Using Circular Error Probable to charcterize rifle performance

C

cfmcmillan

Guest
My son and I have recently put together a small paper on ways for serious shooters to use Circular Error Probable (CEP) to measure the performance of their shooting systems. The paper, as well as supporting material, is available at www.statshooting.com. Based on our analysis, I believe these statistical measures have several advantages over the c-t-c measures we traditionally use. While the paper is, of necessity, somewhat mathematical, it should be fairly clear even if it's been a while since your last math course.
 
Why?

Shoot 5-shot groups, include ALL shots, measure c-to-c.

Do this 5 times.

Divide by 5 and you KNOW what your rifle system was capable of that day. You can say "I've got a rifle which shoots X.XX" on that day.

There is no "probability" involved.

Only probity.

al
 
Interesting idea. CTC in a way ignores all shots but two in a group. For instance, if you have 9 in one hole and one flyer, the flyer determines CTC with no weight given to 8 of the other 9 shots. I have often thought there should be a better way to characterize all shots. But at first glance, CEP, while an improvement, still seems somewhat arbitrary. Why not use mean and standard deviation of radius from the center of mass of the group? Compared to CEP, this would weight all shots (as CEP does with its median radius), but would also characterize the scatter of the shots.

Cheers,
Keith
 
Keith -

In fact, CEP can be calculated several ways, one based on the mean radius from the center for the group, another based on the standard deviations in the x and y directions. There is fundamentally no new information. Rather, it is a standard comparison. It is probably the case that P(90) or P(95) are more useful measures for shooters (most of us are more interested in the radius in which 90 or 95% or our shots will fall than in which 50% will fall) However, these other statistical measures are easily derived from the CEP as shown in the paper.
 
The examples and theory given in the paper by cfmcmillian show that there are much more accurate descriptions of "group size" than C-T-C (also called extreme-spread). Although these results aren't new, they may as well be given that it seems only a very small number of people involved in precision shooting are aware of them.

cfmcmillan -- nice work


alinwa said:
Why?

... There is no "probability" involved. ...
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and,

HovisKM said:
A solution to a problem that doesn't exist....
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Just because you haven't calculated the probability doesn't mean there is none involved; and just because you aren't aware of a problem doesn't mean that it doesn't exist.

The average shooter may not shoot at a level of performance where the effects measured by a more sophisticated target analysis matter, but many of the people reading this forum do. (I'll assume all of the posters so far are better shooters than I am.) But, even if they aren't aware of how to measure those small effects that doesn't mean that they aren't there or that it wouldn't be useful to know how to measure them. There are innumerable arguments on these forums over very small effects, but trying to measure them with C-T-C is like trying to work up two loads using bathroom scales and then arguing that one is better than the other.

A grouping is described by a mathematical probability distribution. By measuring it accurately enough to know the details of that distribution, you can get a lot of information about the performance of the shooter and equipment. People may decide not to use that information, but that doesn't mean it's not there. However, given the amount of effort and money spent trying to make groups just that much smaller I would think any information which could help do that would be useful.

When buying shoes people could just randomly pick a pair that looks to be about the right size, but I would rather take the time to know what size I wear and then find a pair of that size. It takes more effort in the short run, but saves money and time in the long run.

mks said:
... But at first glance, CEP, while an improvement, still seems somewhat arbitrary. Why not use mean and standard deviation of radius from the center of mass of the group? Compared to CEP, this would weight all shots (as CEP does with its median radius), but would also characterize the scatter of the shots.
Click to expand...

The paper doesn't explicitly go into it, but what you are suggesting is contained in the "CEP". You are also right that it appears arbitrary, but it can be shown to be what I would call "statistically efficient". That is, it takes fewer shots to get a certain level of accuracy in the results than other statistics. The C-T-C is a very inefficient statistic in this sense. So one way of judging a statistic without being arbitrary would be to consider it's "efficiency".

Also, what you are saying about characterizing the scatter is there, it can be extracted and presented in a different way to make it a little more clear in the sense of the "bottom line". This is what software can do for you.
 
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Kudos to both “cfmcmillan” and “chisqr” for attempting to enlighten us with “more” accurate methods of quantifying accuracy and giving us the tools to make accurate comparisons.

I’ve always been amazed that gunsmiths work with tolerances to .0001” and they along with shooters fret over the smallest of tuning experiments but then won’t spend the time or study to accurately judge if their work truly represents a significant enhancement in accuracy.

I’ve been working with the “GAP” software http://www.bmotsoft.com/index.html this past year along with spreadsheets I’ve developed and can tell you that with an open mind and a little work, you are all capable of discovering the benefits too.

All truly serious shooters need to at least investigate the possibility of learning something new even if it involves a little extra time. The payback could be enormous.
 
Well, like I said " a solution to a problem that doesn't exist". I do shoot a lot...not as much as some but I manage to burn up several of Mr. Kriegers fine barrels every year and shoot thousands of rounds through BR guns. BUT....I guess the next time the scorer measures my group with that flyer...I'll mention this thread and see how far it gets me....

You can tell more by a group by looking at it than a machine or figures will ever tell you....if you can't....your not taking home wood....


Hovis
 
If I am being shot at

cfmcmillan said:
My son and I have recently put together a small paper on ways for serious shooters to use Circular Error Probable (CEP) to measure the performance of their shooting systems. The paper, as well as supporting material, is available at www.statshooting.com. Based on our analysis, I believe these statistical measures have several advantages over the c-t-c measures we traditionally use. While the paper is, of necessity, somewhat mathematical, it should be fairly clear even if it's been a while since your last math course.
Click to expand...

