I stumbled upon this article today about how to measure groups and discuss the accuracy of an individual rifle or rifle and a certain load. I have been shooting groups and measuring stuff since the mid 1970 and have to agree that this is a superior way to discuss the accuracy of loads or rifles. Anyone shoot 22LR has experience those crazy flyers in the lower priced ammo range that are due to huge shifts in primer/powder or projectile weight that is just not what we need to do to measure total group size and anyone shooting benchrest knows the old " 4 in and 1 out" target. We have advanced in how we discuss the accuracy of a gun or of a certain load in a specific rifle.
Mean Radius for measuring groups and rifle accuracy
- Thread starter Littlecooner
- Start date
I may be wrong on this, but I think I read somewhere where the qualification to make the Berdan Sharpshooters during the Civil War was based on measuring the distance from the center of the bullseye to the shot. To qualify you had to be within a certain radius.
This gave way to scoring rings which represent the radius from the center of the bullseye.
As far as flyers with 22 RF, I just got into target shooting (recreational only but for score) last year and for sure, I get about 2 to 3% extreme flyers per brick of CCI SV ammo. I take alibi shots on these. This allows me to keep the cost down (CCI) yet shoot for score and not get frustrated with an obvious ammo related flyer.
This gave way to scoring rings which represent the radius from the center of the bullseye.
As far as flyers with 22 RF, I just got into target shooting (recreational only but for score) last year and for sure, I get about 2 to 3% extreme flyers per brick of CCI SV ammo. I take alibi shots on these. This allows me to keep the cost down (CCI) yet shoot for score and not get frustrated with an obvious ammo related flyer.
dellet
Gold $$ Contributor
I have seen the qualification test written a couple of different ways.
Within a 10” circle
Average of 5” from center.
You had to qualify both off hand and from rest, 100 & 200 yards.
Matches of the day often had different targets, one that would be almost impossible today is the String match. All shots measured distance from the center with a string, shortest string wins. That’s a pretty harsh scoring system.
Thinking again about the string match, with todays computerized systems like shot marker this could probably be done with todays groups.
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Most folks measure group size by measurement of the “extreme spread” of the group. That is, the distance between the two widest shots. This is quick and easy to do and the way most folks do it. However, this method has the disadvantage of providing limited information on the actual performance of the rifle and ammunition. Another method of measuring groups is “Mean Radius” which is the mean of the distances of all shots from the center of the group. This method provides additional information over that of the extreme spread method. The disadvantage is that it takes more effort to obtain. If you would like to experiment with the Mean Radius calculation follow the link below. http://www.ar15.com/forums/topic.html?b=3&f=16&t=512887
I always counted the flyer in the group. It looks to me like if you dont count it your not telling the truth. Doug
Doug Beach
Silver $$ Contributor
As e-targets become more prevalent, I think a return to “string measurement” would be a fine thing. Cumulative distance from center, low score wins.
Everything from the loading bench to the target......the shooter is responsible for....EVERYTHING! All the loading,all the bench setup/gun handling,all the flag reading/wind calls,shot execution,followthough....
the shooter did it......well,there might have been some Klingons and Romulans out there.
The No. 1 cause of all errant shots is the shooter. Sometimes there's downrange conditions/changes the shooter didn';t see or the flags didn't show.....and remember the flags don't show everything AND they're always late!
This mean radius type of measuring targets is more applicable to score shooting than to group shooting.
In score shooting,you do typically aim for the center.....in group shooting,it doesn't matter where the group
is on the target.
Good luck and stay safe.
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ShotMarker has the option of calculating mean radius in the group analysis feature.
Doug Beach
Silver $$ Contributor
Yes. But I’d like to see scoring by cumulative distance from target center. That would be a permanent solution to all “this target is too hard/easy” issues.
I didnt think it was best 5 out of seven but Im not an internet star. Saw those experts on the internet doing that one day couldnt get out of there fast enough. Doug
I much prefer looking at Mean Radius for evaluating the precision of my gun and loads. . . and I use all shots, including the 1 out. What I don't like about ES as an evaluation number is that in only takes into account just 2 shots. Mean Radius takes into account all shots, whether it's 5, 10 or 50.
dave@aDave
Gold $$ Contributor
A reminder:
There is a difference between the "average" and "mean".
There is a difference between the "average" and "mean".
Alex Wheeler
Site $$ Sponsor
The problem with ignoring the flier is that many rifles have built in accuracy and ignition issues and that flier keeps popping up. And in matches you have to count that flier. Best to get everything dialed in and shoot tighter.
This is mathematically the same thing as mean radius if the number of shots is the same. Because mean radius is just the total error radius divided by number of shots.
Radial error is the only thing we should care about. ES is a terrible way to characterize accuracy because it excludes all but two data points.
The math behind characterizing group dispersion was mature and well known even back before ww2, when they wanted to mathematically describe the distribution of artillery shells landing vs point of aim.
The concepts of Circular Error Probable, etc are not new at all. The problem is that we as shooters haven’t caught up to where the science was about 100 years ago. Because the power of tradition— even if rooted in ignorance or error— is remarkable. We learn from others, who also learn from others— and come to “know” that which just isn’t so.
The math of how to get statistically valid comparisons has been done and done. It’s just that it does indeed involve math. And now that we have fancy technology that can measure and calculate it for us, there’s simply no excuse for not using a better measure of dispersion than ES.
