I like to do a few different days at 10 or so per day. I find it is more useful than doing 50 in one sitting.
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ES vs SD
- Thread starter 3rd Monkey
- Start date
I picked up a 25ft cable for my Labradar.
So I can continue gathering data while shooting off barricade.
Expressed in dollars, at the average cost of factory 6.5, at least $40.
I roll my own and I have sufficient components to last two lifetimes. It’s actually kind of sad how much I still have because it means I haven’t been shooting enough.
Kind of like counting fishhooks and thinking where the hell did all these come from?
P
Obviously, but past a certain point the benefit becomes meaningless.
I use a Magnetospeed and it tends to shade my POI up a bit, so I’m unlikely to use it more than I need to.
dependes on you chrono...
last time i shot 5 shots for group, with one load and labradar show the same velocity: 825 m/s.
and labradar tell me that i have 1 m/s ES and 0,3 m/s SD. probably it is calculated from feet per second.
but... labradar have 0,1% of error. so this is 0,825 m/s. so I could have shots at 824 m/s and 826 m/s, and labradar will show me same value of 825m/s !!
other chronographs are even more inaccurate.
so first thing is to get the best chrono you can afford. but at least magnetospeed or labradar.
What other chronographs are available with similar or better accuracy? I'm only familiar with the "cheaper/older" type and the MS and Labradar.
Magnetospeed website says 99.5-99.9 accuracy, Oehler says .25% error, Caldwell says 99.7%.....
2,800 fps with a .25% error is 7 fps. Kind of the "single digit SD" number that guys like to brag about. So, is that SD really what we think it is? Just bringing up the limits to accurately judging our numbers.
I realize I am the minority report, but I never gave much credence to "single digit" SD's.
2,800 fps with a .25% error is 7 fps. Kind of the "single digit SD" number that guys like to brag about. So, is that SD really what we think it is? Just bringing up the limits to accurately judging our numbers.
I realize I am the minority report, but I never gave much credence to "single digit" SD's.
Along the same lines, most don’t have sub 7-8sd. Even if their chrono is dead nuts.
5sd is basically world class ammo and rare to see over the course of 20-30 shots.
The likelihood of getting that SD or predicting an SD with 20-30 shots is remote in a statistical sample. You would need to to fire upwards of 250 to 275 shots to even arrive a 95% confidence interval assuming a margin of error of 5% FPS. Maybe you as a ammo manufacturer, have fired this many shots through a test barrel and have the data to support it, but I doubt many non commercial folks are going to be willing to fire that many shots.
That’s easily solved via ranges.
With 20 shots and assuming 95% confidence you’d be within 3fps of true SD. The reason I don’t get into that is because it will make more heads explode than already do.
Imagine telling people the 20 shot string with an 8sd and the 20 shot string with 11sd are too close to differentiate from one another?
Baby steps.
Honestly I don't really get caught up in the esoteric analysis of ES vs SD. I come up with a load using OCW, fine tune seating depth, and then measure it w/ a Magnetospeed to get a starting point for the kestrel. I obviously look at the ES/SD/Avg speed, and usually more often than not the numbers are low enough that I'm satisfied.
However there was a time many years ago that I was playing around with 180gr Warner Flatlines and CFE 223 with my .308. I was trying to keep it relative vs the 6.5s. I picked out 10 pieces of Lapua brass that were identical in water weight capacity, and bench rest prepped them in every way I could (trim length, annealing with an AMP, flash hole uniforming, etc) I used both OCW and a ladder test to ensure I had the optimal load. When all was said and done I loaded up 10 rounds and fired them over my Magspeed and got this:
ES 2, SD 1.0. I was blown away. Now it might have been a fluke and if I did it again may not have gotten the same results, but it was pretty awesome to witness. My lifetime best and where else can I brag about it except in a ES vs SD thread?
Now here's the bad part of the story. I worked up that load in 70 degree weather. I then proceeded to attend a long range rifle clinic where temps were in the mid to high 90s. The load completely fell apart and I was popping primers left and right. I had to resort to keeping my rounds in a cooler the rest of the class. Important lesson learned about running on the ragged edge and using a more temp stable powder.
However there was a time many years ago that I was playing around with 180gr Warner Flatlines and CFE 223 with my .308. I was trying to keep it relative vs the 6.5s. I picked out 10 pieces of Lapua brass that were identical in water weight capacity, and bench rest prepped them in every way I could (trim length, annealing with an AMP, flash hole uniforming, etc) I used both OCW and a ladder test to ensure I had the optimal load. When all was said and done I loaded up 10 rounds and fired them over my Magspeed and got this:
ES 2, SD 1.0. I was blown away. Now it might have been a fluke and if I did it again may not have gotten the same results, but it was pretty awesome to witness. My lifetime best and where else can I brag about it except in a ES vs SD thread?
