How important is sd/es

[44 AMP]

Hunters like to say animals don't feel the sd. Actually they do, when the hunter misses the intended poi.

Okay, I'll buy that, BUT, only if you can prove the miss was due to the velocity deviation (SD) and NOT due to other factors, like the shooter, the wind, the distance, the light, the animal moving, and so on....

Its pretty rare that shots are game are chronogaphed, and without that, we don't KNOW the round's actual velocity, so how can you say the miss was due to the difference in bullet speed when you don't know if there WAS any difference in speed?

I think blaming a miss on SD is just a lazy way of avoiding blaming the shooter, who is, ALWAYS the responsible factor. Just my opinion, worth what you paid for it, or possibly less....

 

[tangolima]

Okay, I'll buy that, BUT, only if you can prove the miss was due to the velocity deviation (SD) and NOT due to other factors, like the shooter, the wind, the distance, the light, the animal moving, and so on....



Its pretty rare that shots are game are chronogaphed, and without that, we don't KNOW the round's actual velocity, so how can you say the miss was due to the difference in bullet speed when you don't know if there WAS any difference in speed?



I think blaming a miss on SD is just a lazy way of avoiding blaming the shooter, who is, ALWAYS the responsible factor. Just my opinion, worth what you paid for it, or possibly less....

A smaller sd never hurt accuracy or probability of hitting target, and a large sd never helps. That's what I know.

Can't prove yes for a particular shot, just like you can't prove no.

-TL

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[rclark]

A smaller sd never hurt accuracy or probability of hitting target, and a large sd never helps. That's what I know.

I like to use ES in your statement rather than SD.

 

[74A95]

The article below found no positive correlation between SD or ES and accuracy in a typical handgun at typical handgun distance.

https://americanhandgunner.com/handguns/exclusive-consistent-velocity-accuracy/

 

[mehavey]

Maybe not in handguns.

But with long-range rifles, you want to find a node where both group size & sd are small.

 

[tangolima]

ES and SD are related. ES<4*SD is about right, most of the time.

Vary the powder charge (MV) for best group size, ignoring SD. Then keep the same charge (MV) and try to improve SD, by trickling the powder, weight sorting the brass/bullet etc. That's what I meant. In this way smaller SD can only help, even at handgun distance. At least it won't hurt.

Varying charge to chase best SD only? That most certainly doesn't work. I get it now. I was wondering where the confusion came from.

-TL

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[ballardw]

To reduce SD increase sample size. Unless your load is terrible the division by N-1 in the typical SD estimation calculations will reduce the value the larger the sample.

 

[tangolima]

To reduce SD increase sample size. Unless your load is terrible the division by N-1 in the typical SD estimation calculations will reduce the value the larger the sample.

Hmm... I'm afraid it doesn't work like that.

SD we are calculating on a sample (division by N-1), called sample standard deviation, is just an estimate of the SD of the whole population. Increased sample size makes it a more accurate estimate. Quite often bigger sample size makes the number bigger.

There is nothing wrong to have bigger sample size, if you can afford it.

-TL

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[RC20]

This is a repeat of a previous thread. ES and SD means different things.

I have had poor groups with great ES and SD and the reverse. Statistically the better the ES and SD the better but its not a given.

ES drives SD, best I read was a 50 ES is factory like ammo (not target grade) and anything under 35 is very good. When I hit those areas the SD is down in the mid teens.

To me its just an indicator, I have done some testing for my brother and a 45-70 just to confirm his velocity target and one guy who came from high Montana country and wanted one shot to see how that compared with his velocity at altitude.

While some of the display of the Labrader is clunky, its rock solid data wise and you can tell a good shot pickup from a mistake (if I can see it to 75 yards and its consistent that is good). Easy to use and reliable. Normally I would not let anyone shoot over my old Chrono (it just would not turn on one day and $100 some down the drain, ergo, Labradar as easy to setup and use. I see more abnd more of those showing up.

ps: Get the carry case, the re-cgarable battery and the stand though I made my own stand out of a steel plate just because I can.

 

[Unclenick]

Generally, lower SD and ES mean more consistent performance, but that doesn't always translate to smaller groups. Too many other factors are involved.

Are low SD and ES worth chasing? Statistics estimate parameters. Much more sensible than just blindly working to improve the SD and ES is to figure out what you actually need, gather some data from shooting, and then apply statistics to your measured results to estimate the odds of successfully meeting your needs with it. That will help you decide if it's worth the chase.

The effect of velocity variation alone on rifle precision is tough to predict for real guns. A ballistics program will tell you the effect it will have for shots fired out of a perfect barrel that is perfectly rigid, but none of us has one of those. We tune rifle loads to land on a muzzle deflection phase that narrows our groups. That can closely mimic a rigid barrel's performance, but it is also theoretically possible to achieve a mean barrel time such that your faster loads exit with the muzzle just slightly below where it is when your slower shots exit, and in that way, can produce a range of distances over which the stringing from velocity variation is reduced from what the ballistics software predicts.

