Chronograph numbers

[Aguila Blanca]

Chronographs are wonderful toys tools. They record and spit back all sorts of numbers with esoteric names like "Extreme Spread" and "Standard Deviation." Many of us like to use such numbers to assess the quality of our handloads.

What's a realistic number of shots in a string to have the Standard Deviation be meaningful? Theoretically, you can calculate an SD using only two data points -- but it won't mean much. If we're interested not just in getting a number but in actually having that number be statistically significant -- what's a minimum number of shots in a string for that to happen?

[74A95]

10 is a reasonable number. But keep in mind that if you fired another 10 rounds with that same ammo, the ES and SD can be quite different.

Here's an example with data on the web that you can look over.
https://americanhandgunner.com/handg...city-accuracy/

They used 15-shot groups with the same ammo and found that the ES and SD could vary by a factor of 2. (See the first data set with Power Pistol powder.) If one uses less than 15 rounds, the chance is the ES and SD differences could be greater.

The question comes up as to what you mean by 'statistically significant'? That term is often used when hypothesis testing, often comparing a measured variable and the ES and SD are measures of variation or error.

[5whiskey]

With limited testing to just rough compare starting loads, when components are scarce, I use 5 round groups. I think this sample size is lacking, but saving components is... well... saving components. FWIW I use the chrono, but don’t really care about the SD. I’m looking at the group more than anything from the chrono. In times of past and times of plenty, I made no comparison without shooting a 10 round group.

FWIW, some of the best iron sight groups I’ve ever fired (under 1 moa @ 100 yds) have been from loads that had a rather high SD of around 20 (from a 10 round group). It seems it’s always just one round that really throws it off, as I’ve literally watched my SD go from 9 to 19 on shot number 8 of a 10 round string. I do understand SD will begin to matter more at greater ranges. An extreme spread of 80fps can mean almost a foot POI at the max effective range of a loading sometimes. Either way, I take the statistics with a grain of salt. I like hitting targets at long ranges when I get a chance, and am decent at it. But I don’t have the time and resources to devote to sub moa groups at 1K yards, or the SD numbers that would get me there. YMMV and all that. Everyone has their priorities.

[Shadow9mm]

I remember dealing with this a while back. If I remember correctly 7 is the ideal number statistically. Generally I try to shoot at least 5 for handguns, and 7 for rifle ammo.

I think UncleNick was the one that posted the data about 7 being the ideal number statistically. I did some digging but I could not find the post. I should have save it, really cool article.

[Don Fischer]

Well about chronographs, I have an idea if you load up 40 rounds exactly the same and shoot four ten shot groups you'll get four different SD's and ES's! What do you do with four loads fired in ten shot groups that give four different average velocities?

[74A95]

Originally Posted by Don Fischer

Well about chronographs, I have an idea if you load up 40 rounds exactly the same and shoot four ten shot groups you'll get four different SD's and ES's! What do you do with four loads fired in ten shot groups that give four different average velocities?

What's your point?

[rclark]

I shoot 15 rounds over the chonograph (revolver cartridges). I used to shoot 30 for some loads. Statistically 10 is a realistic minimum for SD calculations. More interested in Extreme Spread though. If you look at your data, you'll notice that SD is usually roughly 1/3 your ES anyway. Obviously what you are really after is good groups in a certain velocity range. A good ES at least gives you the 'potential' of being a good load, but it is not automatically a good load ... if that makes sense. Obviously also the longer distance you intend to shoot, ES becomes more important too.

[Don Fischer]

Don't have a point but have a chronograph. I only use it after I've got a load developed I'm gonna use. I believe a lot of guy simply confuse themselves with one by getting velocity's that have what they call to much SD or ES. than they start all over till they can get a load with the smallest SD and/or ES and end up choosing that over their best shooting load.

