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Multiply a 3-shot group by 1.28 to get your expected 5-shot group?
- Thread starter pk5333
- Start date
Its a statistical rule of thumb but there is no substitute for actual data.
WHy is that? the rule assumes that the group is randomly distributed. OR in english, you are not a factor. For most people, that may not be a safe assumption.
WHy is that? the rule assumes that the group is randomly distributed. OR in english, you are not a factor. For most people, that may not be a safe assumption.
next on news at 5, more stupid shit to come out of Larue
I shoot many 1 hole groups. Firing the second shot always seems to fuck it up tho
So stop at 1 shot
Follow me for more internet “One hole all day long” shooting tips!
So stop at 1 shot
Follow me for more internet “One hole all day long” shooting tips!
my typical 5-shot group is my 4-shot group +.5"
Well shoot only four-shot groups....
Duh!
So you go to the range to practice you precision and shoot several 3 shot groups and then multiply by 1.28 to get your 5 shot avarage(!)?
Heres a wild idea, shoot 5 shot groups and measure what you get. This way you get acctual data and practice at the same time.
Shit, I now I know what Einstein might have felt like.
Heres a wild idea, shoot 5 shot groups and measure what you get. This way you get acctual data and practice at the same time.
Shit, I now I know what Einstein might have felt like.
It's a statistical probability function. Something that is clearly over your head.
3 shots is not statistically relevant, as shown by the 5 shot group.
Maybe you should discuss this with Bryan Litz. I haven't read the book where he explains this probability function.
What I DO know is that in statistics there are several ways to express the confidence interval of a function, so speaking of statistical relevancy without first having an agreement on the confidence interval desired is fucking pointless.
With that I'm out
By a third party who probably knows even less about statistics than you and I
From a statistical perspective, you are 100% correct. Turning a rule of thumb approximation into a statistical probability is ignoring mathematical norms.
If saving $1 per group is something one needs, they have chosen the wrong hobby. Shoot 5 shot groups, or 4, or 8 or 10 and use real data is a much better path than mental masturbation over group size relevancy.
WWWS...
....What Would Wilder Say?
He'd say I have problems
Groups are fun, but hitting what you aim at at 200 yards isn't easy
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What this "rule" really means if you took an infinite number of 3 shot groups from a perfect shooter (like a bench vise or something) measured them, and then added 2 more shots to each group the average difference between the 3-shot and 5-shot group would be a factor of 1.28.
However, if you looked at an individual group it could probably be anything from a factor of 1 (the second shots where within the first 3) to infinity (I'm shooting and I shot the wrong direction). Its the AVERAGE that 1.28.
So to be truly valid, this single example should be repeated (or in English Larue got lucky)
How to lie with statistics....
However, if you looked at an individual group it could probably be anything from a factor of 1 (the second shots where within the first 3) to infinity (I'm shooting and I shot the wrong direction). Its the AVERAGE that 1.28.
So to be truly valid, this single example should be repeated (or in English Larue got lucky)
How to lie with statistics....
Ol Mark Larue fudd posting again. I wish that snowflake that calls everyone else a snowflake wouldn't have blocked me on the gram. I sincerely enjoyed laughing at the idiotic shit he posts and watching people stroke his ego. The siete, one shot groups, whatever this bullshit is, random fudd/boomer musings, etc.
Anyways. I never took stats so I have nothing meaningful to add in the way of that.
Anyways. I never took stats so I have nothing meaningful to add in the way of that.
However you turn a .25” group into .75” group is on you.
Me personally I enjoy punching 4 shots into a nice little cloverleaf. Then, once realizing how good I’m shooting, I like to over concentrate
Which helps me throw the 5th shot. Thus, like a porn star, blowing it
Me personally I enjoy punching 4 shots into a nice little cloverleaf. Then, once realizing how good I’m shooting, I like to over concentrate
Which helps me throw the 5th shot. Thus, like a porn star, blowing it
Unfortunately for me I usually shoot a trued remmy or a savage .22 for groups. With those cost saving measures I usually just say fuck it and shoot all 5.
How about instead of focussing on group sizes which aren't relevant for long range shooting we focus on being able to hit the target where we want to.
