How does one measure group size?


September 13, 2005, 11:32 AM
I guess one bullet hole has a group size of zero.

I guess two bullet holes have a group size of the center to center distance between them.

I guess three+ bullet holes have a group size of the maximum center to center distance between the two holes that are farthest apart.


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Zak Smith
September 13, 2005, 11:53 AM

September 13, 2005, 11:57 AM
Thank Yew. ;)

Brian Williams
September 13, 2005, 12:43 PM
I find the 2 hole that are the farthest apart and draw a line between the 2 and measure from the edge of one hole to the same edge of the other, so I include the distance between the 2 holes and the diameter of one hole. It is hard to find the center of a hole but not the edge.

September 13, 2005, 01:05 PM
Mr. Williams, I like your news better than that BrokeJaw guy, and thanks for the suggestion.

I am building a spreadsheet to figure the group size, so I need the x,y cooridinates of the center of the holes, which I read off a target which I created with 1/8" grids printed on it.

I intend to use the old ((X1-X2)^2 + (Y1-Y2)^2)^.5 (pythagorically speaking) to each pair of holes, then apply a macro to select the largest.

That's why I was asking. :)

Charles S
September 13, 2005, 01:09 PM
intend to use the old ((X1-X2)^2 + (Y1-Y2)^2)^.5 (pythagorically speaking) to each pair of holes, then apply a macro to select the largest.

Insert Mr. Burns voice (of the Simpsons).



September 13, 2005, 04:55 PM
If my group is outside the 9 ring on any target designed for any distance, then it's a BIG group. No need to measure. If my group is well within the 9 ring, then it's something to brag about to most folks. Still no need to measure.

(Two farthest holes, Outside edge of one hole to the outside edge of the other.) I can cover my shots with a dime, nickle, quarter...


September 13, 2005, 05:16 PM
So, Mr. Jack......

When I am working up a load and tweaking it I should just record the group size in my book as;

Pizza Pan
Dinner Plate
Soda Can
Shot Glass (top)
Shot Glass (bottom)
20 gauge

I guess there is no need to go smaller than that. :p

September 14, 2005, 03:08 AM
Depending on what you're shooting, at what distance, your analogy of group size might be commendable. Say, a 5" something or other mounted on a really big boat, with groups the size of a truck at say, four miles, then I guess that's a pretty good group.

Seriously though. I put a ruler across the holes that are the farthest apart. Outside edge to outside edge. That's what I record in my shooting log. It's too difficult to determine center of the hole. Especially if all of them over lap each other.


Smokey Joe
September 14, 2005, 05:25 AM
For group size furthest center to furthest center, measure furthest outside edge to furthest outside edge, then subtract one caliber.

For example: I have a nice group in front of me now. Put the calipers on it and it is 1.044" outside edge to outside edge. Minus 0.308 = 0.736" group size.

Which, while it ain't benchrest accurate, ain't too bad for 100 yds with the load only halfway developed for that rifle, case, bullet, and powder.

BTW, I don't brag about a 0.736" group. I just say it's under 3/4".

MUCH easier than trying to figure out where the centers of the holes are! :)

Zak Smith
September 14, 2005, 11:44 AM
Yep, I measure the outside of the two furthest holes with a caliper (handy, easy to read) and then subtract one bullet diameter.

Note that if you measure and record max furthest edge (without subtracting caliber) you can never get a group smaller than the bullet diameter, which is annoying in 50BMG!


Charles S
September 14, 2005, 12:59 PM
Yep, I measure the outside of the two furthest holes with a caliper (handy, easy to read) and then subtract one bullet diameter.

I find that this is the easiest way to measure group size.


September 14, 2005, 01:11 PM
Isnt' that the point? You can't get a group smaller than bullet diameter! Doesn't that explain the phrase, "One ragged hole". When you can use that phrase, then "group size" doesn't matter. :banghead:

OK, yes, measuring outside edge to outside edge, then subtracting one bullet diameter will get you center of the holes.. I just don't do it.


September 14, 2005, 02:09 PM
Many times I have the "One Ragged Hole" problem, herinafter referred to as ORH, which is why, when working up smally grouping loads, I like to cover each bullet hole with a garage sale sticker before I make the next shot.

Nothing so disconcerting as firing 5 and then seeing only ORH. Makes it hard to work up definitive loads. Takes a lot of time too when I have to keep looking down the barrell to insure that I don't have a lodged one.

Each shot gets it's x,y coordinates logged in along with velocity and then I let the computer do the figgerin'.