[ligonierbill]

There are statistical tests you can apply to a data set that will answer the question. I got an 'A' in my one statistics course, but I hated it, and I don't do it anymore. My guess is that the general answer is "a lot more shots than most of us are willing to spend". But most of us, me included, just want some sense that our loads are consistent. Unusually high SD or ES makes me wonder why, but I don't put any effort into optimizing that aspect of my loads. I have had some very accurate loads that did not exhibit a low SD. And I have had single digit SD loads that had mediocre accuracy. Bet you have, too. It's just one more piece of information.

[Jim Watson]

Standard deviation is a made up number that might be of use to a quality control expert in charge of a high volume widget factory. To the shooter with a short run of results, not much.

Assuming a "normal" (Gaussian, bell curve) distribution, plus or minus one standard deviation will include only about 2/3 of the values.

Extreme spread is more useful to me, it includes all the shots, and you are firing all those shots at a target so they all count.
Kind of like gunzine nonsense, "Four out of five shots were in a minute of angle."

[hounddawg]

95% CEP circular error probability) of a minimum of 20 rounds is the only number I worry about these days. It not only gives me the probable precision of my load but also takes into consideration my shooting ability and environmental effects. In other words it is a real world number that tells me how likely I am to come within XX of my aim point on every shot

It is not surprising that the best groups also have the best ES/SD because ES and SD can be affected by the consistency of your hold, which also affects your POI. Correlation does not always mean causation

edit - here is a real world example of CEP generated by OnTarget software from a target with five groups of five shots each. This tells me that any shot from this load shot from this rifle under similar conditions has a 95% chance of hitting within .65 MOA of my point of aim. I normally like to get that number down to a .5 MOA because mid range F class targets to have a 1 MOA 10 ring and that .5 MOA point of impact could be anywhere to the right, left up or down from my point of aim

[ballardw]

I would be more interested in the distribution of values overall. Which may lead to an actual test for normality of distribution or the statistics Skewness, which measures the tendency of the deviations to be larger in one direction than in the other (not symetrical) and Kurtosis, which measures heaviness of tails (more values away from the mean than you would expect with "normal" or good performance).

An extreme example of large Kurtosis for example would be firing 10 shots and having 5 at exactly 2500fps and 5 at exactly 2550. That would have a mean of 2525, SD 26.35, ES 50, is absolutely symmetrical but the bit of two clusters of values might indicate something else of interest going on.

But I'm a data geek with way too much time using statistics software and playing around with different sorts of analysis.

[hounddawg]

then one day you wake up and find chrono numbers don't make a rats rectum when it comes down to group size. These were shot at 300 and the ammo was loaded at the same session. The only difference is the cases were not annealed (softened) on the far right group and on the middle group I took my jacket off. Otherwise powder charge, primer, and bullet seating depth was identical

[Shadow9mm]

I work up my loads in 3 phases.
Pressure testing. I load up a batch of 1 each and go until I see pressure signs. Or max, whichever comes first.
Velocity testing. I test from max down in groups of 5 or more to find a good stable sd/es
bullet Seating, I take the selected powder charge and shoot 5 shot groups, starting at max col, and pushing the bullet back by 0.003 for each group.

In short, I go to max to preserve as much velocity as possible.
then I go back down to tune the powder load for consistency
then I tune to bullet seating for accuracy.

For example, I have a budget hunting rifle in 30-06. with match grade ammo she would barely hold 1.15 moa, with basic hunting ammo she was in the 1.25 to 1.5moa range.

using the method above, I worked up a load
169g SMK
Varget 49.0g
velocity 2710fps
SD 9.48
ES 25
0.59moa at 100yds. on a fairly windy day.

[Unclenick]

The number 7 is number that gives you the shortest path to a valid evaluation IF you are evaluating group sizes (the distance between the two furthest spaced holes (extreme spread) in the group). It is explained for evaluating groups in this paper by Geoffrey Kolbe that for 15% error tolerance, 42 shots in 6 sets of 7 will get you there. For 5% error tolerance, 385 total shots (55 groups of 7) have to be fired. The same would apply to analyzing velocity by the ES numbers of your strings alone. Kolbe points out 5-shot samples are almost as good as 7-shot samples (45 rounds total, or 9 groups of 5, verses 42 rounds total in 6 groups of 7), though you do use up more target paper.