The beef I have with “mean” radius is that people intuit that the mean represents 50% probability. Of course the 50% probability circle would be the median radius. And depending on the number and magnitude of “flyers”, the disparity between mean and median could be relatively large.
I wanted to make a separate post arguing for an alternative standard for assessing rifle accuracy (precision yes, but since it’s relative to an actual point of aim, it’s still accuracy).
Here’s what Frank Grubbs, PhD wrote in 1964:
So that’s what it all boils down to. I want to come up with a number that represents probability of landing within some distance of the point of aim.
In his writing, Grubbs helpfully provides useful stats tables that can let you arrive at the sigma value (population std error) from samples.
For a 5-shot group, your sample standard deviation should be multiplied by 1.19 to be an unbiased estimate of the population std dev. (Nominal: 50% confidence). To have 95% confidence, that sample std deviation for 5 shots should be multiplied by 1.38.
For 10 shot groups, the factors are 1.084 and 1.3, respectively.
Since 100y is close to 95meters, we could easily then adopt a rule of “the three 95s: the size of the circle representing 95/100 shots landing within it, with 95% confidence at 95meters”
And to arrive at this value, just shoot a 10 shot group at 100y, determine the standard deviation of that group’s radial error from either the group center (precision) or point of aim (accuracy) and add 30%.
If your rifle is perfectly zero’d, then the average point of impact will be the point of aim. So to calculate the standard deviation of your 10 shot group, just measure the individual radial error terms, square them, add them up, the take the square root. If you want to have a 95% confidence estimate for the long run capability, add 30% to that value.
Reverse engineering the stats a bit, you can see just how likely it is for the typical “sub moa all day” claim to be true. That claim translated into stats would be “population standard deviation at 95% confidence of < 0.5 moa” (we use 0.5 moa because we are doing math on radial error against a claim of diametrical error). What does this look like on target? We subtract 30% to get to a sample std dev for 10 shots of 0.35 MOA radial error.
Since basic probability says plus or minus two sigma is 95% confidence, the “sub-moa all day” claim essentially boils down to a 10 shot group with not a single shot outside 0.7 MOA from point of aim. Doable for many on here, but much more stringent than it would first seem to many who make such boasts.
I think I want to make a “Sub-MOA-all day” challenge target scaled to particular sizes that represent real actual capbility. I.E one size for 5 shot groups at 100y, maybe another for 10 shot groups, 20 shots, etc.
Please check my work against this reference and correct as needed: http://ballistipedia.com/images/3/3...lemen_and_Missile_Engineers_-_Grubbs_1964.pdf
Here’s what Frank Grubbs, PhD wrote in 1964:
So that’s what it all boils down to. I want to come up with a number that represents probability of landing within some distance of the point of aim.
In his writing, Grubbs helpfully provides useful stats tables that can let you arrive at the sigma value (population std error) from samples.
For a 5-shot group, your sample standard deviation should be multiplied by 1.19 to be an unbiased estimate of the population std dev. (Nominal: 50% confidence). To have 95% confidence, that sample std deviation for 5 shots should be multiplied by 1.38.
For 10 shot groups, the factors are 1.084 and 1.3, respectively.
Since 100y is close to 95meters, we could easily then adopt a rule of “the three 95s: the size of the circle representing 95/100 shots landing within it, with 95% confidence at 95meters”
And to arrive at this value, just shoot a 10 shot group at 100y, determine the standard deviation of that group’s radial error from either the group center (precision) or point of aim (accuracy) and add 30%.
If your rifle is perfectly zero’d, then the average point of impact will be the point of aim. So to calculate the standard deviation of your 10 shot group, just measure the individual radial error terms, square them, add them up, the take the square root. If you want to have a 95% confidence estimate for the long run capability, add 30% to that value.
Reverse engineering the stats a bit, you can see just how likely it is for the typical “sub moa all day” claim to be true. That claim translated into stats would be “population standard deviation at 95% confidence of < 0.5 moa” (we use 0.5 moa because we are doing math on radial error against a claim of diametrical error). What does this look like on target? We subtract 30% to get to a sample std dev for 10 shots of 0.35 MOA radial error.
Since basic probability says plus or minus two sigma is 95% confidence, the “sub-moa all day” claim essentially boils down to a 10 shot group with not a single shot outside 0.7 MOA from point of aim. Doable for many on here, but much more stringent than it would first seem to many who make such boasts.
I think I want to make a “Sub-MOA-all day” challenge target scaled to particular sizes that represent real actual capbility. I.E one size for 5 shot groups at 100y, maybe another for 10 shot groups, 20 shots, etc.
Please check my work against this reference and correct as needed: http://ballistipedia.com/images/3/3...lemen_and_Missile_Engineers_-_Grubbs_1964.pdf
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I have a copy of the "Grubbs" reference you cite. I have had it for many years and read it many times. It is deceptively simple. I start to read it and understand what I am reading but soon become bogged down and start over. It has some great example problems worked out and if you have a technical background it is not too difficult to follow. Understanding the basic statistical math is a challenge but not necessary for using the information. My vocation at one time involved simulated altitude testing and data analysis of rocket engines and rocket motors so I understand the principals well enough to use them but probably not well enough to teach them. I too see the claims of people having a one MOA gun and you would think that everyone has a one MOA gun.
Doug Beach
Silver $$ Contributor
Except I believe mean radius generally is measured from the center of the group. I’m thinking about score matches, such as Highpower & F-class, and want the radius from the center of the target, regardless of where the group is centered.
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