Not only that, but let's say I shoot 5 and see 4 in ORH with a flyer an inch away. Is that the load? Or the loader? Or the shooter? What?

Duplicate and try again. That's what I say.

Zak Smith
September 14, 2005, 02:10 PM
Then you can't meaningfully compare the accuracy of different calibers, because a 30-caliber rifle could shoot no better than .30", while a 50BMG could shoot no better than 0.51"

September 14, 2005, 04:49 PM
to get the center to center measure you take the measurement from the outside edge of the one of the furthest holes and measure to the inside edge of the other furthest hole. that will give to c-to-c.

September 14, 2005, 05:04 PM
Nothing so disconcerting as firing 5 and then seeing only ORH.
Oh, to be thusly disconcerted!

Smokey Joe
September 14, 2005, 05:26 PM
OBM--You are quite correct in your observation, sir, but may I point out that there is an IF. While your method is theoretically just as good as measuring outside to outside, and avoids the subtraction, I submit that it has a problem, to wit: If you are dealing, as is ideal, with one ragged hole, the inside edge of any one bullet hole will be a little difficult to find.

If the group is spread enough that each bullet makes a separate hole in the target, then your method works, and is more efficient.

The outside edge of all the outer bullet holes, however, are always right there. That is why most persons willingly measure outside to outside edge, then subtract one caliber.

September 14, 2005, 06:17 PM
OBM--You are quite correct in your observation, sir, but may I point out that there is an IF. While your method is theoretically just as good as measuring outside to outside, and avoids the subtraction, I submit that it has a problem, to wit: If you are dealing, as is ideal, with one ragged hole, the inside edge of any one bullet hole will be a little difficult to find. but there's ALWAYS a flier. :)

(point well taken, sir)

September 15, 2005, 01:24 AM
Oh, c'mon now. To be fair you need to shoot one shot, measure the actual size of the bullet hole in the paper (the paper stretches slightly as the bullet passes thru, so the hole is actually slightly less than bullet caliber), and subtract that from any further groups sizes instead of nominal bullet diameter...

If you need to do that, you are shooting a whole lot better than I am!


September 15, 2005, 07:12 PM
"Oh, c'mon now. To be fair you need to shoot one shot, measure" "and subtract that from any further groups sizes"

You've got me confused. One shot does not make a 'group'.


September 16, 2005, 10:24 AM
HOw 'bout just getting one-in-a-row and calling it good? :D

September 16, 2005, 01:31 PM
Never said one shot made a group. Shoot one shot off to the side, call it your 'cold bore zero' shot or whatever trips your trigger. Measure it, and use the actual size of the hole in that kind/type/weight of paper when subtracting bullet diameter from any subsequent groups shot on that kind of target. Really a matter of picking nits, unless you are shooting bona fide 'one holers' three or five shot groups, and really care about the difference (some people do).



September 17, 2005, 06:38 PM
Coming in to the discussion a bit late, but it seems there is some confusion about group size measurement here. Our games are mostly all based on 5 shot groups fired at 50 or 100 yards. This does not lend itself especially well to caliper measuements since nobody's calipers can check 5 axes at once and make any sense of it.

The official method used in our Nationals uses a graduated ring gauge, basically a set of scribed circles on a clear acetate sheet. The ring gauge is set on the target, and moved around to include (cover) the outer edges of all the holes within a ring of whatever diameter it takes, and then the judges measure a single hole or figure in the diameter of the slug reported to have been used, and deduct that from the size of the "group ring".

What you have left is the group size, adjusted for the size of the slug used.

There is no point to judging any competition based on the size of a plate needed to "cover" all the shots, because then nobody firing a large bore gun could ever compete and win against somebody firing a .22, even if the big bore guy was a better shot.

Any more than 2 rounds, you have to use a circular gauge, and to mean anything in accepted competition "group size" has to refer to center distance among the shots measured, not some nonsense like "covered all the holes with my thumb" or whatever.

Everybody is welcome to agree, argue, P&M all they want, but if you are going to play in any of the serious benchrest competitions, whether its ours (American SlugShooting Association, or NRA, or ISP, or any of the rest, all are judged the same way.

An exception is when the contest is limited to a single caliber, where you can rank shooters according to what "covers" their group of shots.

To be meaningful outside that single contest, the actual score should still deduct the bullet diameter if the scores are to be compared to other contests with other size projectiles.

After all, the Ruger 22 guy with a 5 shot group covered by a 3" disk at 100 yards should not be seen as a better shooter than a guy shooting a 12 gauge slug gun at the same target whose shots are "Covered" by a 3 1/2" disk, and actually is grouping tighter than Mr. 22, once the size of the bullets is factored in.

