## Why 3 shot groups are not useful.

years ago the was an article about using one box of ammo to see what kind of accuracy you were getting with a firearm.

The system consisted of using several targets over the top of each other.

The botton target collected all 20 shots.

The next target up collected 10 shots and was replaced with another target that collected the next 10 shots.

The target above that was replaced 4 times after every 5 rounds.

This was a way of economizing on your ammunition.

So with one box of 20 rounds you got 7 targets to analyze.

The system consisted of using several targets over the top of each other.

The botton target collected all 20 shots.

The next target up collected 10 shots and was replaced with another target that collected the next 10 shots.

The target above that was replaced 4 times after every 5 rounds.

This was a way of economizing on your ammunition.

So with one box of 20 rounds you got 7 targets to analyze.

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### Re: Why 3 shot groups are not useful.

This guy feels that a "1 MOA rifle" is a rifle that puts all shots within 1 MOA 68% of the time. Interesting take on it. I think it makes more sense to go out to 2 or 3 standard deviations.

http://www.the-long-family.com/group_size_analysis.htm

I think the industry could accept reporting group size as one standard deviation of diameter of 30 or so shots as the value would look very much like the extreme spread of a typical 4 shot group.

http://www.the-long-family.com/group_size_analysis.htm

I think the industry could accept reporting group size as one standard deviation of diameter of 30 or so shots as the value would look very much like the extreme spread of a typical 4 shot group.

### Re: Why 3 shot groups are not useful.

Well My 1-shot groups are tight as hell. I am a sub MOA shooter all day long

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### Re: Why 3 shot groups are not useful.

Statistics being what they are to the layman, the first company that begins to use the 99% CI is going to hurt their business through honest advertising.rsilvers wrote:I think the industry could accept reporting group size as one standard deviation of diameter of 30 or so shots as the value would look very much like the extreme spread of a typical 4 shot group.

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### Re: Why 3 shot groups are not useful.

With all due respect, I think it's a silly discussion anyway.

I'd rather be competent with the dope on my rifle at 50 yard increments all the way out to 1200 yards, in wind, on moving steel, and have a decent grasp on cosign angles.

A 4" group at 650 yards impresses me a LOT more than a 1 hole group at 100, especially when the guy behind the rifle can shoot the target moving, in the wind, or at an angle.

This is, of course, just my take on it.

I've always liked ringing steel more than punching paper anyway, so perhaps I am just biased.

I'd rather be competent with the dope on my rifle at 50 yard increments all the way out to 1200 yards, in wind, on moving steel, and have a decent grasp on cosign angles.

A 4" group at 650 yards impresses me a LOT more than a 1 hole group at 100, especially when the guy behind the rifle can shoot the target moving, in the wind, or at an angle.

This is, of course, just my take on it.

I've always liked ringing steel more than punching paper anyway, so perhaps I am just biased.

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### Re: Why 3 shot groups are not useful.

http://home.wanadoo.nl/jhogema/skeet..._precision.htm

This seems to show that 40 shots of RSD or MR is as good as shooting 100 shots of extreme spread.

But, if you are going to do extreme spread, then divide your total number of rounds into multiple groups to average.

Quote:

From Figure 3, the following can be seen.

· For less than 10 shots, 1 group is the best.

· For 10 shots or more, 2 groups is better than 1 (i.e., 2 groups of 5 is the turning point).

· For 18 shots or more, 3 groups are better than 2 (i.e., 3 groups of 6 is the turning point).

· For 24 shots or more, 4 groups is better than 3 (i.e., 4 groups of 6 is the turning point).

Further pieces of the puzzle:

· 3 groups of 4 shots are better than 1 group of 12.

· 4 groups of 4 shots are better that 1 group of 16.

· 5 groups of 4 shots are better than 1 group of 20.

· 3 groups of 6 is better than 2 groups of 9.

· 4 groups of 6 are better than 3 groups of 8.

· 4 groups of 5 are better than 5 groups of 4 and better than 2 groups of 10 .

· 5 groups of 6 are better than 3 groups of 10.