Argument starter engaged
Argument starter engaged
I made a study of this 20yrs ago when I was shooting nearly every day. From hundreds of firing sessions over several years I amused myself one day by taking all the data and calculating this very topic. I found that 5 shot groups were 1.33x 3-shot groups, and 10 shot groups were 1.5x 5 shot group, (or 2.0x 3 shot groups). I rounded these results in order to have a Wryfox rule of thumb. It was not a rigid statistical test and analysis, but large numbers of data add to the credibility. I still use this rule of thumb today, and regularly reprove it.
@TheGerman while reading this.
Wtf… is so hard about a five shot group!
Ammo shortage? Puhleeze.
Sirhr
Wtf… is so hard about a five shot group!
Ammo shortage? Puhleeze.
Sirhr
The actual number is 1.27 (I believe 1.28 comes from ballistipedia; they have a small bug in their code which skews the results a little, but their conclusions are still largely correct).
The ratio of x1.27 between extreme spreads of 3-shot groups and 5-shot groups is, strictly speaking, correct. However, I can’t imagine a practical value to this knowledge.
As @DocRDS has said, the ratio of 1.27 applies to the average of infinite number of 3-shot groups vs. the average of infinite number of 5-shot groups.
In other words, one needs to shoot a statistically significant (= quite large) number of 3-shot groups and take the average, then he could estimate the average size of a 5-shot group by multiplying the figure by 1.27.
For the complete picture, here’s how (average of infinite) ES of 3-, 5-, and 10-shot groups relate to each other (expressed in sigmas, standard deviations):
ES(3)= 2.41 σ
ES(5) = 3.06 σ
ES(10) = 3.79 σ
R50 = 1.18 σ
R95 = 2.45 σ
R99 = 3.03 σ
R50, 95, and 99 are respectively the radia where 50%, 95% and 99% of impacts would lie.
This said, measuring rifle precision by extreme spread of a small sample is perhaps the most inefficient way of doing it; we are only using information from 2 shots (the most extreme), while all the rest is ignored. If, however, one goes for this method, 5-, 6-, and 7-shot groups are the most efficient (or should I say – least inefficient) in terms of information obtained per shot. See, e.g., http://ballistipedia.com/index.php?title=Range_Statistics and http://www.geoffrey-kolbe.com/articles/rimfire_accuracy/group_statistics.htm
To get something marginally meaningful, one needs to shoot at least five 5-shot groups. The average would then have a 95% confidence interval of ±23.6%. In other words, if you take an average ES of five 5-shot groups, and you obtain, say, 1 MOA, the actual 5-shot ES of this rifle-cartridge-shooter combo is probably somewhere between 0.764 and 1.236 MOA.
For one single 5-shot group, the result, in terms of engineering validity, is complete garbage. The confidence interval in that case is ±52.8%
To get to a more or less meaningful certainty of the result (confidence interval of ±12.4%) using this method (average ES of 5-shot groups) one needs to shoot 13 groups, that is – 65 shots.
If the goal is to really measure the accuracy of one’s rifle (as opposed to posting a photo of a nice group on a forum), an approach which takes into account information from all shots (rather than just extreme spread) is very much preferred (saves a lot of ammo). See, e.g., here: https://geladen.ch/en/taran-user-manual/ and https://bc.geladen.ch/taran/taran.html
All this said, extreme spread of small samples does have some engineering merit – not to measure the accuracy of a rifle, but to quickly discard inaccurate ones. This can get useful, for example, for load development; the likelihood of a decent load producing a poor result is much lower than of a poor load producing a good result. If two groups of 5 shots do not group very well, for me it is grounds enough to discard the load and not measure it any further – it is statistically very unlikely that further groups would get much better.
The ratio of x1.27 between extreme spreads of 3-shot groups and 5-shot groups is, strictly speaking, correct. However, I can’t imagine a practical value to this knowledge.
As @DocRDS has said, the ratio of 1.27 applies to the average of infinite number of 3-shot groups vs. the average of infinite number of 5-shot groups.
In other words, one needs to shoot a statistically significant (= quite large) number of 3-shot groups and take the average, then he could estimate the average size of a 5-shot group by multiplying the figure by 1.27.
