which almost all of the hits are packed closely together with one flyer, and another group of the same overall size but in which the hits are much more widely spaced out: how tightly the hits are grouped in general is more telling than the mere overall size of the group.  We term this a question of the precision of the group, and it is measured by “mean radial deviation,” i.e., how far the shots average from the center of the group.  Look at groups X and Y below; here we see that Group X is obviously a better group because almost all the hits are packed tightly together, with just one flyer, and yet it has precisely the same group size as does Group Y.  Obviously, just knowing the group size does not tell us anything about the important difference between these two groups.

NB:  Precision, taken by itself, is a measure of the weapon and the load being used, not the shooter, and is usually tested from a rest to take the shooter out of the equation as much as possible, but it is also, when taken in context, an overall part of judging accuracy, or how well the shooter does with that specific weapon and load.

MPI vs. IMPI
In the target diagram below we see two groups of shots, A and B, each with five hits, numbered 1 to 5.  The small black circles indicate bullet hits, the red circles indicate the center of the group or its Mean Point of Impact (MPI), and the large black circle with the red cross indicates the bullseye, with the cross showing the exact center point (known as the Intended Mean Point of Impact, or IMPI).  The black lines show the distance of each hit from the IMPI, the red lines show the distance from the MPI’s to the IMPI, and the dashed rectangles show the group size of each group.  Note that Groups A and B are literally identical in all ways except one: Group B is farther from the bullseye than is Group A, with the distance from MPIa to the IMPI being 1.77 in. and the distance from MPIb to the IMPI being 2.72 in.

Looking at this comparison, we see that the group size of both groups is the identical, as is the mean radial deviation—again, the groups are identical.  The difference is that Group A is much closer to the bullseye, 0.95 inches closer, meaning it’s a better group, and the group size is not as important.  Someone pointed out that me that this is meaningless, all you need to know is the group size and then for the next group you just aim off to make up for the difference.  Unfortunately, that approach doesn't say anything about this group of shots.  If you were aiming at a deer’s heart and sent five bullets six inches over its withers but the group size of those five shots was only one square inch, that’s still five misses despite the excellent grouping—how close the MPI is to the IMPI obviously matters, and Group A is obviously better than Group B.

Conclusion
Ultimately, what matters is hitting the thing you’re trying to hit.  Look at the third diagram below.  Here we see two groups, Black and Red.  Group Red is obviously superb, and no measurement is needed to see how tight it is, it is obviously much better than Group Black in terms of group size.  But despite that, Group Black is still a better group because four of the five shots all hit the heart, the thing the shooter was trying to hit.

As this explanation should make obvious, to judge accuracy we need to examine two things:  How closely packed together the shots are in a given group relative to the center if that group (which is different from the group size), and how close the group is to what the shooter was actually trying to hit, with the latter being far more important, as the heart diagram should make plain.  Group size isn’t meaningless, but it runs a poor, weak third, and can actually be ignored for all practical purposes.

For those thinking that even if all this is true, figuring it all out is too complicated and it’s easier to just measure the group size, fear not, there is a simple, powerful tool that will do all of this very clearly and simply:  The String Test.  I have written about this at length, and even posted a video about it, so I won’t go over it again here except to say that all you have to do is measure the distance from the center of each hit to the IMPI and divide that total by the number of shots and the result will give you the important figure, since it takes both the mean radial deviation and the distance from the MPI to the IMPI into account in one simple number—that’s what the red line in the diagram above really is.  To learn more about this historically authentic method of calculating the String Test, read the article I have posted here:  https://historicalshooting.blogspot.com/2020/12/the-string-test-measure-for-historical.html