THANKS!!! If that second shot doesn't get me, the third shot does. You've solved my problem.
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Multiply a 3-shot group by 1.28 to get your expected 5-shot group?
- Thread starter pk5333
- Start date
The distribution of impacts on the target[*] very closely follows the Rayleigh distribution (2D normal with same sigma vertical and horizontal), rather than a 1D normal distribution; the figures are different from 1D bell curve critical values.1.28 is based on a normal distribution bell curve, and of course, it's a (all things being equal) prediction.... From Brian Litz. Here's the excerpt from one of his latest books:
The ballistipedia guys -- http://ballistipedia.com/index.php?title=Home -- have done a very thorough and complete job of exposing the gory details of the math behind (caution: not for the faint of heart).
Again, for the ones who love pain and suffering, I still may have bits of Perl code I pieced together a few years ago to run a very straightforward montecarlo over 10M+ "virtual shots", for a comparative ES for strings of N shots (N>1).
_____________
[*] at short (<300m) distance where, for the purposes of determining practical group size, variations of muzzle velocity and BC can be ignored, also not considering any systemic iron sights- or target shape-specific aiming errors.
Perl.....
pfft so 1990s
Plus mote carlo sims? SOunds like we need to have a beer and go bowling.
Perl is what God hacked this Universe together with. For weaklings, I can traslate this into LISP, Python, Javascript, C++ or Java, and I think I still remember enough of Go and Haskel syntax to satisfy a perverted cultist.
This said, if you have a closed-form expression for the average size of an N-shot group with a given sigma, pray tell me -- I'm a grateful learner. (Otherwise, better keep on bowling.)
EDIT: or was it a proposal from one dinosaur to another? Then if you ever find yourself around Geneva, Switzerland, I'd gladly bring you to a few places that won't disappoint.
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It means we are old as dirt.
I'll take a FORTRAN copy though if you got it
We're not getting younger, aren't we?
As to FORTRAN... Several lives ago, when I was a kid nerd, I learned FORTRAN to port a Star Trek game from DEC PDP-11 to Sinclair ZX Spectrum BASIC; 35 years down the road, that exercise remains in the top-5 of my personal coding projects hall of fame. I don't think I was ever again so proud in my life. (And it had a graphical front-end instead of a teleprinter-like!)
Oh, well, everything was better before, says I like a mammoth.
This said, I must admit, FORTRAN is something I happily forgot since this only acquaintance.
You don't understand dispersion if you're not talking mean radius and standard deviations of radii at a minimum.
Everything less than 20 shots is (this is not sarcasm) nearly a waste of your time if you're looking to quantify dispersion. You can get a "feel" for things at 10-15 rounds but 20 is where things start getting quantifiable, and 30-35 is where things start getting definitive.
The problem with the OP is that while the average 5-shot group may be 1.28x larger than the average 3 shot group, that doesn't mean that each individual 3 shot group will be 1.28x larger at 5 shots. Not even fucking close. Variability from group-to-group at 3 or 5 shots is significantly larger than the "1.28" multiplier.
If you look at the distribution of shots of a large sample size set in terms of radius from a MPOI, it looks pretty "Normal", but with one tail truncated. This pushes the mean/average radius away from the peak of the curve, and the SD of the radii then drives the width of the truncated bell.
Mean radius is dramatically better than "group size" (each shot in the group has weight vs. just the 'worst' 2), but mean radius alone is a very weak metric next to mean radius + radial SD. Those two together give you a probability distribution that can effectively be used to determine hit probability (in conjunction with decent ballistic software and assumptions) very precisely.
The truth doesn't give a fuck about how good you convince yourself your rifle shoots. Think I'm full of shit? Shoot a 20-shot or especially 30-shot group some time and let me know if it's better than .65-.8 MOA. (This is pointed at you, Mr. .2-.3 MOA all day long)...
ETA: Some of you... SOME of you will get .45-.6. We won't hear from the rest.
Everything less than 20 shots is (this is not sarcasm) nearly a waste of your time if you're looking to quantify dispersion. You can get a "feel" for things at 10-15 rounds but 20 is where things start getting quantifiable, and 30-35 is where things start getting definitive.