For the complete picture, here’s how (average of infinite) ES of 3-, 5-, and 10-shot groups relate to each other (expressed in sigmas, standard deviations):
ES(3)= 2.41 σ
ES(5) = 3.06 σ
ES(10) = 3.79 σ
R50 = 1.18 σ
R95 = 2.45 σ
R99 = 3.03 σ
R50, 95, and 99 are respectively the radia where 50%, 95% and 99% of impacts would lie.
This said, measuring rifle precision by extreme spread of a small sample is perhaps the most inefficient way of doing it; we are only using information from 2 shots (the most extreme), while all the rest is ignored. If, however, one goes for this method, 5-, 6-, and 7-shot groups are the most efficient (or should I say – least inefficient) in terms of information obtained per shot. See, e.g., http://ballistipedia.com/index.php?title=Range_Statistics and http://www.geoffrey-kolbe.com/articles/rimfire_accuracy/group_statistics.htm
To get something marginally meaningful, one needs to shoot at least five 5-shot groups. The average would then have a 95% confidence interval of ±23.6%. In other words, if you take an average ES of five 5-shot groups, and you obtain, say, 1 MOA, the actual 5-shot ES of this rifle-cartridge-shooter combo is probably somewhere between 0.764 and 1.236 MOA.
For one single 5-shot group, the result, in terms of engineering validity, is complete garbage. The confidence interval in that case is ±52.8%
To get to a more or less meaningful certainty of the result (confidence interval of ±12.4%) using this method (average ES of 5-shot groups) one needs to shoot 13 groups, that is – 65 shots.
If the goal is to really measure the accuracy of one’s rifle (as opposed to posting a photo of a nice group on a forum), an approach which takes into account information from all shots (rather than just extreme spread) is very much preferred (saves a lot of ammo). See, e.g., here: https://geladen.ch/en/taran-user-manual/ and https://bc.geladen.ch/taran/taran.html
All this said, extreme spread of small samples does have some engineering merit – not to measure the accuracy of a rifle, but to quickly discard inaccurate ones. This can get useful, for example, for load development; the likelihood of a decent load producing a poor result is much lower than of a poor load producing a good result. If two groups of 5 shots do not group very well, for me it is grounds enough to discard the load and not measure it any further – it is statistically very unlikely that further groups would get much better.
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I have my own system. I fire a two shot group and then multiply by 0.4 and am always the best shooter on the line.
Sirhr
Sirhr
Almost 20 years ago, I was confirming zero on my ‘deer rifle’ at an indoor range. ‘5 shots in about an inch, 3 inches above the bullseye? Ok, I’m good.’ (Im that guy that spends an hour at the range, talks to no one, shoots 5 shots and leaves…) As I pack up to leave, an older guy in the lane next to me asks me how I shot.
(Paraphrases recreation of the conversation…)
‘Not bad.’
‘Yeah, let me see your target.’
I unroll the paper to show the group.
‘Hmph, you didn’t even hit the bullseye’
‘I know, I going on an elk hunt and intentionally sighted…’ (He cut me off.)
‘Look at this’ Pulls down his target.
He shows me a paper that has been absolutely abused by at least 2 boxes of ammunition. There are holes from the extreme left to the extreme right, top to bottom. But, there it is, a single bullet hole in the lower right quadrant of the bullseye. He was the better shooter on the line that day…
I don't see a problem with using multiplying factors for general observance.
Although doing this every time is not truly representative, it does serve one very important purpose of getting shooters to think in terms of group size likely outcomes & not absolute outcomes.
Guys shoot groups & view them in absolute terms which, is exactly how groups of any number should not be viewed.
Rifles always have & always will shoot groups in terms of probable statistical group size based upon the SD of the groups.
There are a couple of tables of multiplying factors I've seen for group size which were used on occasion by grubs while he was testing those multiplying factors to measure their statistical validity. To my knowledge, there are two main tables used depending on number of shots per group & confidence interval.
In my opinion, using multiplying factors would be a great way of teaching shooters how they should regard the way rifles truly perform.
Although doing this every time is not truly representative, it does serve one very important purpose of getting shooters to think in terms of group size likely outcomes & not absolute outcomes.
Guys shoot groups & view them in absolute terms which, is exactly how groups of any number should not be viewed.
Rifles always have & always will shoot groups in terms of probable statistical group size based upon the SD of the groups.