I sure want it to be by a cep shooter, not a CTC shooter.

IMHO
 
I think that part of the problem is that some non-shooters think that when measuring center to center one tries to set one's tape on the center of the hole.......

nothing could be further from the truth.

The difference is between shooters/builders and theorists.

You don't "quantify" groups for Extreme Accuracy. You MEASURE them, ALL of them. And you measure them EXACTLY.... and if there's a question of a record them more people measure them EXACTLY and you average the few thousandths left over......

And that's what you've got.

Incidentally, the resultant measurement may well be expressed accurately using "smallest enclosing circle" terminology but WHY? In many case a rifle will have a problem which exhibits itself vertically, or horizontally, in which case "sec" is no help A'tall.....

Now if you're trying to establish whether a "Weapon System" is a 1 moa rig or a 1.25moa rig then this whole CEP thing has merit. But WHY??? If the rifle only shoots 1moa, sell it. If it shoots that big then all you need to know is that if you want to hit a 3" target then you're absolutely limited to 300yds. Don't even bother taking longer shots, they're LUCK.

al
 
alinwa said:
If the rifle only shoots 1moa, sell it. If it shoots that big then all you need to know is that if you want to hit a 3" target then you're absolutely limited to 300yds. Don't even bother taking longer shots, they're LUCK.
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Numbers have never been my strong point, but from what I recall of probabilities & standard deviations, a MOA gun should have about an 75% chance of hitting that target at 500 yrds - but I agree with what you're saying.
 
Geez

This Forum represents Competitive Benchrest, where every shot counts, and one shot in 25, (or 50 in Unlimited), can ruin an agg.

Trying to re-think the equation to convince yourself that your equipment is better than it is will not impress the Official Scorer one bit.

This type of information might seem usefull in some shooting endevours, but as far as what we do, it is of little value.........jackie
 
I think the difference between c-t-c and CEP comes down to repeatability.

If you take a rifle out each day of the week and shoot 5x5 shot groups and record the average c-t-c and the CEP, the CEP will likely be more consistent than the c-t-c group size.

OK, so why is that relevant?

It's relevant because the CEP is quantifying the precision of your rifle with a higher degree of resolution.

OK, so why is that relevant?

It's relevant because precision measurement is valuable! If you really want to know how much effect variable 'x' has on your precision, you have some choices for how to investigate that variable. You can go out and shoot your experiment, and measure the groups c-t-c, or use CEP to quantify the difference. The benefit of the higher resolution CEP method is that it might only take two 5 shot groups of each sample to know, with certainty, which is best. However, if you're using c-t-c, you either have to shoot many more groups to be certain, or make the decision based on fewer shots and be less certain. The results of a CEP analysis are more repeatable than c-t-c measurements.

Of course the two measures are related. So the folks at the top of the BR game shooting the winning c-t-c aggs would still be winning if precision were measured with CEP. The only difference is that the winners would probably be more consistent, not dropping 20 places in the final standings for the weekend because of 1 shot that was out of a group on day 1 of a weekend long shoot. CEP is simply a 'truer' measure of precision. As Asa mentioned, it's how the military quantifies the precision of our munitions (Asa, you left out ballistic missiles:)) Why isn't it good enough for BR shooters?

Setting that aside for a moment, and accepting that the BR tradition of c-t-c measurement will continue to decide the winners, we can still use it to make better decisions about our equipment as individuals. When c-t-c aggs are used to determine what small effect a variable has, there's no way to gauge the 'confidence' in the observation. For example, using CEP, it's possible to test two different 'loads', and find that there is no significant difference between them. That means if you shot them against each other 100 times, there's no way to know which one would be better. However, if you just look at a c-t-c agg, one will be better than the other, and the 'conclusion' is that the smaller one is genuinely better, and will always be better. Conclusions made in this way often turn out to be false. So you go to your BR match, confident that you're shooting the combination of components that yielded the smallest c-t-c target recently, and proceed to screw the pooch because the result wasn't repeatable.

I applaud the McMillans for sharing their excellent work. Typically, the useful (useful to target shooters) information about statistical methods can only be found locked in obscure and dusty text books in the back of a dark library somewhere. These guys have brought it into the light and made it relevant and comprehensible to us. That's not easy.

-Bryan
 
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jackie schmidt said:
Trying to re-think the equation to convince yourself that your equipment is better than it is will not impress the Official Scorer one bit.
Click to expand...

Scorer's are seldom impressed by chronograph readings either, but we use them to learn things anyway.
 
bsl135 said:
Typically, the useful (useful to target shooters) information about statistical methods can only be found locked in obscure and dusty text books in the back of a dark library somewhere. These guys have brought it into the light and made it relevant and comprehensible to us. That's not easy.

-Bryan
Click to expand...

C'mon Bryan,

Where do you guys get this stuff?

Trying to turn simple group measurement into some arcane art is just silly!

Statistical analysis is not "locked away in musty, obscure textbooks somewhere" .... my kids are learning it in grade school.

al
 
So far, all I have read are some claims of what could be done. At this point someone needs to publish a report, complete with targets, about what HAS been done, and to be of interest to me, it should not be about rockets, artillery, air rifles or rimfire. Claims about the usefulness of this approach are just that until concrete examples are published. Where's the meat? I am particularly interested in the isolation of the effect of one variable when there are several involved in the process. Let's skip the you could part and skip to the I have, with pictures of targets. Also, the idea that we should consider a alternate method of scoring match targets falls into the you've got to be kidding category.
 
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