Handgun barrels are generally short enough and have small enough moments of inertia to be too rigid to exhibit the bending behavior you see in rifle barrels.

As mentioned in an earlier post, SD, the sample standard deviation, is an estimate of sigma (σ), the population standard deviation. For a load, the population is all the copies of it you have ever fired and ever will fire in your shooting system. The closer the sample size gets to population size, the closer the SD estimate gets to σ.

ES and σ are correlated, but the correlation changes with group size, and ES varies from sample to sample even when σ doesn't, so converting from σ to ES only tells you what the average result would be. If I convert SD to ES, I am really using an estimate of σ to find what the average ES for my sample size is expected to be, assuming that the estimate of σ was dead on, so now I've got a sample-to-sample variation on both ends. So, the conversions have quite a bit of their own variation, and I have to accept there is some amount of error.

SD better represents your shooting system performance as the sample size grows. ES represents it less well as the sample size grows. Why? Each additional sample gives SD another building block for its estimate of σ. But each additional sample also gives improbable extreme shots another chance to occur. In other words, if you fire a three-shot group, the odds of a one-in-a-thousand outlier value appearing are small. But if you fire a 1000-shot group, the odds of that one-in-a-thousand outlier value appearing are much higher. The SD calculation method dilutes the influence of outliers on the result, while measured ES gives it full weight.

How are SE and SD correlated? While outliers can occur to ES that don't have a proportional effect on SD, the average value of SE over many groups has a reliable relationship to SD that is unique for each sample size. The statistic that makes the conversion is called zye of n, symbolized as ξ.

To get SD from ES, divide ES by ξ for your sample size.
To get ES from SD, multiply SD by the value of ξ for your sample size.

Here is a table of values for ξ for different sample sizes:

 

[tangolima]

Interesting Unclenick. I found the paper you quoted.

The equation I have always been used is ES < 3*SD. It is indeed oversimplified by ignoring the imprecision caused by small sample size and the "expanding" effect on ES by large sample size.

I myself is not fond of extreme spread, in MV or group size. I think it can unfairly "uglify" a good population because of a rare outlying sample. I tend more to use SD for MV and R50 or R90 for group size.

Thanks.

-TL

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[Unclenick]

Into the weeds

Yeah, I have the same issue with ES. Predicting it from calculated SD seems a much more reliable way to assess what typical performance will look like. The exception would be if you have a number of groups the same size and you can analyze the multiple ES's. Geoffrey Kolbe has an example of this in which he finds the right sample size and the minimum number of rounds needed to guarantee a degree of precision. He wound up with six groups of 7 shots to guarantee 15% precision with 90% confidence, so 42 shots, and he has higher precision and shot counts listed. But a smaller sample and SD will get you the same information.

There is also a good example in Dennis Marshall's article on shooting statistics in Lyman #46. He takes a real sample of 20 and uses the ES/ξ (3.735 for n=20) method to find the SD as well as the standard calculated approach. The former misses the latter by, IIRC, about 10-15%. However, he then breaks the 20 samples up into four groups of five and uses the ξ (2.326 for n=5) method on the ES of each of the four groups and then averages the four resulting SD estimations. That average was very close to the calculated result. So, a bigger sample of ESs is likely to get you closer to SD in this way. That makes intuitive sense. More information generally improves precision.

One other note about the ES/ξ method. Denton Bramwell, who did statistical manufacturing work, points out that when sample size gets to ES/ξ"]7 and below, ES/ξ actually becomes a more reliable estimate of SD than the standard calculation. The other article seemed to think it was better for as much as n=15. The issue is that while the Bessel correction (using n-1 instead of n to calculate sample standard deviation) unbiases the sample mean variance as an estimate of the population mean variance, when the square root is subsequently taken to get the sample standard deviation, it introduces the bias of the non-linearity of the square root function, which is pronounced in making the calculation for small samples. Thus, he suggests switching to the simpler ES/ξ method for small samples. But there is another way that does not sacrifice the use of all the data points in the calculation. That is to divide the sample SD by the c₄ correction value. It is detailed in this Wikipedia article, which gives values for samples up to 10. When I get time, I will calculate it out for a few more sample sizes, though improving it further is really getting into the precision weeds and is unnecessary for most shooting purposes. Meanwhile, here are the first 9 values rounded to four decimal places. Just divide the SD displayed in the chronograph by these numbers to improve the estimate of σ:

n       C₄(n)
2     0.7979
3     0.8862 
4     0.9213 
5     0.9400 
6     0.9515 
7     0.9594 
8     0.9650
9     0.9693
10    0.9727

This is really drilling down into the weeds. I think most shooters don't really care how precise the SD is because they are just using it to confirm consistent performance among same-size test groups. Some might want to correct SD for two or three-shot groups by dividing by C₄, but otherwise, the above table just won't matter to them.



