I see folks posting low SD's with 3 & 5 shot groups. How many rounds should be fired to get a accurate SD on your load?
-
Having trouble using the site?
Contact support
SD's
- Thread starter jinxx4ever
- Start date
10 is good 15 is better for a minimum number.
Smallest group I use is 10 but I suspect you’re going to get a dozen different numbers
I’m wondering if even 20 is good enough. My recent range trip had groups of 10 and 20 shots, just small variable changes. Results had several SD in the 7s and a few 14s and a 10. Same charge weight. Combined all 90 shots had a SD of just over 10.
Had a group of 10 with SD of 6.6 one day and the exact same load from the same loading session next week had SD of 19 with a 10 shot group. Combined SD of 30 rounds this reload session was 14. Similar results with a different powder, great or bad 10 shot SD with combined 30 shot SD of 12.
Had a group of 10 with SD of 6.6 one day and the exact same load from the same loading session next week had SD of 19 with a 10 shot group. Combined SD of 30 rounds this reload session was 14. Similar results with a different powder, great or bad 10 shot SD with combined 30 shot SD of 12.
Anything less than 20 is totally meaningless. The generalizability of your data improves as the sample size increases so it’s up to you where you draw the line. For me, anything beyond 25 and I get bored so I usually quit running the chronograph.
Then you need a class in statistics. Standard deviation will tell you the expected spread, 98+ % of rounds fired will be within +/- 3 SD's of the mean. ES is more or less useless. Fire 5 rounds and take the ES, how many data points is that? 2. Fire 100 rounds and take the ES, how many data points? Still 2. Now, with that said, if you fire a string and the extreme spread is higher than 6 times the SD you are looking for – STOP. That load isn’t going to get you there. ES can be used to reject a load, but it will not reliably help you choose the right one.
20 rounds will provide a mean MV and an SD that has a 90% confidence interval. If your recorded SD is 6 fps, your true SD is probably between 3 and 12 fps.
Unless you are shooting ELR type ranges, say 1200 yards and further, SD, unless it's huge, like 25fps or more, is probably meaningless as well.
Last edited:
SD's for 3 & 5 shot groups is really meaningless, except. . . . if I see a high SD in that number of shots, like a 15 or worse, along with high an ES greater than 30, I feel pretty sure it's not a good load. So, while a low SD with that number of shots won't tell you whether it's a good load, it can tell you if it's not a good load. If I think I've found a good load with that few shots, I need to confirm with what I'm getting on target with 15 or 20 shots. The best SD don't mean you're going to get the best result on target. I look at SD's as an indicator as to how well/consistent I'm putting together my cartridges, not how well they'll perform on targets.
What starts to happen with a "good" system versus a "bad" system can end up costing you more samples to get your answer.
For example, with a tight gun and good ammo, we would be able to get a real good idea of what to expect sooner, say maybe 7 shots.
With a bad gun and bad ammo, you will probably not get a fair estimate of the Avg, ES, SD till you burn roughly 30 shots.
The tighter the ammo/gun, the fewer the shots it takes to get stable stats, the worse your ammo/gun are, the more shots it takes to see the Avg, ES, and SD stop changing.
Here is a screen shot for a 95% confidence in the data. On the vertical axis you see how big the possible error in your SD can be for the number of samples along the X axis. You can see why we tell you that the sample size charts run about 30 samples to have an SD value that stabilizes.
Can you get lucky and have a number in 5 shots that holds up? Sometimes, but it generally only happens when the SD is very small to begin with. The risk is that if you only take 5 shots and your ammo is crap, then when you use your average it won't hold and when you estimate your ES you are wrong. Odds are you get a nasty surprise when you shoot out at distance.
Merry Christmas and Happy New Year!
For example, with a tight gun and good ammo, we would be able to get a real good idea of what to expect sooner, say maybe 7 shots.
With a bad gun and bad ammo, you will probably not get a fair estimate of the Avg, ES, SD till you burn roughly 30 shots.
The tighter the ammo/gun, the fewer the shots it takes to get stable stats, the worse your ammo/gun are, the more shots it takes to see the Avg, ES, and SD stop changing.
Here is a screen shot for a 95% confidence in the data. On the vertical axis you see how big the possible error in your SD can be for the number of samples along the X axis. You can see why we tell you that the sample size charts run about 30 samples to have an SD value that stabilizes.
Can you get lucky and have a number in 5 shots that holds up? Sometimes, but it generally only happens when the SD is very small to begin with. The risk is that if you only take 5 shots and your ammo is crap, then when you use your average it won't hold and when you estimate your ES you are wrong. Odds are you get a nasty surprise when you shoot out at distance.