If you know the location of each shot, rather than firing 42 shots, it takes about fifteen shots to get 15% tolerated error based on radial SD. Kolbe sites a monograph with proof that radial SD is the best measure to use. If you plot radial SD and CEP68%, they are very close for any significant group shot size, so I doubt most shooters will find there's any practical advantage to using one over the other, though CEP50% is more commonly used for CEP.

One problem you run into with the sample standard deviation formula used in every chronograph I've seen is it suffers from what is called square root bias when the sample size gets small. For sample sizes of 7 or smaller, it turns out you can get a better estimate of population standard deviation simply by multiplying the ES by a statistic called Xi of n (pronounced "zye of en"; symbolized as ξ(n)). Above 7, the formula produces more reliable estimates. (Note: for those unfamiliar, the sample standard deviation, SD or s and the mean, X-bar (an X with a horizontal line atop it) are attempts to estimate what the population standard deviation and mean will turn out to be in the future when all such rounds that ever will be fired in history are measured. Population standard deviation is symbolized by the Greek lower case letter sigma (σ). Population mean is symbolized by the Greek lower case letter mu (μ). To better determine SD values for a sample that is 7 or fewer, multiply the ES by ξ(n), where n is the sample sizes:

n      ξ(n)
2     1.128
3     1.693
4     2.059
5     2.326
6     2.534
7     2.704

[TX Nimrod]

We have all the valid information in this thread - yet so many still seem to believe that 5-shot “ladder” groups will tell them their most accurate load…..������




.

[Jim Watson]

An extreme example of large Kurtosis for example would be firing 10 shots and having 5 at exactly 2500fps and 5 at exactly 2550.

I had a case of that once upon a time, never could figure out why.

[Unclenick]

At first glance, it seems to be the statistical equivalent of bi-polar disorder. However, in grouping a gun, it indicates some alternating incremental difference that begs to be discovered, like a loose scope base shifting between two locations, etc. For velocity, it might be a powder measure problem with an offset that comes and goes.

[Shadow9mm]

Originally Posted by Unclenick

The number 7 is number that gives you the shortest path to a valid evaluation IF you are evaluating group sizes (the distance between the two furthest spaced holes (extreme spread) in the group). It is explained for evaluating groups in this paper by Geoffrey Kolbe that for 15% error tolerance, 42 shots in 6 sets of 7 will get you there. For 5% error tolerance, 385 total shots (55 groups of 7) have to be fired. The same would apply to analyzing velocity by the ES numbers of your strings alone. Kolbe points out 5-shot samples are almost as good as 7-shot samples (45 rounds total, or 9 groups of 5, verses 42 rounds total in 6 groups of 7), though you do use up more target paper.

If you know the location of each shot, rather than firing 42 shots, it takes about fifteen shots to get 15% tolerated error based on radial SD. Kolbe sites a monograph with proof that radial SD is the best measure to use. If you plot radial SD and CEP68%, they are very close for any significant group shot size, so I doubt most shooters will find there's any practical advantage to using one over the other, though CEP50% is more commonly used for CEP.

One problem you run into with the sample standard deviation formula used in every chronograph I've seen is it suffers from what is called square root bias when the sample size gets small. For sample sizes of 7 or smaller, it turns out you can get a better estimate of population standard deviation simply by multiplying the ES by a statistic called Xi of n (pronounced "zye of en"; symbolized as ξ(n)). Above 7, the formula produces more reliable estimates. (Note: for those unfamiliar, the sample standard deviation, SD or X-bar (an X with a horizontal line atop it) is an attempt to estimate what the population standard deviation will turn out to be in the future when all such rounds that ever will be fired in history are measured. Population standard deviation is symbolized by the Greek lower case letter sigma (σ).) To better determine SD values for a sample that is 7 or fewer, multiply the ES by ξ(n), where n is the sample sizes:

n      ξ(n)
2     1.128
3     1.693
4     2.059
5     2.326
6     2.534
7     2.704

Thank you Sir. great info. I saved it this time, wont lose it again.