The problem with the OP is that while the average 5-shot group may be 1.28x larger than the average 3 shot group, that doesn't mean that each individual 3 shot group will be 1.28x larger at 5 shots. Not even fucking close. Variability from group-to-group at 3 or 5 shots is significantly larger than the "1.28" multiplier.
If you look at the distribution of shots of a large sample size set in terms of radius from a MPOI, it looks pretty "Normal", but with one tail truncated. This pushes the mean/average radius away from the peak of the curve, and the SD of the radii then drives the width of the truncated bell.
Mean radius is dramatically better than "group size" (each shot in the group has weight vs. just the 'worst' 2), but mean radius alone is a very weak metric next to mean radius + radial SD. Those two together give you a probability distribution that can effectively be used to determine hit probability (in conjunction with decent ballistic software and assumptions) very precisely.
The truth doesn't give a fuck about how good you convince yourself your rifle shoots. Think I'm full of shit? Shoot a 20-shot or especially 30-shot group some time and let me know if it's better than .65-.8 MOA. (This is pointed at you, Mr. .2-.3 MOA all day long)...
ETA: Some of you... SOME of you will get .45-.6. We won't hear from the rest.
I agree with the definition you outline. I'm sure by now I don't have to tell you that.You don't understand dispersion if you're not talking mean radius and standard deviations of radii at a minimum.
Everything less than 20 shots is (this is not sarcasm) nearly a waste of your time if you're looking to quantify dispersion. You can get a "feel" for things at 10-15 rounds but 20 is where things start getting quantifiable, and 30-35 is where things start getting definitive.
The problem with the OP is that while the average 5-shot group may be 1.28x larger than the average 3 shot group, that doesn't mean that each individual 3 shot group will be 1.28x larger at 5 shots. Not even fucking close. Variability from group-to-group at 3 or 5 shots is significantly larger than the "1.28" multiplier.
If you look at the distribution of shots of a large sample size set in terms of radius from a MPOI, it looks pretty "Normal", but with one tail truncated. This pushes the mean/average radius away from the peak of the curve, and the SD of the radii then drives the width of the truncated bell.
Mean radius is dramatically better than "group size" (each shot in the group has weight vs. just the 'worst' 2), but mean radius alone is a very weak metric next to mean radius + radial SD. Those two together give you a probability distribution that can effectively be used to determine hit probability (in conjunction with decent ballistic software and assumptions) very precisely.
The truth doesn't give a fuck about how good you convince yourself your rifle shoots. Think I'm full of shit? Shoot a 20-shot or especially 30-shot group some time and let me know if it's better than .65-.8 MOA. (This is pointed at you, Mr. .2-.3 MOA all day long)...
ETA: Some of you... SOME of you will get .45-.6. We won't hear from the rest.
However, in the interests of educating shooters though, I wonder if it might be a good thing overall, to relax the hard stance on statistical validity in favour of promoting a multiplication factor to encourage shooters to think in terms of a range of group sizes for their rifles, ammunition, ability & etc.
The use of multiplying factors isn't absolute but, I think it's much preferred over that of the stupidity we see at the moment.
Truth be told, very few will bother to undergo a thorough analysis in any event so, it could be argued that in practical terms, valid statistical results will probably never become a normal part of how most shooters perceive accuracy. Far better to go with a system which at least lends itself to a more realistic outcome.
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So most of that was way above my head, but I think it means that I shouldn’t be embarrassed by my 20 shot groups when someone shoots 5 in a group and calls me a blow hard?You don't understand dispersion if you're not talking mean radius and standard deviations of radii at a minimum.
Everything less than 20 shots is (this is not sarcasm) nearly a waste of your time if you're looking to quantify dispersion. You can get a "feel" for things at 10-15 rounds but 20 is where things start getting quantifiable, and 30-35 is where things start getting definitive.
The problem with the OP is that while the average 5-shot group may be 1.28x larger than the average 3 shot group, that doesn't mean that each individual 3 shot group will be 1.28x larger at 5 shots. Not even fucking close. Variability from group-to-group at 3 or 5 shots is significantly larger than the "1.28" multiplier.