This seems to show that 40 shots of RSD or MR is as good as shooting 100 shots of extreme spread.

But, if you are going to do extreme spread, then divide your total number of rounds into multiple groups to average.

Quote:

From Figure 3, the following can be seen.

· For less than 10 shots, 1 group is the best.

· For 10 shots or more, 2 groups is better than 1 (i.e., 2 groups of 5 is the turning point).

· For 18 shots or more, 3 groups are better than 2 (i.e., 3 groups of 6 is the turning point).

· For 24 shots or more, 4 groups is better than 3 (i.e., 4 groups of 6 is the turning point).

Further pieces of the puzzle:

· 3 groups of 4 shots are better than 1 group of 12.

· 4 groups of 4 shots are better that 1 group of 16.

· 5 groups of 4 shots are better than 1 group of 20.

· 3 groups of 6 is better than 2 groups of 9.

· 4 groups of 6 are better than 3 groups of 8.

· 4 groups of 5 are better than 5 groups of 4 and better than 2 groups of 10 .

· 5 groups of 6 are better than 3 groups of 10.

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### Re: Why 3 shot groups are not useful.

That makes me wish I could remember something from the 3 semesters of calculus I took in college.rsilvers wrote:http://home.wanadoo.nl/jhogema/skeetn/b ... oc96439743

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### Re: Why 3 shot groups are not useful.

Not really helpful anyway. I know a guy that can shoot tiny groups all day long with his super-expensive custom rifle that cant mil-range, read wind, and has no DOPE out to any significant distance.

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### Re: Why 3 shot groups are not useful.

Silvers, have you seen the program called shotgun insight or something like that? You take a picture or a shotgun pattern and it analyzes it for you giving all kinds of data. If your going to shoot 30 round groups you may as well use it.

Make it easy for ya, amazing program actually.

http://www.shotgun-insight.com/

Make it easy for ya, amazing program actually.

http://www.shotgun-insight.com/

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### Re: Why 3 shot groups are not useful.

Jeroen gave me more results.

If you want to be able to detect the difference between two rifles that differ in actual performance by 20%, then with the following groups you can correctly predict which rifle is more precise with the following percent certainties:

1 group of 2 shots, 59% certainty.

1 group of 3 shots, 63%

2 groups of 2 shots, 63%.

3 groups of 2 shots, 66%

10 groups of 3 shots but then you only look at the best group, 66%

1 group of 5 shots, 68%

5 groups of 2 shots, 71%

1 group of 10 shots, 75%

1 group of 10 shots using mean radius, 77%

1 group of 10 shots using radial standard deviation, 78%

10 groups of 2 shots, 78%

5 groups of 4 shots, 82%

4 groups of 5 shots, 83%

15 groups of 2 shots, 83%

5 groups of 5 shots, 86%

10 groups of 3 shots, 86%

50 groups of 2 shots, 96%

2-shot groups seem to take more total rounds to get the same percent certainty as other group sizes.

http://home.wanadoo.nl/jhogema/skeetn/b ... oc96439743

This means that a 3-shot group can only differentiate a 0.25 MOA from a 0.30 MOA rifle about 63% of the time but if you average 10 such groups then you can tell a 0.25 MOA rifle from a 0.30 MOA rifle with an 86% confidence level. Still not great actually. This is why it seems 25-30 shots is only starting to begin to be enough testing to know how the rifle compares.

If you want to be able to detect the difference between two rifles that differ in actual performance by 20%, then with the following groups you can correctly predict which rifle is more precise with the following percent certainties:

1 group of 2 shots, 59% certainty.

1 group of 3 shots, 63%

2 groups of 2 shots, 63%.

