## Group Size

24-Apr-12 – 17:30 by ToddG

People talk about group size all the time, but how often do they actually think about what they’re measuring?

The simplest way to measure groups is to use extreme spread (ES). The vast majority of the time someone reports group size, it’s based on ES. Essentially, ES is the distance between the two most distant bullet holes in a group measured from center to center.

A much more complicated but informative way to measure groups is mean radius (MR). MR is complicated because you need to find the mathematical center of the group. From there, you measure the distance of each individual shot from the mathematical center and average them. Because MR is so complicated, it’s rarely used unless you’ve got a computer analyzing your groups for you.

MR is more informative because every bullet counts. In ES, only the two most distant shots count. Take this group for example, which consists of one bullet (green dot) that is five inches to the left of point of aim, and nine bullets (red dot) that miraculously all landed exactly at point of aim:

The extreme spread is five inches. If the red dot was just one bullet, or 99 bullets, it would still be an ES of five inches. If you put a hundred bullet holes in between the red dot and the green dot, it is still an ES of five inches.

But the MR is just 0.9″!

That’s because every shot counts, and when nine of the shots land very close to the target’s mathematical center the one flyer has much less impact on the group size. If the red dot was only one bullet hole, the MR would be 2.5″ giving us a diameter of 5″ … the same as the ES. That’s because now both the ES and the MR are counting all (both) of the holes.

Since we normally can’t — or won’t — do the math to calculate MR, ES has become the accepted way of measuring groups for most people. But this in turn means we need to pay attention to another important piece of information: the number of rounds in a group. Some folks incorrectly assume that a 10-round group is “better” than a 5-round group for measurements. But that’s not actually true. Remember, when we’re using ES we are literally ignoring all but two rounds fired. So as you fire more and more rounds to get your group, you’re providing more chances for one bad hit to skew all your results. You cannot know whether that one bad hit was the gun’s fault, the ammo’s, or the shooter’s. But nine perfectly landed bullets will still look like a horrible group if that tenth round is a significant outlier.

Therefore, you have competing interests. Shooting more rounds will have a better chance of showing you if there are inconsistencies, but one inconsistency out of a hundred rounds skews everything. How to resolve this? Shoot multiple groups. For example, I normally shoot five 5-shot groups. This provides a reasonable balance between putting enough rounds downrange to matter (25) while still counting the “data” from a significant percentage of them (10 out of 25).

Train hard & stay safe! ToddG

(thanks to the folks at mp-pistol.com for the discussion that sparked this post)

1. ## 6 Responses to “Group Size”

2. There’s a cool free program called OnTarget that will allow you scan in your targets and calculate group size and other metrics. It works well with my rifle targets.

http://www.6mmbr.com/ontargetsoftware.html

By Eric on Apr 24, 2012

3. And there’s also Robb Allen’s Handy Dandy Shot Group Analyzer: http://blog.robballen.com/apps/SGA/

4. And then there is me ” Nine shots in a 1″ group and 1 flyer not measured”.

By Ga Shooter on Apr 26, 2012

5. I just shoot a one shot group……….makes it easy to measure.

By Sean M on Apr 26, 2012

6. You’re right in saying many people have no clue what they’re actually measuring. I didn’t for the longest, and was embarrassed to ask because I didn’t want to look silly. It’s always better to understand, and it gives you the tools to then improve.

7. Actually, I believe that the “official Soviet Army method” for zeroing an AK-type rifle uses a formula to approximate the mathematical center of a zeroing group, so that the armorer zeroing the rifle can adjust the sights to match the mathematical center to point-of-aim. I believe they took that approach to better account for variable shooter skill and variable ammo quantity.

Without the AK-specific technical details, it goes like this:

– Fire a 4-shot group at a small dot/square on your zeroing target at your zero range;
– Draw a line between the 2 shots furthest apart and mark the midpoint of that line;
– Draw a line from that midpoint to the next-most distant shot remaining, and mark that midpoint;
– Draw a final line from that midpoint to the fourth shot, and mark that midpoint.

The final midpoint is the approximate mathematical center of the group, and from that point you can measure the mean radius of the group. If the MR as calculated exceeds an acceptable standard, then that indicates that either the rifle is out of spec, the ammo is faulty, or the shooter needs re-training(the Soviet Army would have the best marksmen in a given unit do all the zeroing to minimize the last factor)…

By Phil Wong on Apr 26, 2012

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