If you look at the distribution of shots of a large sample size set in terms of radius from a MPOI, it looks pretty "Normal", but with one tail truncated. This pushes the mean/average radius away from the peak of the curve, and the SD of the radii then drives the width of the truncated bell.
Mean radius is dramatically better than "group size" (each shot in the group has weight vs. just the 'worst' 2), but mean radius alone is a very weak metric next to mean radius + radial SD. Those two together give you a probability distribution that can effectively be used to determine hit probability (in conjunction with decent ballistic software and assumptions) very precisely.
The truth doesn't give a fuck about how good you convince yourself your rifle shoots. Think I'm full of shit? Shoot a 20-shot or especially 30-shot group some time and let me know if it's better than .65-.8 MOA. (This is pointed at you, Mr. .2-.3 MOA all day long)...
ETA: Some of you... SOME of you will get .45-.6. We won't hear from the rest.
The problem with the multipliers is that the distribution is random normal.... But still random. You're rolling dice, was that the best group you're ever going to roll? The worst? Average???? No way to know.
You can do confidence intervals which will tell you the error budget is gigantic and the information gleaned will be so watered down to be nearly meaningless.
I totally get it. You want to waste the least amount of ammunition and time with evaluation, but I still contend that if a true evaluation is not worth your time and supplies, what good is a half assed one? Go whole hog or don't waste the ammo at all.
3-5 shot groups are a placebo.
You can do confidence intervals which will tell you the error budget is gigantic and the information gleaned will be so watered down to be nearly meaningless.
I totally get it. You want to waste the least amount of ammunition and time with evaluation, but I still contend that if a true evaluation is not worth your time and supplies, what good is a half assed one? Go whole hog or don't waste the ammo at all.
3-5 shot groups are a placebo.
Yes Ledzep, I agree with you 100% &, I'm not advocating that there's any other solution to statistical validity.
What I'm proposing is the promotion of a method which allows shooters to see the reality or, at least a version of reality by introducing the concept of "RANGE" into their thinking. The people you & I & others are trying to convince have not grasped the purpose of statistical analysis & what it was designed to achieve or have any clue of how it works or how to interpret any data. It's a gulf that can't be bridged.
I think a multiplication factor will serve to introduce the most important concept & that is the concept of "RANGE" & not some absurd absolute figure that they erroneously believe they have.
There's no denying that a multiplication factor is a blunt force instrument however, it serves a purpose beyond that of pure statistical validity, particularly when analysis of the type that we know to be necessary is simply not a viable alternative to the unwashed masses.
Not what I had in mind.
They shoot their 3 or 5 shot group & simply apply a multiplication factor to simulate a 10 shot group.
This gives them 2 figures. One is the measured figure (what they will always consider to be right tailed) & an adjusted figure which will serve as a the left tailed range.
The idea is to give the concept that any & all results are within a range. If the correct multiplication factors are used based upon reasonable confidence intervals, I believe that would serve very adequately to achieve far more realistic results &, expectations.
I'm in the process of gathering some info on the tables which Grubbs & others have devised to be applied in just such a way.
I don't think it works well. Again, there's a window of variability that swallows up the multiplier.
If I shoot a million 5-shot groups and a million 10-shot groups, the average of the 5x groups would be like .45 MOA (pulling numbers out of my ass, but fairly representative from my experience), and the average of the 10-shot groups would be more like .6-.7". Okay cool so we can get a multiplier off of that information. ~1.5x
Here's the rub... My single 5-shot group is going to vary anywhere from .1-.2 MOA all the way up to .8-.9 MOA (roughly 4x span) and it's a random draw anywhere in between. Obviously most will be closer to the average than the 'tails' of the distribution curve, but low probability events still happen and with just a single 5 shot group you don't know what it is. So I shoot a .3 MOA group, multiply by 1.5x and think I have a .45 MOA 10-shot rifle... Next 5-shot is a .77 MOA, now I'm looking at 1.16 MOA 10 shot prediction. The problem with this is that the test-to-test variability drops off sharply in the first 20-30 samples of an "infinite" test. Basically you get bad noise until you have 20-30 samples, then everything levels out. So your multiplier reflects small sample noise, but if you were to shoot both of the above groups out to 10-shots, they'd be more like .55 MOA and .77 MOA and your multiplier data meant fuckall. If you took them both to 30 shots, they'd both be .8 MOA +/- .05 MOA. There's no cheating it.