3 groups of 2 shots, 66%

10 groups of 3 shots but then you only look at the best group, 66%

1 group of 5 shots, 68%

5 groups of 2 shots, 71%

1 group of 10 shots, 75%

1 group of 10 shots using mean radius, 77%

1 group of 10 shots using radial standard deviation, 78%

10 groups of 2 shots, 78%

5 groups of 4 shots, 82%

4 groups of 5 shots, 83%

15 groups of 2 shots, 83%

5 groups of 5 shots, 86%

10 groups of 3 shots, 86%

50 groups of 2 shots, 96%

2-shot groups seem to take more total rounds to get the same percent certainty as other group sizes.

http://home.wanadoo.nl/jhogema/skeetn/b ... oc96439743

This means that a 3-shot group can only differentiate a 0.25 MOA from a 0.30 MOA rifle about 63% of the time but if you average 10 such groups then you can tell a 0.25 MOA rifle from a 0.30 MOA rifle with an 86% confidence level. Still not great actually. This is why it seems 25-30 shots is only starting to begin to be enough testing to know how the rifle compares.

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### Re: Why 3 shot groups are not useful.

http://home.wanadoo.nl/jhogema/skeetn/b ... gs/sgs.htm

Here is something people won't want to hear.

So back to this paper. Around figure 6 and 7, it shows that the standard deviation is determinable by the average group size and number of shots per group.

He determined a constant of .2691 for 5 shot groups, and 0.1947 for 10 shot groups. I am asking him for it for 3 shot groups.

So if a 5 shot group is 0.250 MOA, then 95% of the groups will be within +- .250 * .2691 * 2.

So .250 +- .13455, which means that 95% of the groups will be from 0.115 to 0.385.

So a rifle which averaged 0.250 MOA is really only a 0.385 MOA or better rifle for 5-shot groups 95% of the time.

If you wanted to be able to shoot 5-shot groups that were 0.250 or less 95% of the time, you must average 0.160 groups!

Once I have the constant, I will report what one must average for 3 shot groups in order to have 95% of your 3-shot groups 0.250 or less.

Here is something people won't want to hear.

So back to this paper. Around figure 6 and 7, it shows that the standard deviation is determinable by the average group size and number of shots per group.

He determined a constant of .2691 for 5 shot groups, and 0.1947 for 10 shot groups. I am asking him for it for 3 shot groups.

So if a 5 shot group is 0.250 MOA, then 95% of the groups will be within +- .250 * .2691 * 2.

So .250 +- .13455, which means that 95% of the groups will be from 0.115 to 0.385.

So a rifle which averaged 0.250 MOA is really only a 0.385 MOA or better rifle for 5-shot groups 95% of the time.

If you wanted to be able to shoot 5-shot groups that were 0.250 or less 95% of the time, you must average 0.160 groups!

Once I have the constant, I will report what one must average for 3 shot groups in order to have 95% of your 3-shot groups 0.250 or less.

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### Re: Why 3 shot groups are not useful.

The constant for the standard deviation for an average of 3-shot groups is 0.370

So if you are doing 3-shot groups and average 0.250, then:

0.250 * 0.370 * 2 = 0.185.

So 95% of the time, the rifle is a 0.250 +- 0.185 rifle. Or a 0.435 rifle for the every worst group out of 20 groups.

Which means to be a 0.250 or under rifle 95% of the time, you have to average 0.144 or less.

So fire 10 groups of 3-shots each on a single piece of paper. If the average of those groups is 0.144 or less, then you have a rifle which will not exceed 0.250 rifle 95% of the time, based on 3-shot groups.

Or you can just average .250 or less and say "my rifle averages 0.250 or less" and skip the part about mentioning the max group size for that one out of 20 groups.

So if you are doing 3-shot groups and average 0.250, then:

0.250 * 0.370 * 2 = 0.185.

So 95% of the time, the rifle is a 0.250 +- 0.185 rifle. Or a 0.435 rifle for the every worst group out of 20 groups.

Which means to be a 0.250 or under rifle 95% of the time, you have to average 0.144 or less.

So fire 10 groups of 3-shots each on a single piece of paper. If the average of those groups is 0.144 or less, then you have a rifle which will not exceed 0.250 rifle 95% of the time, based on 3-shot groups.

Or you can just average .250 or less and say "my rifle averages 0.250 or less" and skip the part about mentioning the max group size for that one out of 20 groups.

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### Re: Why 3 shot groups are not useful.