Now here's the bad part of the story. I worked up that load in 70 degree weather. I then proceeded to attend a long range rifle clinic where temps were in the mid to high 90s. The load completely fell apart and I was popping primers left and right. I had to resort to keeping my rounds in a cooler the rest of the class. Important lesson learned about running on the ragged edge and using a more temp stable powder.
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We have really gotten into the weeds so here is a little more to look at. When using a chronograph there is a point where the chronograph accuracy begins to effect the reading. If we consider a set of measurement with a LabRadar with an accuracy of 0.1% of reading and measure a mean (average) velocity of 2800 fps and a standard deviation of 9 fps the error due to the LabRadar accuracy is 2.8 fps. With getting deeper into the weeds the LabRadar accuracy begins to become a significant source of error when the error approaches 4x the error. As the SD begins to approach the accuracy of the instrument the Instrument becomes the controlling source of the standard deviation. When we measure in the range above 11.2 fps the instrument accuracy can be ignored but by 2.8 fps it is significant and comparing sampled values between those two points based on measurement alone is in error.
When we take data for a given number of points our goal is to hopefully use that data to predict how other rounds will perform and to do that we are faced with the application of probability. This is what the Precision Rifle Blog discusses. This means that we have to establish confidence intervals. It is often taken that the the confidence interval to be used is 95%. At a 95% confidence interval applied to the mean we would expect that 95% of a large number of rounds tested would fall within a range of both the mean and the standard deviation. The standard deviation confidence however is not a normal distribution since it is bounded by zero, there is no chance at all that the standard deviation can be less than zero. The range of the confidence interval is a strong function of the number of rounds tested or sampled. The two graphs below show what happens to the 95% confidence intervals as the number of points tested increases from 3 to 30 points for a mean sampled velocity of 2800 fps and a measured sample deviation of 9 fps. This is what your test data says about what you can expect from the larger population of rounds. Note that tests of more than twenty rounds does decrease the confidence interval but only slightly and sampling beyond 30 yields even smaller improvement.
When we take data for a given number of points our goal is to hopefully use that data to predict how other rounds will perform and to do that we are faced with the application of probability. This is what the Precision Rifle Blog discusses. This means that we have to establish confidence intervals. It is often taken that the the confidence interval to be used is 95%. At a 95% confidence interval applied to the mean we would expect that 95% of a large number of rounds tested would fall within a range of both the mean and the standard deviation. The standard deviation confidence however is not a normal distribution since it is bounded by zero, there is no chance at all that the standard deviation can be less than zero. The range of the confidence interval is a strong function of the number of rounds tested or sampled. The two graphs below show what happens to the 95% confidence intervals as the number of points tested increases from 3 to 30 points for a mean sampled velocity of 2800 fps and a measured sample deviation of 9 fps. This is what your test data says about what you can expect from the larger population of rounds. Note that tests of more than twenty rounds does decrease the confidence interval but only slightly and sampling beyond 30 yields even smaller improvement.
Your post has great timing in that it illustrates what happens with small SD. If we assume a 0.1% accuracy for the Magnetospeed (I've seen both 0.15% and 0.1%) the accuracy of the instrument is +/-2.9 fps. That accuracy is based on a 95% confidence interval so the SD of the instrument is +/- 2.9/2 or +/-1.45 fps. Your tested SD is less than the instrument so the actual SD that can be assigned is 1.45 fps.Honestly I don't really get caught up in the esoteric analysis of ES vs SD. I come up with a load using OCW, fine tune seating depth, and then measure it w/ a Magnetospeed to get a starting point for the kestrel. I obviously look at the ES/SD/Avg speed, and usually more often than not the numbers are low enough that I'm satisfied.
However there was a time many years ago that I was playing around with 180gr Warner Flatlines and CFE 223 with my .308. I was trying to keep it relative vs the 6.5s. I picked out 10 pieces of Lapua brass that were identical in water weight capacity, and bench rest prepped them in every way I could (trim length, annealing with an AMP, flash hole uniforming, etc) I used both OCW and a ladder test to ensure I had the optimal load. When all was said and done I loaded up 10 rounds and fired them over my Magspeed and got this:
View attachment 7858624
ES 2, SD 1.0. I was blown away. Now it might have been a fluke and if I did it again may not have gotten the same results, but it was pretty awesome to witness. My lifetime best and where else can I brag about it except in a ES vs SD thread?
