Home Forums Hunting & Shooting Handguns Primer: How To Measure a Group

Okay, having been justly chastised for incorrectly "correcting" Travis on the other thread, here's what I meant to provide by way of illustration. I've used circles drawn around pushpins to illustrate the centers and the edges of bullet-holes.



The centers of the holes, measured by calipers, are easy to do here because they're not holes. The only way you can accurately measure from center-to-center on REAL bullet-holes is to use a transparent caliber-specific overlay, which will give you a fairly precise center estimate to measure from. But even then there's a lot of room for measurement error, so it's less precise than a caliber-specific obturator, which will give as precise a center-to-center measurement as you can get without a computer and optic.

The best way to measure without using an overlay is usually to measure from the same-side edge of the two holes. Since the edges of real bulletholes are ragged, with a "grease ring" around the hole. Typically we measure edge of the hole rather than the greasering, hence the popularity of semiwadcutter bullets--which cut nice clean circular holes--for Bullseye shooting. So sameside edge to edge measuring is my preferred method:




The alternative method, which Travis suggested, is to measure the opposite-side edges of the two farthest holes ("outside edges", as he calls them):



...and then subtract the bullet diameter from that measurement.

When I was a regular Bullseye shooter, the guy who ran our league (and was an ex-Navy Pistol Team member) alwasy insisted we measure from sameside edge to sameside edge, as that is the way they apparently do it at Camp Perry.


In the end, it really comes down to this:

Do it however you want.

Well Doc, that about sums it up for me until someone comes up with a 4th way of measuring.

Since I can never find a calculator (or touch my wife's), I zero my calipers on the appropriate bullet, then measure outside/outside..

Doc, the confusion comes from the fact that what you posted on the other thread isn't what you posted here....

Travis posted this...


Which is exactly what you posted above...


But after Travis posted exactly what you did, you corrected him by saying this...



Center to center and outside to outside being the same defies the laws of physics, unless you subtract the bullet diameter, which Travis said to do. This confused everyone, because if we can defy laws of physics I recommend doing it for cooler stuff than measuring bullet holes.

Travis was as confused as the rest of us, so he posted this...


And although you have shown how to measure a group, you haven't shown how outside to outside is the same as center to center (unless you subtract the bullet diameter, which he had already told us to do and you told us not to).

I'm really not trying to be a dick here, but the confusion is becuase you're both posting the same thing. I think somewhere along the way you misread what he said and then everybody got confused about you defying the laws of physics, which obviously isn't what you meant to say.

Anybody here preparing for the Olympics?

LOL

I do the "same side", unless the group is one big ragged hole. Then I measure OD and subtract bullet diameter. But, this hasn't been a problem too often.

Yup. Same sides or span and subtract.

(I'm going to give DocRocket a pass on his error, chalked up to senioritis or the full moon or something.)

Measuring to the two furthest apart holes and ignoring all the rest is flawed on two fronts. First, it might not produce a circle that encompasses the entire group. And if you're measuring a group of more than three shots, the more the shots, the less statistically relevant extreme spread becomes.


Note: please excuse the oblong-ness of my circles. My scanner did that to me and I don't have the motivation to fix it. They originally were circular so just pretend they still are.

This "target" shows three "POIs" at exactly equal distances. If it'll help you sleep better, pretend the one POI lying outside the circle is 1mm closer to the center than it is. Then this will perfectly describe the classic definition of a measurement of extreme spread. Yet it does not describe a circle that would contain all three bullet holes.

To do that, you'd have to somehow determine the centerpoint for a circle that will encompass all three holes. Something like this:



The true size of this group is described by the circle that is 2.26" in diameter, not by the one that is 1.97". The extra 0.29" represents a linear error of ~15% but, more importantly, it underestimates the area of the true extreme dimension circle by ~24%, so you're off by nearly a quarter.

The trick then -- if you want to call it that -- is to find the center of the group, which also will be the center of the circle. There are several ways you could determine the center of this circle. You could plot the POIs on a grid, then plug the X,Y coordinates into a spreadsheet and let Excel's fingers do the walking. Or you could pull out a compass (the tool for drawing circles, not the tool for finding the North Pole) and your high school geometry text book and construct the center (which is what I did here).

But the easy way is to buy a template of incrementally graduated circles, like this one:



You just plop it down on the target and figure out which hole fits. They're about $5 at your local office supply store.