Of course everyone is welcome to enter our contests and find out how good they really are, when the results get judged correctly............. :neener:

September 18, 2005, 12:28 PM

So, I got on my cad system and I drew a circle with a diameter of .308 with the coordinates of 0, 1.

Next I created a circlular array around the origin with 3 entities equally spaced, namely 120 degrees apart. Which is about as far apart as one could get.

So per the REAL way to measure the group, namely a circle which covers all the centers has a diameter of 2 inches. A 2.0 inch group as it were.

The center to center dimension of each hole to the others was 1.7321 inches.

Finally, if I array the holes with 4 of them at 360 degrees, the REAL group size is actually the distance between the centers of the most distant holes.

In conclusion it appears to me that one should never shoot groups larger than nor smaller than 4. Solves the problem.

Otherwise, does anybody know a simple algorithm, by which I can compute the actual group size of 3 shots on a spread sheet?

Zak Smith
September 18, 2005, 09:54 PM
I'm pretty sure a CAD system, graduated rule gauges, is not needed to practically measure group size. :neener:

Anybody who understands how to use a ruler can find the pair of holes with the maximum distance. And I can just as easily be done for any number of shots, not just 4. :neener:

Zak Smith
September 18, 2005, 10:00 PM
Otherwise, does anybody know a simple algorithm, by which I can compute the actual group size of 3 shots on a spread sheet?
Superimpose a grid on the shot target. Define 0,0 whereever you want. Get the position for each shot fired (center) by whatever method you want: P1=(x1, y1), P2=(x2, y2), etc.

The distance between set 1 and set 2 is:
dist(P1,P2) = sqrt( (x2-x1)^2 + (y2-y1)^2 )

then the group size would be MAX( dist(P1,P2), ... , dist(Pn,Pm) )
where every combination of points is represented.

By similar methods, you could relate every sho to the POA, or the geometrical center, etc.

But the important thing is the group size, which you only need a ruler/caliper and maybe a calculator to figure.


September 18, 2005, 11:23 PM
Sorry, Mr. Smith, but not so, not so.

If Mr. OneInchGroup is correct, which I have no reason to doubt, 3 bullet holes equally spaced around the origin at a polar distance of 1 inch would have a group size of 2 inches. If, however, you measured the distance between them, it would measure up at 1.7321 inches.

Yes, I can do the pythagorical solution dist(P1,P2) = sqrt( (x2-x1)^2 + (y2-y1)^2 )

The question remains........How to draw an arc through the center of the most remote 3 holes, mathimatically.

Like I said, 4 is easy. The 2 most distant (with the other 2 inscribed) is the group.

Zak Smith
September 19, 2005, 12:49 AM
Ah, I see what he's trying to get at now. Thanks for the explanation.

I've never seen it defined as the size circle that can cover all the impact centers before.

In fact, the NBRSA doesn't either (,

GROUP MEASUREMENTS. Groups are to be measured by any method approved by the
NBRSA in .001 inch. The Sweany Type Reticle Rule (or its equivalent)
will be the only official measuring device used at all Registered
Matches. In measuring groups fired with calibers larger than .22
(unless the Reticle is calibrated for the caliber to be measured) the
measurement shall be made from the extreme outside edges of the 2
widest bullet holes and the actual differential of the larger calibers
shall be subtracted from the measurement read on the measuring scale.


September 19, 2005, 01:30 PM
Well, Zak, looks like you've put your finger on an area of disagreement amongst the various target shooting Associations. Over at ASSA, the plan was to try to match up with the type of judging done in Bullseye competition, where the scoring is based upon shots being inside one or another of the numbered rings, smallest being best score, etc.

The NBRSA method simply measures the center distance between the two shots in a group that were farthest apart, a one-axis Caliper measurement that adjusts for the size of the bullet. The advantage is that the measurement is so simple that it can be done in the field without any complicated calculations required. It also gives an artificially good result compared to running a circle gauge.

Depending upon what you are used to doing, either approach is fine, as long as everyone understands that you are comparing apples and oranges.

Here is why the two methods can give very different scores:

Just to make everybody happy, ASSA has decided to include results calculated both ways, so everyone can know where they stand, no matter whose method is used. We think the NBRSA method gives "Rosy Scenario" results in some situations, per the example we've posted, but they've been at it a while, and we'll just make another score column to try to be all-inclusive, "big tent" kinda guys. :what:

September 19, 2005, 02:06 PM
To correct my previous post. A 4 shot group which has 3 of the holes as shown above and with the additional 4th shot somewhere included in the circle would have the same effect as if the 4th shot was not made.