There are a couple of tables of multiplying factors I've seen for group size which were used on occasion by grubs while he was testing those multiplying factors to measure their statistical validity. To my knowledge, there are two main tables used depending on number of shots per group & confidence interval.
In my opinion, using multiplying factors would be a great way of teaching shooters how they should regard the way rifles truly perform.
You are only as good as your last shot.
Mine was a perfect three shots of bourbon.
Hit the spot nicely.
Mine was a perfect three shots of bourbon.
Hit the spot nicely.
It is only the next morning that you really know how good it was.
I agree. Statistical “cone of fire” can be a reality check. I tell the average deer hunter that I feel if I can shoot 1/2 MOA on the range I double that in the field (at least) under hunting conditions. Since a lot of these guys are happy with “minute of pie plate” it’s not a wonder they miss.
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I would add that being both an end-to-end barrel maker and end-to-end rifle maker in large quantity that actually test fires their guns before shipment....Larue probably has enough data to be considered a "large sample size" tester for the purposes of this discussion.
Don't get me wrong, there is plenty of opportunity to dick shot Larue IMHO...but this might not be the best place.
Interesting, thank you! I'd be curious to know their testing protocol.
I've read that the Soviets used a 4-shot group extreme spread to QC every military AK at the Izhevsk plant, discarding whatever was above a certain threshold (and double-testing the whole batch if it happened). That was enough to give a reasonable guarantee that the barrels are in specs.
The Swiss had a different definition of "reasonable", and, per the army requirements, every military Stgw90 went through 24 shots at Neuhausen (and, if my memory is good, they used a 50% impacts rectangle rather than extreme spread, to threshold acceptable accuracy).
It'd be interesting to know what exactly Sako and Tikka do to sustain their "1 MOA or better" claim.
To be honest, I believe most makers these days trust their process instead of testing each unit when it comes to commercial sales for accuracy.
I say that because bore alignment aware CNC machining these days is so good, and factory ammo got so much better.
1moa is no longer a challenge.
Maybe you're right. I certainly don't know enough about the capabilities of modern metalworking machines to have an idea of the cost equation.
There is actually a method to calculate how many defects you would "miss" by reducing your sampling size. (going from 3 shot to 5 shot), but that does require usually up to 1000s of samples, a statistician, and a stable process. It usually only found in large mfg.
ANd there are serious convos about "how much does a defect cost us" that we get a lot of B movies about bean counters failing to realize that blowing up cars on burning babies or some crazy crap. Usually its just a return and replacement.
ANd there are serious convos about "how much does a defect cost us" that we get a lot of B movies about bean counters failing to realize that blowing up cars on burning babies or some crazy crap. Usually its just a return and replacement.
- Nov 3, 2010
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You talk to people at the range?Almost 20 years ago, I was confirming zero on my ‘deer rifle’ at an indoor range. ‘5 shots in about an inch, 3 inches above the bullseye? Ok, I’m good.’ (Im that guy that spends an hour at the range, talks to no one, shoots 5 shots and leaves…) As I pack up to leave, an older guy in the lane next to me asks me how I shot.
(Paraphrases recreation of the conversation…)
‘Not bad.’
‘Yeah, let me see your target.’
I unroll the paper to show the group.
‘Hmph, you didn’t even hit the bullseye’
‘I know, I going on an elk hunt and intentionally sighted…’ (He cut me off.)
‘Look at this’ Pulls down his target.
He shows me a paper that has been absolutely abused by at least 2 boxes of ammunition. There are holes from the extreme left to the extreme right, top to bottom. But, there it is, a single bullet hole in the lower right quadrant of the bullseye. He was the better shooter on the line that day…
Indeed there is a statistical method to reliably estimate defects & rifle accuracy repeatability/variability within set limits.
The U.S gov along with a host of other govs around the world commissioned men like Grubbs to conduct many thousands of shots/samples to establish statistical methods to determine all manner of likely outcomes.
I'm no proponent of 3 shot groups but, if probability factors are applied to show the real world likely outcome, I see no problem.
Those tables have been established using hard data & verified statistical principals & are more reliable representation than not using them than firing 3 shots & calling it good.
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Lets be honest, you show up the range with the shit we got, you gonna attract a crowd....
I can sit alone in a crowded theater, but I am the goddman beatles at the range.
- Nov 3, 2010
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