P.S. Well, forget the calculation. Here is a huge table of C₄ up to n=500.

 

[Unclenick]

I know a lot of the details above are not meaningful or useful to most people, but for the few who are interested, I have created an Excel file that lets you put in your shot count for velocity and your chronograph's calculated SD and returns the unbiased (more accurate) estimate of population standard deviation as well as the expected size of the average extreme spread. It has another row where you can enter the hole count and group size, and it will return the expected radial SD from that. I left the tables of statistics used by the file visible, but you aren't expected to do anything with them. They are just for reference.

Download from here. Note that you have to use the button at the top, three over from the Sign In button that says "download" near the top of the page. If you click on the download arrow in your browser, you just get the PDF version that is displayed on your screen.

 

[tangolima]

Unclenick, thanks for the info. I am half way through Wan's paper. It is very insightful. I have already adjusted the way I have been interpreting 3-shot or 5-shot groups. Even though they have questionable statistical significance, for practical considerations I have to use them as prescreening tools.

The paper was from maths department of Hong Kong Baptist University. I came to America from Hong Kong some 30 years ago.

-TL

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[Unclenick]

If you look at Kolbe's paper or at the old Lyman #46 article by Dennis Marshall, they both work with ES because they are focused on the group size probabilities that target shooters are interested in, and for which expectation limits of each measurement matter. But they both do it by working with collections of groups to refine the expected limits, and not single groups, which prove little in isolation. I may look at adding those to the Excel file when I get a minute.

My wife and I will spend a couple of days in Hong Kong next year as part of an Asian tour (Singapore, Thailand, Vietnam, Hong Kong, Japan). If you have any suggestions for something we should look for there, please PM me.

 

[MarkCO]

I do look at SD and ES in all of my loads. I tend to only look at 5+ rounds for that, and groups as well, usually more. 3 shot groups, nah, that is cheating.

For precision rifle, I want the SD under 5 and the ES is going to be small as well, so I don't really worry about it much.

For 3Gun and Hunting rifles, I'd like the SD to be under 15 and the ES not over 30, and most of mine are actually much better than that. For Magnum Revolver, about the same.

For semi-auto pistols, I want the SD under 25 and the ES under 40. I have worked on a few loads, and got a 9mm load with Zero bullets and WSP down to an ES that is repeatedly under 5. But I that load is what I use to check accuracy with and rarely do much else with it.

 

[rclark]

ES... I think it can unfairly "uglify" a good population because of a rare outlying sample.

I agree. That is why when I load my samples into a spreadsheet, it is really obvious when you have a 'flier'. I just throw it out. That is the reason I shoot 15 too for each load. Gives me a good sample size to eye-ball on the computer (or even in the notebook) and throw out the bad one if necessary and still be over minimum 10 shot sample.

 

[tangolima]

I agree. That is why when I load my samples into a spreadsheet, it is really obvious when you have a 'flier'. I just throw it out. That is the reason I shoot 15 too for each load. Gives me a good sample size to eye-ball on the computer (or even in the notebook) and throw out the bad one if necessary and still be over minimum 10 shot sample.

I do that too. But mostly on fliers that I have called correctly, or if there is good reason to believe it is a bad sample. The flier could be a legitimate part of the population. I can't throw it out just because I don't like it. That actually is one of the reasons I stay away from ES. SD at least has the built-in ability to average out the fliers, and ES doesn't.

-TL

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[tangolima]

If you look at Kolbe's paper or at the old Lyman #46 article by Dennis Marshall, they both work with ES because they are focused on the group size probabilities that target shooters are interested in, and for which expectation limits of each measurement matter. But they both do it by working with collections of groups to refine the expected limits, and not single groups, which prove little in isolation. I may look at adding those to the Excel file when I get a minute.

My wife and I will spend a couple of days in Hong Kong next year as part of an Asian tour (Singapore, Thailand, Vietnam, Hong Kong, Japan). If you have any suggestions for something we should look for there, please PM me.

Unclenick, I will PM you later.

-TL

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[tangolima]

Finished reading the paper, and readjusted my methodology once more after the simulation results. I like it.

It made me remember the take-home exam of the detection theory class I took. We were supposed to give analytical proof on certain derivation. I couldn't do it. Instead I ran similar simulation (I called Monte Carlo analysis) to give numerical proof. The prof wasn't too amused but he couldn't totally discredit my approach. I got a B.

-TL

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