A gun which puts 99.7% of its shots into 1.0 MOA will average 0.400 MOA 3-shot groups. Many people would call such a gun a 0.400 MOA gun. I would consider calling it a 1 MOA gun. Some people would call it a 1/8 MOA gun.

Such a gun would shoot 1/8 MOA groups once every 73 groups. It would shoot 1/4 MOA groups once every 6.4 groups. It would shoot 1/2 MOA groups once every 1.3 groups (I think that is called "all day long").

Now if we pick an inferior gun which averages 1.0 MOA 3-shot groups, it would shoot 1/8 MOA groups once every 1886 groups. It would shoot 1/4 MOA groups once every 174 groups. It would shoot 1/2 MOA groups once every 12.8 groups. Some people would call this a 1 MOA gun. Some would call it a 1/2 MOA gun. I would consider calling it a 2-1/4 MOA gun as that is where 99.7% of shots would go.

This is why the exact test must be defined to have any meaning.

Such a gun would shoot 1/8 MOA groups once every 73 groups. It would shoot 1/4 MOA groups once every 6.4 groups. It would shoot 1/2 MOA groups once every 1.3 groups (I think that is called "all day long").

Now if we pick an inferior gun which averages 1.0 MOA 3-shot groups, it would shoot 1/8 MOA groups once every 1886 groups. It would shoot 1/4 MOA groups once every 174 groups. It would shoot 1/2 MOA groups once every 12.8 groups. Some people would call this a 1 MOA gun. Some would call it a 1/2 MOA gun. I would consider calling it a 2-1/4 MOA gun as that is where 99.7% of shots would go.

This is why the exact test must be defined to have any meaning.

### Re: Why 3 shot groups are not useful.

rsilvers wrote:A gun which puts 99.7% of its shots into 1.0 MOA will average 0.400 MOA 3-shot groups. Many people would call such a gun a 0.400 MOA gun. I would consider calling it a 1 MOA gun. Some people would call it a 1/8 MOA gun.

Such a gun would shoot 1/8 MOA groups once every 73 groups. It would shoot 1/4 MOA groups once every 6.4 groups. It would shoot 1/2 MOA groups once every 1.3 groups (I think that is called "all day long").

Now if we pick an inferior gun which averages 1.0 MOA 3-shot groups, it would shoot 1/8 MOA groups once every 1886 groups. It would shoot 1/4 MOA groups once every 174 groups. It would shoot 1/2 MOA groups once every 12.8 groups. Some people would call this a 1 MOA gun. Some would call it a 1/2 MOA gun. I would consider calling it a 2-1/4 MOA gun as that is where 99.7% of shots would go.

This is why the exact test must be defined to have any meaning.

In a perfect world, turning this into a math equation might work.

I think most would agree that keeping field data on a precision rifle in a log book is more of a determining factor of accuracy on rifle and shooter than punching numbers in a calculator.

As for the factory match ammo issue, some barrels like different pressure nodes. Saying a rifle is not accurate because it does not shoot Federal match ammo well is funny.There are too many variables that contribute to accuracy or inaccuracy to try and make this strictly a math game.

As to the title of this thread. I feel 3 shot groups are good during load development and never @ 100 yds. Load development for me is done @ 300 yds. 5 Shot groups would determine the rifle's accuracy. Anything over that wears on the shooter and is not useful for most people.

Another thing to consider is distance fired. Shoot for group @ dawn with no wind @ 600 yds.

Fire 3, 5 shot groups with cool down in between. If it shoots an average 1/2moa, I think most would feel it is a 1/2 moa rifle.

A rifle is either accurate or not.

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### Re: Why 3 shot groups are not useful.

/threadHoop wrote: A rifle is either accurate or not.

You are either pregnant or you ain't.

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### Re: Why 3 shot groups are not useful.

5 shot 100 yard groups are more useful than 3 shot 300 yard groups.I feel 3 shot groups are good during load development and never @ 100 yds.

It is not that 3 shot groups are literally useless but they cannot differentiate small changes as well as larger groups.

You can have your own opinion, but you cannot have your own facts.