If the shots were "stringed" like mostly in a line, none of this would matter even to the extent that a circle with its diameter drawn through the center of the most remote 2 holes would qualify with both methods of measurement provided all the other holes fell inside it.

So, there we have it.

The only time the two methods are in conflict is when there are 3 holes which when an arc is drawn through their centers would create a circle which is larger than that which would be created by drawing a circle through the 2 holes that are the most distant.

We could be talking about zillionths occurances here, but I can see where it could occur.

Fortuantely, most of my groups are sort of stringed. So the conflict may be like the fly crap in the pepper.

Yet, if necessary, I could plot out the holes on my cad system and let it work its wonders.

I guess I will stick with Pythagoras.

Thanks both of youse guys for the help and clarification.


Zak Smith
September 19, 2005, 07:38 PM
The fundamental difference between Bullseye or High Power vs. Benchrest is that Benchrest does not care exactly where the bullets go, as long as they are in the correct target region, while Bullseye & HP shooters shoot at a specific aiming point (the X) surrounded by scoring rings. Bullseye and HP are not scored based on group size, they are scored based on, well, score on the defined target. Different games with different goals.

September 19, 2005, 08:27 PM
In highpower it is not always clear either. To score a higher value in NRA highpower the shot must be tangent to the line of the next higher scoring ring. I have seen so many shots so close that even with a plug it is hard to make an accurate measurement. The nice thing about highpower VS bench rest for scoring is that if the shot is SO close that it requires a plug to tell if the shot is tangent to the line then "most" shooters will simply give the benefit of the doubt to the shooter. Trying to measure groups to some infinitely small measurement seems to be futile to me, but then again I am not interested in BR.

Zak Smith
September 19, 2005, 08:39 PM
Yeah, there is that call if it broke the next scoring ring or not.

But my point was that HP and B. neither score based on group size as such.

Jon Coppenbarger
September 19, 2005, 11:45 PM
Just a different game thats all. I even watched a 10 meter air rifle and pistol match at the OTC on sunday. They had scoring rings also. Well the 10 ring was just a dot in the middle on the rifle target. I loved the shoot offs when you score in 10ths. like a 10.5 or 10.8 or what ever. Interesting watching all those great shooters from up close. how many times do you get to watch shooters from Russia or the Czech team shooters or our best from 20 feet away.
More olympic medal and world record holders and any other type of champion you could think of shooting. Humbling experience in the least. If they use scoring rings and count the rings instead of measuring groups I guess it is good enough for a duffer like myself.

John I got my space gun back and putting new sights on it this week and I plan on getting used to those apeture sights. Should be fun.


September 20, 2005, 12:20 AM
Group size is a useful simplification, because no math is required. That makes it the universal currency of measuring consistency.

But if you're going to use a computer, you can invent other measurements. For example, you could determine the geometric center of the group, compute the distance from it to each shot, and then compute the mean, median, and max of those distances. You could do a barchart of the distances.

What would that tell you? Heck, I dunno. But it'd be fun to try.

Somewhere, someone's got a program that lets you scan your target, puts the image on the screen, and then click on the bullet holes on the screen to tell it where each shot landed (a poor man's digitizer). Then it does calculations for you.

September 20, 2005, 09:26 AM

Sounds like the Target Analysis module in RSI Shooting Lab... you go thru a 'calibration' step to take into account some specific characteristics of your monitor, and then basically you put the target up against the monitor, and then click the mouse cursor under each bullet hole. Obviously some room for error there; don't really think it's meant for measuring say, point-blank BR targets, but it works fairly well for some other things, like ladder load tests where you are looking for vertical 'plateaus' as you can isolate the horizontal and vertical x/y coordinates of the center of the group vs. the point of aim. I've used it to analyze some targets that would have been too close for me to call by eye, and it's helped me find that 'sweet spot' pretty much dead on. It has a couple different methods for calculating group size, including mean radius, string method, etc. Whatever floats your boat. Fun to play with, anyway.


September 23, 2005, 02:17 PM
I measure outside edge to inside edge of the two furthest holes. No subtraction necessary.

September 23, 2005, 02:59 PM

Works fine if everyone is using the same caliber bullets and not working to the "ring measure" method. In our contests we have to allow for anything from the .44 cal sabot to a .410 gage solid slug to a 12 gauge solid, etc., so measuring the outside would always be an unfair measure to the guy firing the biggest bore. :what:

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