Merry Christmas and Happy New Year!
No worries. Your ammo is probably fine and your ES would be estimated at roughly 16 to 24.
4.3 with ES of 21. If I remember correctly it was only 2 or 3 shots that made that ES. I agree SD is a much better number.
An SD of 5 fps at 2800 fps is +/- .18%. BC variation (ES) with unsorted berger hybrids is probably going to be 0.7%-1.2% based on the data I’ve seen. Group size and the bullet bc itself is likely contributing to the vertical spread at 1000 as much or more than the velocity once you are at that low SD.
Because of having multiple factors, I generally will just run it to 1000 right away and see if it will hold tight vertical. I’ve also settled on a load with higher SD, because it shot tighter groups up close (400-500 yards) but had the same vertical at 1000 as the tighter SD load. We shoot most targets at 400-700 yards where SD is less of a factor than group size, so it made sense to pick the load with the best on-target result across the board.
Because of having multiple factors, I generally will just run it to 1000 right away and see if it will hold tight vertical. I’ve also settled on a load with higher SD, because it shot tighter groups up close (400-500 yards) but had the same vertical at 1000 as the tighter SD load. We shoot most targets at 400-700 yards where SD is less of a factor than group size, so it made sense to pick the load with the best on-target result across the board.
That’s not how sd works at range. The lower sd will have less vertical stringing in the same environment. I agree under 6-7 sd there is very little difference at range.
But an sd of 6 vs an sd of 15 at 1000 yards will have different vertical stringing and the lower sd will shoot better vertically regardless of “group size” at some short range.
Since you said you were shooting at 400-700 yards I assume you’re shooting steel and not shotmarkers so I’d really question what 1k testing you did if not over shotmarker.
What data do you have on sorting hybrids for bc deviation???!
Let also not discount that people are putting groups in paper that are smaller than the stats would say is allowable.
You can ignore your velocity stats until you stop hitting what you are aiming at.
You can ignore your velocity stats until you stop hitting what you are aiming at.
Oof. 15 fps SD is horrible. I guess I should qualify my statement. I’m comparing something like 4 fps vs 6 fps not 5 vs 15. And group size I’m talking about out .3 vs .5 moa, both still relatively tight, and the difference on target (a clean piece of steel), is an inch or two at 1000 yards. The reality is both loads are probably good enough. 15 SD indicates something is wrong with your process or components.
I have zero data for sorting hybrids, but I’ve run a few lots across the AB doppler and the BC extreme spread was enough to change the vertical impact on target by a couple of inches. I can imagine sorting by weight, length, and diameter could tighten that up.
It's going to depend on the acceptable results for the individual person.
For example in my area, taking a shot over 200 yards while deer hunting would be considered very rare.
On the other hand in some competition circles you absolutely should measure frequently if not always. Especially with tech like that new radar chronograph from Garmin there really isn't a good reason not to collect data on everything (if applicable).
For me, I shoot semi auto all the time and I don't participate in competitions yet. For my purposes I spent a few days gathering data and haven't visited it again (yet) since.
There is no way to know the skill level of the shooter or reloading capabilities unless they specifically tell us that or what the end goal in mind is.
If I am doing anything that requires SD info for me the basement number is 10 shots. In my situation anything less than 10 isn't worth bothering with. That said the last time I jumped into that stuff I got something like 50 to 75 shots on record each time, mainly because I was too lazy to reset the machine all the time and because to me more data is better data.
Assuming we have covered the OP's first question about how the risk of the SD goes down with sample sizes, we are leaving out very important concepts about having something in ammo or the gun that is starting to go out of control but is subtle. If we are starting a tribal ego battle about SD being better than ES, then we are doing folks no favors.
If you consider the concept of barrel fouling or a firing pin spring that is just starting to wear out, your normal (Gaussian) distribution will not hold. You will want to be on guard for signs that you really have something in your load or gun that is going out of control.
The advice that SD is important because it utilizes all of the shots is good, but it is also wrong if that is also telling you to ignore the ES at the same time. When a second distribution due to a failure starts to show up, or when your ammo is bad but you just got lucky with a low SD, then your normal risks will not hold up.
We watch them both. When an SD and ES don't make sense with each other, the data is telling you something is not "normally distributed" or your test wasn't done filling out, or both. That is the whole point of having those numbers instead of just the average.
The OPs original question wasn't wide open. He just asked about sample size and the accuracy of an SD.
If your ES doesn't make sense compared to your SD, then your SD is cold comfort regardless of sample size. When we teach ballistic science, we do not tell students to ignore one over the other. We teach them how to use both together.