I have shown that 1 group of 3 shots can determine which load is more precise with only 63% certainly when there is a 20% real difference in the loads. If you want to detect which load is better when there is just a 10% difference, then the certainty drops lower than 63%. That is not reliable enough to make a decision. Therefore, it is not very useful for load development unless the two loads are very much different in performance.

5 groups of 5 shots is 86% certainly, which is starting to become significant.

It is an inconvenient truth.

### Re: Why 3 shot groups are not useful.

A rifle in good working order is not going to all of a sudden blow shots with the same load, same conditions, same cleanliness etc..rsilvers wrote:5 shot 100 yard groups are more useful than 3 shot 300 yard groups.I feel 3 shot groups are good during load development and never @ 100 yds.

It is not that 3 shot groups are literally useless but they cannot differentiate small changes as well as larger groups.

You can have your own opinion, but you cannot have your own facts.

I have shown that 1 group of 3 shots can determine which load is more precise with only 63% certainly when there is a 20% real difference in the loads. If you want to detect which load is better when there is just a 10% difference, then the certainty drops lower than 63%. That is not reliable enough to make a decision. Therefore, it is not very useful for load development unless the two loads are very much different in performance.

5 groups of 5 shots is 86% certainly, which is starting to become significant.

It is an inconvenient truth.

The shooter might.

When working a load I feel the other 2 shots to make a 5 shot group are useless and you are just testing yourself, not the load. An experienced shooter who is disciplined in the shooting fundamentals should only need 3 shots to verify the validity of a load during load development.

Once the shooter feels he has reached the load the rifle likes, then fire a 5 shot or 10 shot group. As a verification string.

But anything over 5 shots is really just testing the shooter.

The best way I have found to work a load is to take 5 pieces of brass same lot new.

Work that brass during load development to find the load. Take all the variables out that you can.

Same with Suppressor POI shift tests.

Fire 5 shots without suppressor

Cool

Fire 5 shots with suppressor

cool

Fire 5 shots without suppressor

cool

etc... until repeatable results are attained.

compare and note changes in POI. This is essential in knowing where the first shot will go. Ever see a guy blow a match when otherwise would be a great shooter? CCB shots need to be known. If you do not know the CCB shot @ distance, you will start to compensate for it thinking there is wind or other variables that you did not pick up on. When all it was, was the CCB shot.

Every shot means something. If fired @ distance, you should see some variation in the very first shot each time fired with the suppressor and the first shot after being taken off. Maybe it will take 3-4 shots to settle in. Not all sticks are like this, but it is best to know if you have one that is.

Do not think you blew the shots. Log it and note change. See if it is duplicated in the next group. Minute of man shooters might not care, but when you spend the time developing a precision load, why not know what the rounds do every shot.

Thank you for the rational and informative back and forth. This is the only way we can learn and become better shooters.

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### Re: Why 3 shot groups are not useful.

It is not blowing it. That is within the normal distribution pattern of the rifle. That is the true MOA of the rifle starting to appear. That is what the rifle really is.Hoop wrote:A rifle in good working order is not going to all of a sudden blow shots with the same load, same conditions, same cleanliness etc..

Sigh. No. That is not the case. Read about bell curves and normal distributions. It takes 30+ shots to start to see the distribution pattern of a rifle/ammo, not counting the shooter. Two shots can appear out of the group in a 10 shot group and that is neither abnormal or necessarily shooter induced. It is just likely within the normal distribution that you would start to see if you fired 30+ shots.Hoop wrote:But anything over 5 shots is really just testing the shooter.

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### Re: Why 3 shot groups are not useful.

I'll say it again...GlockandRoll wrote: I'd rather be competent with the dope on my rifle at 50 yard increments all the way out to 1200 yards, in wind, on moving steel, and have a decent grasp on cosign angles. A 4" group at 650 yards impresses me a LOT more than a 1 hole group at 100, especially when the guy behind the rifle can shoot the target moving, in the wind, or at an angle.

This is, of course, just my take on it.

I've always liked ringing steel more than punching paper anyway, so perhaps I am just biased.