[Sarge]

I've had an old BetaMaster for about 15 years. When I first got it, I was obsessed with extreme spread & standard deviation. At the time I had very accurate and powerful loads I'd been using long before I got the Chrony. My first inclination was to tweak those loads for 'better numbers'. Then I came to my senses and decided to not fix what was working.

These days I use it to see what velocity a given load is producing from a specific firearm. Five shots give me that. If the load is producing velocity range established as safe pressures by published reliable manuals and it produces acceptable accuracy, I'm done. I'm not Jonesing for a Nobel Prize for Ballistic Science. I'm just looking to clobber a groundhog, deer or coyote out across the pasture.

[hounddawg]

Just my opinion here but I am at the point where I believe that barrel harmonics smooth out vertical dispersion in small differences (100 FPS or less) and that a consistent hold yields smaller ES's. My evidence for those statements comes from the prepped vs non prepped experiment.

Two things to note is the POI did not correlate with the FPS in that experiment and the best chrono numbers came with my jacket removed, 20 rounds fired from ammo loaded at the same time and just randomly pulled from the box. 10 were fired with jean jacket on and 10 with jacket off and a just a long sleeve T shirt. Radically different ES and SD

Now I will say this, the lowest ES/SD had the smallest vertical spread but a 47 FPS ES still had less than .5 MOA vertical at 300 yards

My Shot Marker target system was delivered yesterday so combined with my chrono I will be able to get a better idea of whether that theory is correct

[jmr40]

Depends on your goals.

I can find out what I need to know with 3-5 shots. When I'm working on a new load the main thing I'm concerned with is making sure I'm not overloading the cartridge. I've seen loads faster than they should be while still 1-2 gr below book max.

I don't worry about SD. If the bullet holes are all close enough on the target then I'm happy. And if the actual velocity is within 50 fps of what the chronograph says that is close enough when calculating trajectory. At the ranges I shoot, (usually 300 or less), 50 fps at the muzzle just doesn't make that much difference down range.

[WESHOOT2]

For my 'standard' commercial stuff it would get tested hundreds of times over multiple-year periods after being subjected to various environmental stressors.

If its life is hole-punching, then only close holes matter.
If its life is meat-punching, perhaps more rigorous standards need apply.

If its life is life-saving, then oh my......

[GeauxTide]

Have used 10 for 40 years. 5 shot strings are not statistically significant for SD.

[Aguila Blanca]

Originally Posted by jmr40

I can find out what I need to know with 3-5 shots. When I'm working on a new load the main thing I'm concerned with is making sure I'm not overloading the cartridge. I've seen loads faster than they should be while still 1-2 gr below book max.

Originally Posted by WESHOOT2

If its life is hole-punching, then only close holes matter.
If its life is meat-punching, perhaps more rigorous standards need apply.

If its life is life-saving, then oh my......

I know this is an Internet forum and the unwritten rules say that staying on topic is not allowed, BUT ... in this case, could we please make an exception, and just answer the question?

This has nothing to do with deciding which load shoots best, which load generates the fastest muzzle velocity, using ladders to arrive at an optimum load. The question specifically asked about Standard Deviation, and nothing else. In an e-mail exchange with a fellow shooter, the question came up as to how many shots are required in a series to have the SD number be meaningful.

He uses three, which I said is not a large enough sample. In the past, I have shot 5-shot groups and reported the SD (along with max, min, avg, and ES), and been told that five shots is not enough for the SD to be statistically meaningful. I have long thought that a sample of ten is probably the minimum but I'm sure there are people here who have forgotten more about statistics than I ever knew, so I decided to ask.