As you open your checkbook to add sample sizes in your load testing, remember to watch both the ES and the SD, not just one or the other. You could say you don't need an SD for low shot count and your eyeballs tell you the data is good or bad without the math, but not when the ES is big.
If for example you bring me data that shows you got an SD of 5 and it was based on 15 speed readings, but you show me an ES that is skewed compared to the average, or one that is like ES 50 when your (SD 5 x 6) ES should be 30 or less, then we know something will go wrong because we looked at the ES and not just the SD.
An ES should be roughly centered over the average, and ES should be roughly 4x - 6x the SD or something smells wrong. Carry on and Merry Christmas.
If you consider the concept of barrel fouling or a firing pin spring that is just starting to wear out, your normal (Gaussian) distribution will not hold. You will want to be on guard for signs that you really have something in your load or gun that is going out of control.
The advice that SD is important because it utilizes all of the shots is good, but it is also wrong if that is also telling you to ignore the ES at the same time. When a second distribution due to a failure starts to show up, or when your ammo is bad but you just got lucky with a low SD, then your normal risks will not hold up.
We watch them both. When an SD and ES don't make sense with each other, the data is telling you something is not "normally distributed" or your test wasn't done filling out, or both. That is the whole point of having those numbers instead of just the average.
The OPs original question wasn't wide open. He just asked about sample size and the accuracy of an SD.
If your ES doesn't make sense compared to your SD, then your SD is cold comfort regardless of sample size. When we teach ballistic science, we do not tell students to ignore one over the other. We teach them how to use both together.
As you open your checkbook to add sample sizes in your load testing, remember to watch both the ES and the SD, not just one or the other. You could say you don't need an SD for low shot count and your eyeballs tell you the data is good or bad without the math, but not when the ES is big.
If for example you bring me data that shows you got an SD of 5 and it was based on 15 speed readings, but you show me an ES that is skewed compared to the average, or one that is like ES 50 when your (SD 5 x 6) ES should be 30 or less, then we know something will go wrong because we looked at the ES and not just the SD.
An ES should be roughly centered over the average, and ES should be roughly 4x - 6x the SD or something smells wrong. Carry on and Merry Christmas.
Let me turn the tables on you for just a second. We have to cut this topic/question in two big halves.
One is the part about not trusting the measurement (the metrology), the other is the statistical definition of the data point to be called an outlier.
The part of the discussion about making mistakes in the test and what to do about them can swirl down a rabbit hole.
The part about the typical definition of what is an outlier is a shorter discussion.
In my world we ran Bayesian Statistical controls. In that world we have what are called false positives as well as false negatives.
With some measurements you have almost an equal chance that what you called good was really bad, and what you called bad was really good. In the real world, we talk about the uncertainty of all calibrated measurements.
Things like chronographs, micrometers, analytical balances, etc., all have an uncertainty and god help you if getting paid or not depends on being near those levels.
Now to your scenario, maybe we are talking about measuring MV of a round. You were mostly happy with your testing, then you noticed that one or more of your shots was what you want to call "an outlier".
The odds it is an anomaly with the chronograph will depend on your previous experience and the type of chrono being discussed.
It isn't impossible that a Doppler reading can be wrong, but the odds are very slim if we are being honest. The difference between how far off one measurement has to be in order to be called a outlier, is way bigger than the uncertainty in a typical Doppler. The odds it was a bad reading are small. With a sky-screen optical chronograph, there is a bigger chance it wasn't real.
If the topic was target analysis instead of velocity measured near the muzzle, then we have too many things to discuss on such a fine day. I work for free if there is Macallan 18 flowing, but since folks are not buying my Scotch here, I will keep this shorter by leaving target analysis alone today.
That said, let us not lose focus on the OP's original question, which was how many shots to spend before you consider an SD "accurate".
If we have beat that sample size question to death with the explanation of the risks and the T-Charts, then we should call it a day.
Your new question is fair.
If you have what the Student's T-Chart would say is a fair sized sample and you get something that looks way out, let me start by congratulating you for looking at more than just the SD. You get to pass go and understood the lessons.
If we want to drill down on what the typical velocity data is telling you when you have only 7 or so shots versus 30, and more specifically what you would call a flyer...
In the industrial world when you have hourly operators taking data, the software is tracking short and long term averages and SDs.
When a trend moves more than 1 SD on the average, or any given sample is more than 3 SD away, the screen turns the value red in order to bring it to their attention. Something is wrong or about to go wrong.
To make sure we don't miss the direct answer to your question, it is an outlier when it sits more than 3xSD away from the average.
Suppose we have as you said 30 shots in the sample and we suddenly get a reading of one that is at 4 sigma (four times the SD) away from the average.... we can only say for sure we have a flag or warning because a 4 Sigma should not exist when we have everything under control.