Okay so maybe we just keep track of multiple 5-shot groups and average them... So now you have 15-25 rounds invested. Does it make more sense to have it fragmented with (most likely) no correlation of POA between them, or just put them all into a single dot drill or a single target where you get solid data on everything.
If I shoot a million 5-shot groups and a million 10-shot groups, the average of the 5x groups would be like .45 MOA (pulling numbers out of my ass, but fairly representative from my experience), and the average of the 10-shot groups would be more like .6-.7". Okay cool so we can get a multiplier off of that information. ~1.5x
Here's the rub... My single 5-shot group is going to vary anywhere from .1-.2 MOA all the way up to .8-.9 MOA (roughly 4x span) and it's a random draw anywhere in between. Obviously most will be closer to the average than the 'tails' of the distribution curve, but low probability events still happen and with just a single 5 shot group you don't know what it is. So I shoot a .3 MOA group, multiply by 1.5x and think I have a .45 MOA 10-shot rifle... Next 5-shot is a .77 MOA, now I'm looking at 1.16 MOA 10 shot prediction. The problem with this is that the test-to-test variability drops off sharply in the first 20-30 samples of an "infinite" test. Basically you get bad noise until you have 20-30 samples, then everything levels out. So your multiplier reflects small sample noise, but if you were to shoot both of the above groups out to 10-shots, they'd be more like .55 MOA and .77 MOA and your multiplier data meant fuckall. If you took them both to 30 shots, they'd both be .8 MOA +/- .05 MOA. There's no cheating it.
Okay so maybe we just keep track of multiple 5-shot groups and average them... So now you have 15-25 rounds invested. Does it make more sense to have it fragmented with (most likely) no correlation of POA between them, or just put them all into a single dot drill or a single target where you get solid data on everything.
I prefer the Bayesian Approach. "I believe I can shoot 0.25 MOA"
Thus if I never produce evidence (0 shots) I never update my beliefs!
nbviewer.org
Thus if I never produce evidence (0 shots) I never update my beliefs!
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nbviewer.org
Yep, all true. There's no mean sample variation set to determine an applicable multiplier &, I've considered that.
Since all they do now is a hand full of 3 or 5 shot groups anyhow &, don't even consider an SD, I can't see a problem with setting 3 SD brackets; eg/ 1) F class, 2) PRS 3) Hunting which, there is a multiplier all ready to go, applicable to the category they deem themselves to be. We can even give 2 or 3 categories of confidence interval multipliers to choose from so they don't just dismiss the whole thing & revert back to the absurd absolute.
Someone should have done it years ago now that I think about it.
You have to admit, it's a much better alternative to the situation at the moment.
Yes well, we'd all prefer that but it's just not that interesting.I prefer the Bayesian Approach. "I believe I can shoot 0.25 MOA"
Thus if I never produce evidence (0 shots) I never update my beliefs!
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I've found the paper that Grubbs wrote. First printed in 1964 with a second print in 1991.
The paper is Titled
"Statistical_Measures_for_Riflemen_and_Missile_Engineers_-_Grubbs_1964"
It would be good if you would download it & give it read.
The main emphasis is on estimating a population sigma from a very low sample # using Grubbs & others population sigma for specific shot numbers of the population data. The tabulated population data has been averaged so is in a very useful form.
You'll notice the tables specifically arranged for CEP, EHD+EVD, MHD+MVD, RSD, MR, ES, Covering Circle & Diagonal.
Obviously there are really only two systems of interest to the everyday shooter & they are ES & MR.
Grubs shows clear examples of rationalizing small sample sigmas derived from the population sigmas in the tables & includes a 95% confidence multiplier column.
Instead of printing the relevant tables, it would be preferable to tabulate the necessary ratios to be used with the shooters own data & basically set it out for them.
Tabulated data ranges from 1 to 20 consecutive shots however, we would only need to list 3, 5, & 10 shot data with the pre-calculated figure to be used.
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