Now here's the bad part of the story. I worked up that load in 70 degree weather. I then proceeded to attend a long range rifle clinic where temps were in the mid to high 90s. The load completely fell apart and I was popping primers left and right. I had to resort to keeping my rounds in a cooler the rest of the class. Important lesson learned about running on the ragged edge and using a more temp stable powder.
You have a 10 shot mean of 2888 fps with a standard deviation of 1.45 fps. In applying the confidence interval for ten shots says that you would expect 95% of the future rounds to fall between a mean of 2887 and 2889 fps! your SD range would be 1 to 2.6 fps.
This is some great reloading. Now if you can keep those types of numbers for every batch that would be great. Unfortunately it probably can't be done consistently but you know you have great technique and a very consistent load. Sorry to hear it didn't hold up.
Thank you but I know for a fact it can't be done consistently (at least for me). I've accepted the fact that it was basically a one-time fluke where everything likely just happened to line up in my favor. First off I haven't come anywhere close to this in all the years since. I have gotten single digit ES & SD, but not like this. Also those 10 cases I chose out of 100 and measured the water weight down to two decimal points and got as close as I possibly could for each case. At that level, its very difficult to keep a consistent technique of filling the case to the same exact level each time. I went through all 100 cases - I just don't have that kind of time or inclination anymore..
This is another "it depends" answer since you used the word "confidence" but didn't specify it.
In many contexts, like legal contracts or performance specifications for high reliability agreements, there are specified statistical values for the confidence and probability of error that drive what our sample schedule must be in a quality control plan to meet the contract. Heavy weapon ammo habits are different than small arms ammo.
Without going down the rabbit hole of actuarial math and statistics.... for a well behaved system you should expect to need 30 samples to see the SD value close in on the 95% value. A well behaved system allows you to make a pretty good estimate of the ES roughly around 15 samples.
You are drilling down on sample standard deviation versus the actual population standard distribution. I'll try to find a tutorial example link to keep from typing that all out. Here is a 17 minute video that goes through understanding an average and SD with less than 30 samples and the Student's T Distribution.
When it takes more than 30 samples, my own opinion is that the process isn't under good control. YMMV
Of course, it's really hard to get really low SD's (like single digits) and the smaller the number that harder it is to do. When I started to precision reload my goal was to get my ES's into the single digits, since so may good precision reloaders were doing it. So, when I started, I was getting mid-teens to mid-20's for SD's and eventually I got to where, on a regular basis, my SD's stay in the single digits (like between 4 and 9 with 5 or 10 shot's chronoed). Now, I know that 5 or 10 shots really doesn't tell me how a particular batch I've loaded will actually produce in terms of SD's for the batch. But when I look at my history I've recorded, I can see they're regularly in the single digits. And because that's over the years of thousands of reloads where those cartridges are a random sample of what I've reloaded, the single digits tell me my reloading is pretty consistent and where I want to be. And that's what I depend on to tell me if my reloading is good enough (for me). As long as I keep seeing single digit SD's with a sample of 5 or 10 shots from my reloads, I'm a happy reloader.
The real question should be something like this:
You shoot a 5 shot string of 30.0gr and a 5 shot string of 30.3gr.
You get:
30.0: 5sd
30.3: 8sd
When we look at a 95% confidence interval, we can be 95% certain the true SD lies within the following ranges:
30.0: 3.0 - 14.4fps
30.3: 4.8 - 23.0fps
Knowing that tidbit of info, how would you know that 30.0 is “better” than 30.3?
Because almost every shooter out there would immediately pick 30.0 as the “better” or more “stable” charge weight.
You shoot a 5 shot string of 30.0gr and a 5 shot string of 30.3gr.
You get:
30.0: 5sd
30.3: 8sd
When we look at a 95% confidence interval, we can be 95% certain the true SD lies within the following ranges:
30.0: 3.0 - 14.4fps
30.3: 4.8 - 23.0fps
Knowing that tidbit of info, how would you know that 30.0 is “better” than 30.3?
Because almost every shooter out there would immediately pick 30.0 as the “better” or more “stable” charge weight.
This tends to illustrate the need to sample more than one session and batch, and in different weather.
As time goes on, even the condition of the barrel will change and cause some changes to the "tune" and the hope is that the changes to the barrel are slow and graceful so that we don't chase our tails.
Agreed. But most people never go back and shoot the “bad” powder charges.
So they have no idea it was likely too close to consider one better than the other.
Add in potential changes in your reloading process from batch to batch. You may get a so called amazing batch one day, the next few being terrible. But you don’t run those over the chrono because you already have the load.