We start an investigation where we increase the inspection criteria and sample size to some contract level in order to either exonerate the batch or reject the whole batch.
As an individual doing this out of their own pocket as a target competitor or hunter, what you do about getting velocity outliers is up to you. Clear by now that if you get one with stats based on just 3 to 5 shots, you are going to have more risk than if your stats were based on 30 shots. But the definition of an outlier is still >3 SD away from the average.
I recommend you don't kid yourself and go double check everything if the stakes are high. You can take risks and get lucky now and then, but if you are being honest with your workmanship and keep your gun maintained, you will have very few surprises. YMMV
Merry Christmas.
Last edited:
I was being a lot more simple than that. If you shot 30 shots... and 29 of them were between 2,850 and 2,865... and the one was 2,510fps... you don't have to throw away the entire data set because of that one anomaly. Take it as a benefit of having larger samples.
If you have 30 shots and throw out one, ok big deal. On the other hand if you have 5 shots only and then toss the one 'bad' shot that takes that person out of Internet bragging turf, the difference between those scenarios is huge.
In a lot of ways bigger samples are not only a lot more honest on a ton of levels, they are also way easier to interpret.
Agree, the stat on the 29 shots stands and the one shot is defined as an outlier. We got what we got.
Now, suppose you got an average of 2858 on the above, and you find that one shot at 2873?
Bad measurement?
Bad Ammo?
Bad Gun?
Time for Scotch?
SD is a statistical measure, as has been said, based on a "normal" or "gaussian" distribution (Gauss was a cousin of Darwin - long history there).
One of the tenets of statistical testing is that you don't selectively report data. you need ALL the data. You are trying to take a sample and compare it to an expected mean result from the TOTAL population.
So, when you do a SD on 3-5 shots, your sample size is at risk of not representing the total population.
Then you go shoot a whole population (a 100 round box of ammo, or 10 of them), your SD from your small sample of 3-5 shots doesn't represent it.
Now that we all have the GARMIN, this problem is going to come into clearer focus, because the results of 20 shots today is not going to be representative of the next 500 shots, which we're probably measuing.
So we're probably going to need to start accumulating more data. Problem is, ambient and barrel temperature changes, barrel fouling changes, powder lot changes, etc.
I think what we're going to find, as we increasingly measure every shot with the GARMIN, is that our notions of what a reasonable expectation for SD over long data series, is going to change.
As far as outliers. And this is killing me with my 50 BMG shooting with the GARMIN at range (over 1 mile) this winter. I'm really having trouble with the vertical outliers. But if I shoot a string of 10-20 50 BMG (at almost $7 a pop with reloads!) and I get SD 14, but I can remove one and the SD is 7, I remove the outlier and take the 7 fps SD. I figure, "that's the shot that's gonna miss, out of every 10-15 shots."
Because I honestly don't know what else to do with that one that was inexplicably and unexpectedly 50 fps faster and went 1 MRAD high at 2250 yards. Should I go rework my trusted $7 a pop 50 BMG load because one "outlier" out of every 10 just goes rogue on me?
One of the tenets of statistical testing is that you don't selectively report data. you need ALL the data. You are trying to take a sample and compare it to an expected mean result from the TOTAL population.
So, when you do a SD on 3-5 shots, your sample size is at risk of not representing the total population.
Then you go shoot a whole population (a 100 round box of ammo, or 10 of them), your SD from your small sample of 3-5 shots doesn't represent it.
Now that we all have the GARMIN, this problem is going to come into clearer focus, because the results of 20 shots today is not going to be representative of the next 500 shots, which we're probably measuing.
So we're probably going to need to start accumulating more data. Problem is, ambient and barrel temperature changes, barrel fouling changes, powder lot changes, etc.
I think what we're going to find, as we increasingly measure every shot with the GARMIN, is that our notions of what a reasonable expectation for SD over long data series, is going to change.
As far as outliers. And this is killing me with my 50 BMG shooting with the GARMIN at range (over 1 mile) this winter. I'm really having trouble with the vertical outliers. But if I shoot a string of 10-20 50 BMG (at almost $7 a pop with reloads!) and I get SD 14, but I can remove one and the SD is 7, I remove the outlier and take the 7 fps SD. I figure, "that's the shot that's gonna miss, out of every 10-15 shots."
Because I honestly don't know what else to do with that one that was inexplicably and unexpectedly 50 fps faster and went 1 MRAD high at 2250 yards. Should I go rework my trusted $7 a pop 50 BMG load because one "outlier" out of every 10 just goes rogue on me?
