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Old July 8, 2019, 01:51 PM   #1
Bart B.
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Shot Group Mean Radius .....

....... and what it tell you about the accuracy it represents?

Accuracy spec for arsenal 7.62 M118 match ammo was 3.5" mean radius at 600 yards.

The 1965 National Match lot's 270 shot test group had a 1.9" mean radius at 600.

The Extreme Spread was about 10 inches.

About 40% of the shots were inside 4 inches ES.

About 70% were inside 7 inches ES, 30% of all shots between 4 and 7 inches ES.

Near 90% inside an ES of 9 inches, 20% of all shots between 7 and 9 inches ES.

100% inside the 10 inch ES, 27 shots, 10% of all 270 shots, in the outer 1 inch ES.
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Old July 8, 2019, 02:23 PM   #2
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bart, didn't you do this before??

reminds me of a similar one that was an actual plot of 270 bullet holes shot at 600 yards for the 1965 National Match lot of 7.62 NATO M118 Match ammo. The group was about 10 inches extreme spread and had a mean shot hole radius of 1.9 inches from group center. I took it to a person then asked him to pick 3 holes for his first "imaginary" group then I would pick 3 more for my first group. We would repeat that 45 more times until all 270 holes had been picked. We each had some very tiny "groups" as well as some very large ones. He then understood why Lake City Army Ammo Plant fired 270 shots in that test group to get an excellent statistical assesment of that ammo lot's accuracy.
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Old July 8, 2019, 03:54 PM   #3
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Old July 8, 2019, 03:56 PM   #4
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Quote:
Originally Posted by old roper View Post
bart, didn't you do this before??

reminds me of a similar one that was an actual plot of 270 bullet holes shot at 600 yards for the 1965 National Match lot of 7.62 NATO M118 Match ammo. The group was about 10 inches extreme spread and had a mean shot hole radius of 1.9 inches from group center. I took it to a person then asked him to pick 3 holes for his first "imaginary" group then I would pick 3 more for my first group. We would repeat that 45 more times until all 270 holes had been picked. We each had some very tiny "groups" as well as some very large ones. He then understood why Lake City Army Ammo Plant fired 270 shots in that test group to get an excellent statistical assesment of that ammo lot's accuracy.
You know without asking.

Is that a cross post from another forum?

Last edited by Bart B.; July 8, 2019 at 04:14 PM.
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Old July 8, 2019, 04:40 PM   #5
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(Dirty Math)
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Old July 8, 2019, 05:11 PM   #6
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Well done, Mehavey, well done.

Some washtubs I have seen and bathed in are 30" or more in diameter.

Last edited by Bart B.; July 8, 2019 at 05:20 PM.
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Old July 8, 2019, 05:34 PM   #7
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Where is the group center? Is it the bullseye (POA)?

-TL

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Old July 8, 2019, 06:09 PM   #8
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For "precision" purposes, the center is wherever the group center happens to end up.
(as opposed to true accuracy, which takes sight adjustment to move the group)
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Old July 8, 2019, 06:31 PM   #9
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Quote:
Originally Posted by tangolima View Post
Where is the group center? Is it the bullseye (POA)?
It is the average horizontal X and vertical Y shot hole position. Shot hole radius from group center is the hypotenuse of the shot's X and Y values.

Group center can be superimposed on targets to see shot positions relative to scoring rings.
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Old July 8, 2019, 06:45 PM   #10
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In statistics 50% and 95% are interesting data points. The mean is important as is the average deviation from the mean (std dev) that and sample size. Assuming enough shots, the data should fit a normal distribution. If you can deal with that, then fine. If not beyond this level of discussion.

The mean circle which holds 50% of the hits is interesting (to me).
The circle that holds 95% is another interesting data point (to me).

The radius is 1/2 the circle size and is the standard measure. I think of it as radius = error.

The data with no regard for point of impact is 'precision'. Beyond an initial equipment check it is pretty useless number. Ok not uselss, good basis for comparison or bragging rights.

As already mentioned 'accuracy' is distance from POI and if you think about it, this is all that really counts. Think about hitting what you aim at or how close you are and how often. It should be small comfort to miss 5 times in a row to the same one hole group!

What do any of the numbers mean! NOTHING, unless you have a history for other guns as a basis for comparison. If you get into this radius % mindset, then you have to forget group size and more traditional 5/10 shot moa data.

Last edited by fourbore; July 8, 2019 at 07:20 PM.
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Old July 8, 2019, 07:09 PM   #11
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The obvious advantage to using a statistical based approach is the bottom line data (which ever way you represent it) is determined primarily by the typical shots. Using groups size, the result is primarily influenced by the worse case shot or a collection of very few outliers.