Agree, that falls under the concept of doing more than one batch.
In my world, we also tried to produce in more than one plant, and had to test in many different guns. On some days, you had to question your faith and it kept you very humble.
We always hear about loads “falling apart at distance.”
Leaving BC variance out of the conversation and just focusing on chrono data…..
That’s why you see guys who chrono’d a 5sd and never chrono again getting a 1.5 moa group at distance and then saying it fell apart. Or say you must validate at distance.
So, do 10 a day and just add each day's to the growing list of data points. Do it in excel and use the SD function and its easy to add data to the data set as you collect more.
Actually, shoot 5 and look at ES and SD. Then up the total to 10-15 and again look at ES/SD. I believe you will find as I did that these figures will most likely increase in magnitude until about 30-50 shots when you will see them stabilize.
Well, at least I found it interesting after watching the statisticians vs OCW fans battle it out. Now, I don't feel the need to enter that debate as I've proved how it works to my satisfaction with various factory and hand loads.
Cheers
That is where ANOVA come into play and the comparison of two SDs to determine if they are statistically significant using F-Test or ChiSquared tests.
Also to RegionRats comment, in many industries there are test codes that specify the type of statistical methods to be used when testing and analyze results. Testing is often required to prove the performance of a piece of equipment or system to meet a performance specification.
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Yeah pretty much that. I am not super structured with data. Kind of focusing on the leaves in the forest.
I like just enough detail to create a working package. Pick away at the low hanging fruit as it comes. No sense wasting all my time loading a .25moa load when I may be a 1.75 Moa shooter. To that 1.75 moa shooter a lucky 1.25” group is now “the load” and if they focus more time and energy on reloading they may hit a that coveted 1” group.
The real answer is likely elsewhere in the forest.
The good news is, you’re 95% likely between:
7.0 - 12.5sd
Which means for each, 95% of the time the es will be:
28 at best (if the sd is 7)
50 at worst (if the sd is 12.5)
And bippity boppity bacon you magically have a very good idea of what your ammo is really doing. Somewhere in that range.
...But when I look at my history I've recorded, I can see they're regularly in the single digits. And because that's over the years of thousands of reloads where those cartridges are a random sample of what I've reloaded, the single digits tell me my reloading is pretty consistent and where I want to be. And that's what I depend on to tell me if my reloading is good enough (for me). As long as I keep seeing single digit SD's with a sample of 5 or 10 shots from my reloads, I'm a happy reloader.
same here.
'single digit' SD (in europe we have meter/second so single digit is 3× fps
is a proof, that with my reloading technique and components, I'm able to reload to 'perfection'. with beam scale RCBS M500, in 223REM cartridge, this powder - primer - bullet - brass combination (and of course my present barrel) this is achievable. groups were horrible (0.6MOA), but at least I have a proof that consistency is not a problem for my reloading technique.
@Feniks Technologies ok smarty pants.
Make a spreadsheet, xls or whatever, where the user inputs some simple data. SD/ES, number of shots, and group size. It then outputs (bacon magic) numbers for a statistical confidence. As thry enter more shot data, the confidence reflects that.
Then make it a phone app, and sell it for $2.99 WITHOUT FUKING ADS or whatever.
Bonus points if you make the API back end and sell it to ballistic-X as an addon to their app, and you get a % of sales ontop. (have it as a pro-version without ads, which is payware, rather than free like they have.. aka "strelok vs strelok pro").
Ill even pre-order now, with deposit.
Make a spreadsheet, xls or whatever, where the user inputs some simple data. SD/ES, number of shots, and group size. It then outputs (bacon magic) numbers for a statistical confidence. As thry enter more shot data, the confidence reflects that.
Then make it a phone app, and sell it for $2.99 WITHOUT FUKING ADS or whatever.
Bonus points if you make the API back end and sell it to ballistic-X as an addon to their app, and you get a % of sales ontop. (have it as a pro-version without ads, which is payware, rather than free like they have.. aka "strelok vs strelok pro").
Ill even pre-order now, with deposit.
I understand that you are starting with an SD and mean velocity and applying the normal bell curve distribution to it to get your (+/-) SD and velocity range. How would chronograph margin of error factor into your calculation? You are assuming that the SD and mean velocity that you are starting with is accurate. Wouldn't the margin of error that you are willing to accept in the population affect your sample size? Wouldn't the error above in the measuring devices be included in the sample calculation?
it already exists in numerous statistical packages (including excel) with a single line of code. Bruh do you even program?
This is like 100 year old math. Get with the times!
