Number of shots in a group, group size, and relation to precision

S

solyanik

Guest
I am sure this was probably covered a number of times, but I searched and could not find :-(.

What is the mathematics of precision? If I have shot a group of 3 and got X, what is the probability that a subsequent group size would be Y?

Any pointers would be greatly appreciated. Having taking probability theory 20 years ago in college and having thoroughly forgotten everything, this is currently beyond my skills :-(.
 
The probability of your 5th shot going low is very high. Likewise, the probability of your 5th group being large is very high. The probability of both increase dramatically when the first 4 shots or the first 4 groups are very small.

Ryan
 
The greatest probability is : The smaller the group at the completion of the 4th shot the greater the probability that the 5th shoot will increase the size of the group:
Historical data shows: The smaller the group at the completion of the 4th shot the larger the group will be at the completion of the 5th shot.

Scientific testing shows: The more monkeys that sit behind the benches the greater the probability that one of the monkeys will shoot a world record for both biggest and largest group.

Ted
 
If i go to Hooters with the Rimfire guys for the tution class will my groups get any smaller at 1000yds??..JR..Jeff Rogers
 
I could care less about theories on probability, but there are only a few things that will cause a bullet to take the exact same path as the one before, but an infinite number that will cause it not too.

Shooting is a lot like playing the piano. You can read every book ever printed on how to do it, but untill you actually sit down at the bench and do it, a lot, you will not be able.

That being said, I am a little intrigued about this Hooters thing:D..........jackie
 
solyanik said:
What is the mathematics of precision?
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There is an example table of group size versus number of shots here: http://www.border-barrels.com/articles/rimfire_accuracy/group_statistics.htm

But radial standard deviation (circular error probable) is a more efficient way to compare accuracy. See the references to Frank Grubbs' work on the Border Barrels website, and this:

APPROXIMATE PROBABILITY DISTRIBUTIONS FOR THE EXTREME SPREAD.
Taylor, Malcolm S.; Grubbs, Frank E. Source: Naval Research Logistics, v 22, n 4, p 713-719, Dec 1975

Enjoy,
Keith
 
Thank you Keith. I remember reading 30 or so years back in some year old Speer manual that their stats determined that 7 shots was the most practical amount of shots to fire when doing load development.
That has to be the best write-up on the number of shots to use in load development I've ever read.
 
Probability is when you have 4 shots in a tiny hole at a big match getting the 5th to go into the group is much tougher than when you are just practicing.
 
Well that is interesting. Ill have to read Kieth's link a few more times to let it all sink in.
I was talking to Jerry one day while trying to tune a rifle and he shared with me that a 3 shot group was about worthless but if it shoots try 5 but just because 5 will shoot you should try 8 to really see if it will shoot.
I tried that and he was right or so it seemed. I cant remember who told him that theory though.

Hey Kieth if I meet you at Hooters can you splain that to me in english?
As a side to that maybe we can convince Jackie to serve Hooters famous Hot crawdaddy wings at the Crawfish this month?
 
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Vern said:
he shared with me that a 3 shot group was about worthless but if it shoots try 5 but just because 5 will shoot you should try 8 to really see if it will shoot.
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I agree 3 shots does not tell you much but if a rifle won't put 3 together there is not much reason to shoot 5.
 
Great find, Keith - I can't believe I've never seen that before.

For those who just want the punch line:

Firing six 7-shot groups will tell you as much about your load's true accuracy as firing sixteen 3-shot groups - a savings of six rounds. Interestingly (to me at least), using 10-shot groups will take fifty shots to get the same confidence - eight more rounds than using 7-shot groups.
 
Damon said:
Great find, Keith - I can't believe I've never seen that before.

For those who just want the punch line:

Firing six 7-shot groups will tell you as much about your load's true accuracy as firing sixteen 3-shot groups - a savings of six rounds. Interestingly (to me at least), using 10-shot groups will take fifty shots to get the same confidence - eight more rounds than using 7-shot groups.
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It takes even less shots with CEP or GAP http://www.bmotsoft.com/index.html


Landy
 
Damon said:
Also cool. But man, that looks like a lot of fiddling with a ruler...
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Damon,

Something like 10 years ago, I was using a ruler and calculating the “mean radius” statistic for groups because it was more efficient than ES for testing comparisons and accuracy information.

Now, with the help of the experimental physicist who developed GAP and Jeff Block the developer of On Target….it’s somewhat automated.
The On Target software I’m working with hasn’t yet been released to the public, but it automatically locates POA and all bullet hole locations. After that, it exports all the x,y point data to my specialized Excel spreadsheets and to the GAP software.

I’ve learned more about accuracy in the last 3 or 4 years than I did in the previous 30 years I’ve been testing.

Omaha huh. I live 230 miles west of you and shoot at Isaac Walton in Lincoln once in awhile, but most of the time I shoot in a tunnel I built.

Landy
 
mks said:
Landy,
Thanks, the Extreme Spread Shot Probability Calculator on this website may be the best answer to the original posters question.

Cheers,
Keith
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Keith,

The “Extreme Spread Probability Calculator” is fun to play with, but it’s only useful if you know the “Width” of your grouping and the “Width” is different than ES or C-T-C.
You probably already know that, but others may not realize it if they visit the link.

Landy
 
Landy, That sounds very interesting. I've always been half-assed about my load testing, and it's always left me feeling like I'm doing it wrong. (Heck - I *know* it means I'm doing it wrong.) I look forward to seeing what you come up with with On Target.

I just moved to Omaha, so I'm still looking about for a good long range. Looks like there's a nice one about half an hour south of town. I'll forgive the "Husker" in your username - I went to the University of Colorado! :)
 
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