Converting Group Sizes

denton · Dec 14, 2020

As more shots are added to a group, it tends to grow. This is because no shot added to a group makes it smaller, and some shots make the group larger. Over the long term, three-shot groups tend to be smaller than five-shot groups.

Here's how to convert the long term average of group size:

To convert from 3 shots to 4 shots, multiply group size by 1.16.

To convert from 3 shots to 5 shots, multiply group size by 1.27.

To convert from 4 shots to 3 shots, multiply group size by .86.

To convert from 5 shots to 2 shots, multiply group size by .79.

All this assumes that all sources of assignable cause have been removed: shooter flinch, barrel rubs, loose hardware, wind, etc., so that nothing is left but the normal random variation.

Hjalkarsson · Dec 14, 2020

so after you miss a few times, it's physically impossible to hit a bullseye.

Ru4real · Dec 14, 2020

denton said:
As more shots are added to a group, it tends to grow. This is because no shot added to a group makes it smaller, and some shots make the group larger. Over the long term, three-shot groups tend to be smaller than five-shot groups.

Here's how to convert the long term average of group size:

To convert from 3 shots to 4 shots, multiply group size by 1.16.

To convert from 3 shots to 5 shots, multiply group size by 1.27.

To convert from 4 shots to 3 shots, multiply group size by .86.

To convert from 5 shots to 2 shots, multiply group size by .79.

All this assumes that all sources of assignable cause have been removed: shooter flinch, barrel rubs, loose hardware, wind, etc., so that nothing is left but the normal random variation.

I have a lot of questions as to how you derived these. But I should think on it a while before I ask. Thanks for posting!

How about 10 shots to 3 shots?

Ru4real · Dec 14, 2020

Hjalkarsson said:
so after you miss a few times, it's physically impossible to hit a bullseye.

I tend to start drinking when that happens. My targets seem to get bigger and I usually have 2 to shoot at.

denton · Dec 14, 2020

Ru4real said:
I have a lot of questions as to how you derived these. But I should think on it a while before I ask. Thanks for posting!

How about 10 shots to 3 shots?

Creighton Audette worked it out a long time ago. Not knowing about his work, I derived the same information a few years ago.

The method was a Monte Carlo simulation using 20,000 groups. When the going gets tough, the tough resort to Monte Carlo. The math for group sizes is nasty.

Working out the Monte Carlo for just 5 shots is very tedious, and 10 shots is much, much worse. So I decided that my curiousity only reached to 5 shots.

Edited to add: Audette's coversion from 3 to 5 shots is 1.23, slightly different from my value of 1.27. His conversion from 3 to 10 is 1.53, and his conversion from 3 to 20 is 1.79.

Ru4real · Dec 14, 2020

denton said:
Creighton Audette worked it out a long time ago. Not knowing about his work, I derived the same information a few years ago.

The method was a Monte Carlo simulation using 20,000 shots. When the going gets tough, the tough resort to Monte Carlo. The math for group sizes is nasty.

Working out the Monte Carlo for just 5 shots is very tedious, and 10 shots is much, much worse. So I decided that my curiousity only reached to 5 shots.

Edited to add: Audette's coversion from 3 to 5 shots is 1.23, slightly different from my value of 1.27. His conversion from 3 to 10 is 1.53, and his conversion from 3 to 20 is 1.79.

So then 10 to 3 shots is 0.65?

My 223 will shoot several different bullets into 10 round 3/4 inch 100 yard groups. I consider it an MOA gun.

I can expect 1/2” 3 shot groups? 0.75” x 0.65 = 0.49”

Interesting

hardheart · Dec 15, 2020

What do you multiply by? Do you need an average of 5 (or more?) three shot groups to then multiply that by 1.27 to estimate a 5 shot average?

mshootnit · Dec 15, 2020

Hjalkarsson said:
so after you miss a few times, it's physically impossible to hit a bullseye.

correct

ms6852 · Dec 15, 2020

I don't want to ever convert group size. If my 10 shot group is not the same as my 3 shot group, I need to stop drinking coffee before shooting or make an appointment to see if I have Parkinson's.

Nature Boy · Dec 15, 2020

If you could convert a 0 shot group size I wouldn't need to do load development or practice my rifle handling or wind reading skills

Walkalong · Dec 15, 2020

Denton is right, shoot enough rounds and the group will get bigger.

Heck, sometimes the first two shots blow a group, which is why I see Denton’s figures almost as best case scenario.

murf · Dec 15, 2020

denton said:
all sources of assignable cause have been removed:

not necessary with your method. all these variables become constants at 20k iterations (just like the overall group size variance). never an exact number but close enough for shooters.

thanks for that,

murf

murf · Dec 15, 2020

denton said:
it tends to grow.

but always the growth is smaller eventually so close to zero as to be the same.

is this the concept of your calculations? if not, my bad. either way ... thanks

murf

wiscoaster · Dec 15, 2020

And what's the usefulness of all this math?

P89DCSS · Dec 15, 2020

denton said:
The method was a Monte Carlo simulation using 20,000 groups. When the going gets tough, the tough resort to Monte Carlo. The math for group sizes is nasty....

What variables did you use and what were the ranges? Were there any correlated variables?

Converting Group Sizes

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