Confidence Interval for a Standard Deviation Calculator - Statology
This calculator finds a confidence interval for a population standard deviation, based on input provided by the user.
www.statology.org
TO be less troll and more helpful--the proper way to frame the question is
"If I want to spread of my speed to be X Fps or less, within y Standard Dev (1 in a million is 4.5 SD, Physics uses 6 sigma for detection), at what point of measurement am I confident that I have measured the SD correctly"
Because even if you get a good measure of SD, you total spread will be roughlly +/- 3 SD (99.9 % of your shots).
Lies
Damned Lies
Statistics.
TLDR: I laugh my ass off at SDs measured with 5 shots (in my practice we are ok at about 40 for a known process). But you can make a rough guess that 6xSD = ES if your data is PERFECT.
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So it is free to play with that web tool.
TL;DR you need roughly 30 samples. It is borderline silly to crank SD numbers or extrapolate six sigma from five shot samples.
For the same reason that a sample average can continue to update as more samples are poured into it, the probability of estimating the actual average, actual ES, and actual SD gets better and better with more samples. (Remember that the acceptable risk is set at CI of 95%, but you can raise that or lower it too).
But, before we loose the attention of the audience who is still asking a simple question... How many samples does it take to study an SD good enough to estimate an ES... to answer your question in the light of a 95% Confidence Interval, with a well behaved (normally distributed) muzzle velocity performance....
If the chrono, ammo, and gun are well behaved, we can start to see the estimate converge somewhere between N=15 to 30.
When it doesn't, it is because something is sloppy.
To watch this with the web site tool, just plug in a single digit SD of say 5, and using the 95% confidence level, watch the error band in the value change as you go from N=5, to 7, to 10, 12, 15, 20, 25, and finally N=30.
You will notice how the low sample numbers leave a lot of room for error, and how after 15 or more things start to look much better, and as you get to 30 the improvement slows considerably. Nobody is saying 30 is perfect, just that we get close enough by then when the data looks smooth.
Even at 30 samples, and SD of 5 is supposed to be good enough to estimate an ES of 30, isn't it?!? Well, in reality we are saying the answer is really 95% C.I. = [3.9820, 6.7216] So if we multiply those high low values by 6 the ES can range from 23.9 to 40.3 for 95%CI.
So, even after you took your 30 samples and got an SD of 5, your ES still runs a risk that it is really 40.3 instead of 30.....
The take away then, is not just that you need nearly 30 samples to have decent stats for your DOPE...
It is that N (the number of samples) and CI (the confidence interval) are still really two different things, and you need to understand them both. They tell you what you think you know about your dope when you set that risk level and budget your number of samples.
If you are taking samples, and see that your sample average, sample SD, and sample ES is not stable, then you keep taking more samples.
You also learn to accept load development risks and not stop and take that many samples till your method and process says you think you are in tune and have a good reason to want to know the average, SD and ES.
Taking large samples of half baked garbage makes as much sense as generating SD or ES values with three shots. YMMV
At some point you have to draw the line. If the chrono is within spec, it’s 1% or less.
You can always run 2 or 3 chronos at the same time and if they disagree enough to matter, cross that bridge.
The main idea behind all this stuff is for the end user to know what they are actually looking at.
IE: a 3 or 5 shot string with different barge weights, with something like a 5 and 8sd respectively…….
You absolutely don’t have data to know the 5sd is better.
When we do an analysis of calibration errors and their effects on calculations, we call that an uncertainty analysis.
We then start taking measurements, apply the stats, and then if we need to be formal, we then run things like WCS (Worst Case Sum), RMS (Root Mean Squared), etc. on those tolerances, and combine the effects.
In ballistics, we end up running a CEP (Circular Error Probability) analysis for where projectiles will land, and that folds it all in.
You can eventually also start to separate process variation and measurement variation. If you know your measurement is 1% you can can start to add that into the calculation. Thus once you establish the measurement SD, the total Variance (SD*SD) minus the measurement varirance (SD*SD) gives you your "process" variance (SD*SD).
Assuming your measurement variance is of course normal/guassian.
Of course when I was doing this I had multiple measurement tools and multiple process tools, which actually makes things easier as I have a TON of data. But we were also able to see tool to tool variance among other subdivisions. And we also had standards to measure and calibrate our measurement tools. That is a LOT harder in the shooting world.
Assuming your measurement variance is of course normal/guassian.
Of course when I was doing this I had multiple measurement tools and multiple process tools, which actually makes things easier as I have a TON of data. But we were also able to see tool to tool variance among other subdivisions. And we also had standards to measure and calibrate our measurement tools. That is a LOT harder in the shooting world.
