# Group size

On Sunday Barb and went to the range and used the “Training Bay”. Barb practiced drawing from the holster. I set up my chronograph and tested 17 different .40 S&W loads with four different powders and two different bullet types (both 180 grain). I ended up firing 170 rounds of .40 S&W and 20 rounds of .22 into the same target. All the .40 S&W was from about 28 yards. It made for, what I thought was, an interesting target:

I wasn’t doing my best with each shot but I was reasonably careful. My primary goal was to not shoot the chronograph screens and having a constant point of aim helped.

But after pulling the target I wondered, “What would be the equivalent five shot group size made from the same sample of ammo?”

“Group size” has always bugged me. A better measure would be standard deviation. But that’s not what the shooting world uses. I understand why. Standard deviation is much more difficult to compute in our situation. Group size is extremely easy and as long as you are honest with yourself (don’t find excuses to throw away a bad group and always use the same number of shots when comparing) it can give you a fairly decent indication of the accuracy of your system (gun, ammo, and shooter).

One of the problems with group size is that you can’t easily compare a three shot group to a five shot, seven, or ten shot group. I spent a lot of time manipulating equations and running simulations and built a solution into Modern Ballistics. If you edit a cartridge and have it calculate the “5-shot Group Size” via “Calculate via group” you can input a set of one or more groups at various ranges and various shots per group and it will compute the equivalent 5-shot group size in minutes of angle.

Sooo… I put in the group size 13” from the target above for a 170 shot group and it immediately complained. I had programmed in error checking which said, basically, that if you are shooting a group with more than 100 shots you don’t know what you are doing. Heavy sigh.

So I went with a 100 shot group with 13 inches and came up with a 20.84 MOA five shot group. Okay. Not too bad considering the variations in the ammo (the mean velocity on any given loading varied from 907 fps to 1033 fps), iron sights, with a pistol, and not originally intending to shoot for a good group. And it would have been better had my program allowed for 170 shot groups. Converting back to inches and rounding down a bit to compensate for the 170 versus 100 shot group it comes out to 5.75 inches.

I’m okay with that.

Share

## 8 thoughts on “Group size”

1. Try elimination of all but single holes in the target when determining number of shots for your calculation.

That big hole in the middle – one shot. The other 70 or so fliers all around – those count a lot in comparison!

This would be a measure of the MOA you might expect around your point of aim for any one given single shot, perhaps not statistically perfect, but better than many other measures.

Simply put, if you pick up a handgun and shoot one shot at the center of a target, about all I can predict is that it will likely be on the paper, and have about a 50% chance of being within the center hole you made on this target.

Any one shot may deviate a lot from point of aim, as demonstrated by your 170 shots.

• What is the basis for rejecting the single holes and claiming the result “better than many other measures”? There are statistical methods to reject outliers. Are you invoking one of these? If so, which one?

2. Interesting; you and I were doing practically the same thing on Sunday, and pondering the same issues. That’s not too much of a coincidence though, as my thinking has been influenced by years of using a Modern Ballistics.

It’s hard enough getting people to agree on what the term “group size” means. Imagine trying to get standard deviation used widely. And, deviation from what; mean center of group I guess, or POA? The former would be more fair to the system being tested, while the latter would be more important to the shooter.

Standard deviation from POA sounds to me like a match scoring system. It’s going to be pretty close to the typical bull’s eye type target and scoring rings though.

You’d have to measure and record the location of each shot relative to that chosen reference point? So build a system to do all that as automatically as your chrono records each shot in a string, and Bob’s your uncle.
Yup; the age-old scoring ring system works pretty well for that, huh?

• Variance, by definition, is the sum of the squares of the difference between each point and the mean (arithmetic average) of the points. Standard deviation, by definition, is the square root of the variance.

If you want a measure of the repeatability of the system (firearm, ammo, and shooter) under the conditions being tested you would be interested in the standard deviation.

If you want a measure of the aiming error (sights and/or shooter error) you would measure the difference between the POA and the mean of all the shots.

3. Any weapon system is qualified not on absolute group size, but on a statistical measures of accuracy such as CEP96.

So what you did there is pretty much industry standard for weapon system.

And, it also happens to be the way I measure performance as well, although I use 3-Sigma.

Earl