If the increments between the hole sizes are too large to suit you, you can interpolate. Or you can use the four cardinal points marked on the template's next largest hole to determine the center of your circle, then use a compass to construct the correctly sized circle. What this method lacks in sheer precision it makes up for in simplicity and foolproofness. For my personal examination of shot groups, it's perfectly sufficient.

Second, the further you get from the three-shot group, the less effectively the extreme measurement group size describes what's going on inside the circle, and that could be where all the action is.



Above, a representation of three 5-shot groups. All three groups are exactly the same "size" (by extreme dimension) but each demonstrates a different level of accuracy. In these instances, using an extreme measurement is essentially throwing away the statistical information provided by any shot not lying on the perimeter of the group. Which is a real loss, because those were the best shots of the lot.

For 4-shot groups, it's less a loss but for 5 shots and over, you're really doing yourself a disservice if you don't switch to one of the more sophisticated methods, like mean radius or radial standard deviation.

They might sound complicated but all it takes is plotting the locations of your POIs, then entering those numbers into a spreadsheet. And if you don't have a spreadsheet application, you can get quite a good one online, free, at either LibreOffice or OpenOffice.

XL5... WOW!!! Thanks for posting this!

The bottom group in your photo, above, is one that is familiar to me (and, I suspect, most reloaders who shoot a lot of "test" groups). You look at that nice tight group on the right, and then you have to explain the "flyer" way out there in left field... was it a gust of wind? a flinch? or does my new rifle shoot flyers with unpredictable regularity? If the latter, you don't want to hunt with that rifle!

I recall reading an explanation for using 3-shot groups years ago and sort of understood it, so I've done 3-shot groups ever since when sighting-in a scope or when doing load development. But it didn't make sense to me as much as your explanation does. Thanks again.

I have been intimidated by Excel for years. Now I have a reason for overcoming my fears....

FWIW, I posted the OP not as a statistics lesson, but simply to illustrate the way groups are measured for competition purposes.

After reading that, I'm going into the mexican beer again..

You know, I read through it and I think I understand as I'm going, and then I get to the end and realize that I don't.

Done it several times, too.

I have been using the wrong lingo.

Yeah, good illustration, I like that.

Precision and accuracy fine and dandy, but they're relative terms that change dramatically when performance at speed and distance are forced upon you, as the POATAL match results illustrate very nicely. You'll note that all the pie plates resemble diagram #4.

My brain interprets this thread like this:

deflave was right.

deflave was right.

deflave was right.

deflave was right.

deflave was right.



Travis

Yeah, your brain would...

I think I "under-explained" my earlier criticism of the method that relies on only measuring the distance between the two POIs that are furthest apart so I ginned up this as sort of a mathematical proof.

First, I constructed a 2" circle and added two 'POIs', which represents what the target would have looked like if the two furthest POIs had been exactly 2" apart and I were measuring the extreme dimension:




Next I constructed arcs 1.9" from the center of those two "bullet holes." Those arcs represent the furthest from the two original POIs that any third POI possibly could be (to within 0.10") without the third POI being further from either of the two original POIs than they are from each other:




So the red colored "cones" (below) describe an area that is outside of the original 2" circle but still is no more than 1.9" from both of the original POIs. Red represents an area where a third (or fourth, or fifth, or 12th, or 163rd) POI could fall without changing which two POIs are furthest apart. Nonetheless, they enlarge your "group" to an area that is not, and can not, be encompassed by the original 2" circle.




Provided there are no POIs that fall within the areas described by the red cones, the two furthest holes method is completely valid. But that leads to two further questions. First, how do you know to a certainty none of your POIs are in the red cones? And, second, if they are, how then do you properly measure the size of your group?

The easiest and cheapest answer to both questions is to use the graduated circle template like I showed in my first post. Not as easy, or as cheap, but it is a more "authoritative" method, is to use a target analysis software, like QuickTarget, the external ballistics component of QuickLoad software.


(QuickTarget output)

You only have to feed it a number of straight line distances, which most of us who have calipers easily can measure with hundredth of an inch accuracy. This amounts to providing the application with the X,Y grid coordinates of the POIs, and the computer does the rest.

But the overarching point is, and I hope I have been convincingly clear, if you're only measuring the distance between the two POIs that are furthest apart, it's entirely possible you are substantially under-reporting the size of your groups.

damnit XL5, that made my head hurt

Allow me to summarize for most of us:

"Nice group."

"Chitty group."

(Measured with Ball, Eye, Mk1)

How about just eyeball it, and round to the nearest 1/4"?