The first method, more shots fired the better. The latter, the more you shoot the more meaningless the results become and too few shots is just as bad.

The industry standard of many smallish 5 shot 'groups' is something we can easily understand has a lot going for it. Easy to compare guns. Easy to understand. Easy to measure.
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Old July 8, 2019, 07:34 PM   #12
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Quote:
Originally Posted by fourbore View Post
The industry standard of many smallish 5 shot 'groups' is something we can easily understand has a lot going for it. Easy to compare guns. Easy to understand. Easy to measure.
What entity established that industry standard?

"Many" is what number?

What size is "smallish?"

Is a specific range defined?

Will everyone testing the same stuff the same way get identical results?

Last edited by Bart B.; July 8, 2019 at 07:46 PM.
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Old July 8, 2019, 07:46 PM   #13
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Quote:
Originally Posted by Bart B. View Post
It is the average horizontal X and vertical Y shot hole position. Shot hole radius from group center is the hypotenuse of the shot's X and Y values.



Group center can be superimposed on targets to see shot positions relative to scoring rings.
Thank you. So the group has been "normalized". That makes big difference in the meaning of radius.

We automatically think everything statistical follows normal (Gaussian) distribution, supported by Central limit theorem. But it may not always be the case. Rayleigh distribution may be more accurate model here. https://en.m.wikipedia.org/wiki/Rayleigh_distribution
But all and all, the mean is quite close to median; any shot fired has probability of 0.5 to hit within the mean radius.

I record shot coordinates in Excel spreadsheet, with called flyers taken out. With that I don't even care about the technicality minutiae. Instead I just use the percentile function. I am mostly interested in radii corresponding to 50 and 90 percentiles.

-TL

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Old July 8, 2019, 07:54 PM   #14
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Group size (sample size) determines statistic significance of the data. For preliminary load development, I use groups of 5. Then increase to 10 once good loads are identified. The final "qualifying" shoot has group size of no less than 20.

-TL

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Old July 9, 2019, 09:23 AM   #15
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bart, your getting old, it's from here.
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Old July 9, 2019, 09:53 AM   #16
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Originally Posted by old roper View Post
bart, your getting old, it's from here.
You may have violated forum rules with that cut-and-paste.
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Old July 9, 2019, 11:46 AM   #17
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The three degrees of lies from best to worst:
Lies
Dam*ed lies
Statistics

As posted by a retired statistical/quality engineer. As soon as you start averaging averages, you've covered up a lot of sins.
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Old July 9, 2019, 12:06 PM   #18
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bart are you now moderator send me private message.

cross post violation?

https://thefiringline.com/forums/pri...m&pmid=1108298
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Old July 9, 2019, 12:16 PM   #19
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bart why don't you tell poster where you got your information from here it is

http://kysrpa.org/2010/history-of-na...fle-ammunition
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Old July 9, 2019, 12:36 PM   #20
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Quote:
Originally Posted by old roper View Post
bart why don't you tell poster where you got your information from here it is

http://kysrpa.org/2010/history-of-na...fle-ammunition
Wrong source for my information. Never seen that article until a few minutes ago.

Last edited by Bart B.; July 9, 2019 at 01:35 PM.
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Old July 9, 2019, 05:45 PM   #21
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Quote:
Originally Posted by NoSecondBest View Post
The three degrees of lies from best to worst:
Lies
Dam*ed lies
Statistics

As posted by a retired statistical/quality engineer. As soon as you start averaging averages, you've covered up a lot of sins.
Like firearms, statistics is a tool for good and evil. Average of averages is fine if it is explained and understood. It is no difference from aggregated average if the averages have same sample sizes.

Was that said statistician a liar, a damn liar, or worse?

-TL

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Old July 9, 2019, 05:52 PM   #22
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What I want is 19 shots out 20 within one inch, 95% of the time.
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Old July 9, 2019, 06:04 PM   #23
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Was that said statistician a liar, a damn liar, or worse?
Mark Twain said that over a hundred years ago. Seems like everything new is old again.
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Old July 10, 2019, 07:43 AM   #24
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Old July 10, 2019, 07:53 AM   #25
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Opening questions of a statistics class instructor:

Quote:
If you have one pair each of green, red, white and blue dice, roll each color pair once, which color pair will roll the biggest number? The smallest?

Last edited by Bart B.; July 10, 2019 at 08:01 AM.
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