different ways to measure a shot group

[mazzgolf]

This conversation came up among a couple friends of mine recently. We were at the range talking about MOA and we got on the topic of "how do you measure shot groups?"... because before you can start talking MOA, you need to know what your shot group measures.

I've always thought to measure shot groups that you measure the longest distance between any two shots and that was it. One of my friends who has been to a long-distance shooting school said that's not how to do it - you find the center of the shot group and average the distance from there to all the shots in the group.

Long story short, I was surprised to learn there are at least EIGHT different ways to measure a shot group! I had no idea. Who knew?!?! They even have names for them. The way I was used to doing it is called "extreme spread" measurement... my friend's way is called the "mean radius" measurement. There are others ways of measuring shot groups -- Figure of Merit, Diagonal, et. al. 

The U.S. Military has an interesting (and complicated, unless you have a doctorate in mathematics!) report here that discusses three ways to measure shot groups ("extreme spread", "mean radius", and "radial standard deviation"):

https://apps.dtic.mil/dtic/tr/fulltext/u2/1034885.pdf

This webpage documents those 3 plus 5 others:

http://ballistipedia.com/index.php?title=Describing_Precision

Now, here's the interesting part. Depending on how you measure the spread on your shot group, your shot group's MOA calculation will be wildly different.

Checkout the example here: 

You can see at least 4 different ways to measure this shot group:

1. Extreme Spread (ES) = 3.0"
2. Mean Radius (MR) = 0.85"
3. Diagonal (D) = 3.5"
4. Figure of Merit (FoM) = 2.4"

Assume this is a 100 yard target. Here's what's funny - if I measure it the way I am used to (extreme spread), it's a crappy 3 MOA. BUT! If I measure it using the "Mean Radius" way, that is shooting sub-MOA!

HA! So depending on how you measure a group, you can be a sharp-shooter at sub-MOA... or you could be an amateur who can't hit a barn door  

So there's your lesson for today. There are more ways to measure a shot group than I ever knew, and if you want to shoot sub-MOA, learn how to calculate the mean radius measurement.  Here's a cool webpage that you can upload a photo of your target with your shot group, click on the holes and tell it where you aimed and how many inches your target is, and it will tell you your "mean radius" measurement along with the "extreme spread" measurement plus the offset from your aiming point:

https://www.ammoman.com/blog/sga/

[Cousin Brown]

That's a horrible grouping.

[mazzgolf]

4 minutes ago, Cousin Brown said:

That's a horrible grouping.

Whatchoo talking 'bout?? That's sub-MOA!   

[Trophy8]

I always measured center to center of farthest shots.

I think your friend was referring to moving the tighter group, flyers be what they are.

[Trophy8]

Here's an example...one could say move the 200yd group 1" left.

[mazzgolf]

11 minutes ago, Trophy8 said:

I always measured center to center of farthest shots.

I think your friend was referring to moving the tighter group, flyers be what they are.

What started this was we were talking MOA - what is the MOA of our groups. He was saying he was shooting a lower MOA than what me and my buddy thought. That's because we (like you) always just measured the distance from the farthest shots (which basically eliminates every shot except for the 2 worst ones from the calculation). He was calculating his shot group's dispersion another way (the "mean radius" measurement) and that's why he was getting a lower MOA because it took into account all of his shots, not just the 2 worst.

Hearing about a second way to measure groups is what sent me down this rabbit hole and finding out there is literally 8 different ways (at least) of measuring a shot group.

[Trophy8]

Fact remains, after 10 shots...6 inside 4" and the other 4 out at 6 inches...group is still 6".

Always go with majority of hits and move accordingly, that gives you the best score opportunity. 

[mazzgolf]

4 minutes ago, Trophy8 said:

6 inside 4" and the other 4 out at 6 inches...group is still 6".

That's only if you measure your shot group using the "extreme spread" method (and how I normally do it, too) - but measure it one of the other 7 ways, and that "6 inch group" comes out to a different number, and so will the MOA for that group (e.g. calculating using "mean radius" will usually result in a lower MOA for a group when compared to an "extreme spread" calculation, assuming the outlier shots in the group are few).

That's what I was surprised about - all the different ways to measure shot groups (which results in MOA being different for all the different methods). I always thought it was just what you described - but I come to find out that is only 1 of at least 8 ways to measure a group, and that way is one of the least accurate calculations.

The U.S. military doesn't use that "extreme spread" method we use - they mainly use the "mean radius" method of calculating shot groups (which is the average of the straight line distances between each shot and the center of the shot group):

US Army ASC: https://asc.army.mil/web/news-keeping-design-on-target/

Quote

"Traditionally, the definition of accuracy has been in terms of target effects (e.g., a weapon in a stand must meet a 5-inch mean radius impact at 300 meters)."

DoD DTIC: https://apps.dtic.mil/sti/pdfs/ADA387108.pdf

Quote

The primary measure of marksmanship precision is the mean radius, which refers to the average of the straight line distances between each shot and the center of the shot group. Secondary measures of marksmanship precision include the horizontal range, the vertical range, the area of dispersion, the diagonal of dispersion, the standard deviation of the horizontal component, the standard deviation of the vertical component, and the radial standard deviation. The most useful statistics are shooting error, constant error, the shot group coordinates, and variable error as indicated by the mean radius.

 

[Trophy8]

With the mean radius the group is more precisely measured. 

10 shots...6 basically touch each other, other 4  are 4 inches out.

10 shots...all 10 are spread out about the 4 inches.

Speaking precision using mean radius the 1st group is better.  Accuracy Speaking there the same. Either way you still move the group. Center to Center is a easy way to calculate Accuracy at the range.

 

 

[Nomad]

Generally minute of pie plate is used in these parts.