mean radius conversion to group size

[coyotejoe]

I just read where the military accuracy requirement for a new service pistol is 3.15" mean radius of ten shots at 50 meters.  I do realize this can never be exactly converted to our more familiar "extreme spread" since a shot or two could be quite far from center and still make the cut when averaged against the 8 or 9 shots closer to center.
 What I was wondering is if someone good with statistical analysis could come up with a "probable representation" of what a 3.15" mean radius would look like in our more familiar terms, barring any really wild flyers. It would certainly be well over a 6" group and just guessing I'd think more like 10" or so.
Anyone inclined to do some calculations?

[parkergunshop]

I'm not an expert,

But the mean radius seems to the the distance from the aiming point on the target the or the supposed central point of the shot grouping to the outer most shot on the target.  This means that the group size in most shooters terms would be over twice the mean radius as you stated.

Your 6 inch supposition is close, but did they account for wild fliers, a 6 inch plus group at fifty yards from a machine rest is from my viewpoint poor is grouping for a pistol using good ammo.

For the earth or other orbs it's from the center to the outer most part of the surface crust or roughly 1/2 the diameter.

This is an interesting question?

[coyotejoe]

Well no, "mean radius" would not be the "extreme radius" but more like the average radius, some closer and some still farther out.  The overall group size would be considerably more than twice the mean radius, definitely not a "braggin' group".

[coyotejoe]

I've learned a bit more on this subject. "Mean radius" is that radius which will enclose 50% of the shots, no consideration at all is given to how far out the other 50% may spread. So that is even worse than I had thought, a group of 18" extreme spread could very well have 50% of its shots inside that circle of 6.3" diameter. I think a flintlock smoothbore horse pistol could met that standard. So even though we civilians expect our carry guns to keep 100% of its shots in a 6" bull at 50 yards, it seems the Army recognizes the fact that no one really shoots very well while being shot at and so they see no need for fine accuracy in a military pistol.

[ole 5 hole group]

it seems the Army recognizes the fact that no one really shoots very well while being shot at and so they see no need for fine accuracy in a military pistol.

You probably got that right since the majority of shootouts between our men in blue & the bad guys result in no one getting struck by bullets.

[coyotejoe]

I've learned a bit more about this, here's a link which shows how it is calculated.
http://www.m4carbine.net/showthread.php?t=64906
The examples used in this link show why one can not convert mean radius to group size with any degree of accuracy. One group in the example has a mean radius of 0.78" and the other is 0.43" but both are 2.1" groups by the more familiar method of measuring center to center of the two widest shots.
The point I found most interesting is that the accuracy standard for the new service pistol is about the same as for the 1873 Colt single action army model. I guess good enough is good enough.

[Mohawk]

Wow...... WAY too much thinking into this. But I will say this. The general shooting public said that a .38 Spl is inadequate for deer. But, the science proved it is fine and it was right.

[coyotejoe]

I guess I don't know how much thinking is too much but too little really stands out.

[Mikey]

Problem solved.  Question answered.  From Gun Tests magazine we have that the old and new group measurements, the average group radius and average group size, are comparable. 

The average group radius is more likely to describe how a gun will actually shoot because it contains about 5 times more data than the average group size, but if you want to compare performance between two guns the average group size (if I read the article correctly) is sufficient.  Mean radius and average radius are a close enough measurement to be sufficient for government work...

When you look at it, average group radius is just the radius (1/2 the diameter) of the group.  The diameter is twice the radius.  The old school sez to draw a straight line from the center of your most distant shots, those farthest apart, to get the diameter of your group.  The new measurements just measure the radius.  So, if your new service pisto shoots a 3.15" radius at 50m that should translate to twice that for the group diameter which would measure to 6+". 

Coyote Joe - you're right, good enough is good enough.

[williamlayton]

Most of the conclusions here are based on human involvement. I don't think that the requirements of the gun have anything to do with people being involved.
I think what we are talking about is the mean accuracy of the weapon---I also think this is a pretty sloppy requirement for a gun not in the hands of a person but a machine.
Blessings

[coyotejoe]

Problem solved.  Question answered.  From Gun Tests magazine we have that the old and new group measurements, the average group radius and average group size, are comparable.
The average group radius is more likely to describe how a gun will actually shoot because it contains about 5 times more data than the average group size, but if you want to compare performance between two guns the average group size (if I read the article correctly) is sufficient.  Mean radius and average radius are a close enough measurement to be sufficient for government work...

When you look at it, average group radius is just the radius (1/2 the diameter) of the group.  The diameter is twice the radius.  The old school sez to draw a straight line from the center of your most distant shots, those farthest apart, to get the diameter of your group.  The new measurements just measure the radius.  So, if your new service pisto shoots a 3.15" radius at 50m that should translate to twice that for the group diameter which would measure to 6+". 

Coyote Joe - you're right, good enough is good enough.

No, "mean radius" is the average distance each shot of the group falls from the center of the group. Averages cannot be converted to extremes with any degree of reliability but certainly the group size will never be only twice the mean radius. The examples given in the link above make that clear, both are 2.1" groups but one is 2.69 time the mean radius while the other is 4.88 times. Someone on another forum took the trouble to go over a bunch of his old targets to calculate mean radius and compare to group size. He found that on average of the targets he measured 3.2 times the mean radius equals group size.  There was a lot of variation within those numbers but 3.2 probably is a fair guesstimate and is reinforced by Townsend Whelen who wrote the group size will average roughly three times the mean radius. So from all that we can say the new military pistol is likely to produce roughly 9-10" groups at 50 meters.
 I don't know what Gun Test Magazine means by "average radius" but that is not how the military calculates "mean radius". There is now software available to calculate mean radius from a photo of the group but I won't be investing, I only wanted to know what the army expects of it's proposed new pistol and how it compares to the older pistols.