When you collect velocity data, how many shots do you consider relevant?

It has been many years since I've taken stats, with a whole bunch of things that I don't remember anymore. One thing that I have experienced though is that the rolling stats at 10 data points, 20 data points, and 30 data points can be different - sometimes significantly. Granted, we can argue progressives vs weighing each charge; centerfire vs rimfire; light recoiling vs "I can't shoot 30 uber-magnums in one sitting," etc. You may need more or less data points for your own confidence interval depending on how consistent you know your handloaded ammo to be.

There have been times when after 10 or even 20 shots, I thought I had an excellent set only to find that the average caught up with me by the time I got to 30 data points. If I would have stopped at 10 or 20, my conclusion would have been different than going the full 30.

Call me old fashioned, but I like 30 data points. After "about 30" you've got what you've got. Going to 40 or 50 doesn't change a whole lot. But, in some applications - like a known, handloaded precision rifle load or a hard -recoiling caliber, some may call 20, 10, or less data points good enough. What the shooter is looking for is reliable information that can give a basis for comparison. While nobody gets a trophy for having the lowest SD or ES, those descriptive statistics can help shooters choose consistent loads. The tale of the tape after all is the target, not the stats. Remember, the stats and the targets don't always coincide. Which is why one must consider the stats, but also harmonics, twist rates, barrel preferences, etc.

Stats as an applied field really isn’t difficult, but threads like this make it obvious how foreign it is to most folks.

Terms like confidence interval, average, mean, standard deviation, spread, range, normal distribution, etc get thrown around because they sound great, but it’s very rare to see apt application of statistical methods in this type of discussion.

A conversation about estimating my mean velocity to within +/-25fps would not hold interest for me, most of my current rifle loads are less than 25fps extreme spreads, let alone some foolishness of estimating mean to within a 50fps range! In shooting long range precision, impacts on target are another measurement device - if I were only getting my average velocity to within +/-25fps, the targets at range would tell me...

Required precision, required accuracy (not the same thing), inherent variability of the population, systemic variability of the population, variability of the test method (inherent and systemic), population size, and a host of other aspects impact the required sample size to reach confidence.

Chronographs like the Lab Radar or Magnetospeed do make it a lot easier to collect a lot more data.

Getting outside of theory and working with empirical results myself, I have done the “excessive” confirmation testing to run Monte Carlo simulations for combinations of different subsets of my shot strings. For example, leaning my Magnetospeed hooked up for the entirety of a hundred round practice day, then simulating different 5, 10, or 20 round strings with those hundred rounds, and comparing the resulting statistical metrics for each set against the 100rnd set. I ALSO confirm my velocity before every match with a 10-25 round string, which can also be totaled together (within a reasonable portion of barrel life) to act as a mother sample set, smaller real child sets, and also simulated child sample sets of 5, 10, or 20 rounds, again, comparing the statistical results of the smaller subsets against the larger set. For loads with an ES if under 30, 10 rounds has always shown the same average, SD, and ES, within the accuracy of the chronograph I was using in the conditions used - less the systemic variable of shoulder pressure effect on MV. For standard factory ammo, or poorly baked reloads with excessive ES, say 70-80fps, even 30 rounds may not be enough to develop a relevant average.

With low ES loads (<30), a sample size of 5 shots is ALMOST ALWAYS enough to reach a sufficiently accurate muzzle velocity for 0-1200yrd shooting.

If I ever shoot a load which required 30 rounds just to get my results within +/-25fps of the true average muzzle velocity, I would stop long before 30 rounds and write that load off as “dog don’t hunt,” as the entire endeavor with that load combination would be a waste of time.

You have the Labradar so you can measure every shot you fire pretty easy. You are questioning average velocity but I would encourage you to look for things like velocity change on a clean barrel versus a fowled or dirty barrel, changes brought about by temp changes air or barrel, etc. You will find a lot of answers that you didn't know you had questions for.

When I'm screening loads (think workup) I normally shoot groups of 3-5. After the first run I start loading 5-10 rounds each as I narrow it down. Once I'm satisfied I load a larger pool of 25-50. I gather crony data on all shots, including weather conditions.

460Shooter said:

And there in lies my question. Variance on 5 shots could be huge, or it could be really small for hand loads. But either way the stats generated for those shots are based on the sampled shots only. You aren't going to really develop a confidence interval, nor an overall error unless you apply a sample to a larger population. I know, I know................. I'm over thinking it. It's still very useful data in my opinion. I guess I'm going to start doing ten or twenty shot series, because I believe a larger sample will have more important implications than a smaller sample, look at the extreme spreads and average velocities, and just have fun.

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Your basic thought process is right. The more variation your load has, the less precise your estimate of true mean will be, for a given sample size.

If you average several samples, and take the mean, then the Standard Error will be the SD of the sample divided by the square root of the number of items in the sample.

The true mean will be found between plus and minus 2 Standard Errors, 95% of the time. (At least close enough for practical purposes.)

So if you shoot 5 rounds and the SD of the sample is 25 FPS, then the Standard Error is 25/(square root 5) = 11.2. You basically know the true mean within plus or minus 22.4 FPS.

Those are typical real numbers for most rifle loads. There isn't much practical reason to need numbers more precise than that, but I have no quarrel with anyone who wants to take more data.

Using a light .223 target rifle load with thin jackets I can get 15 or 20 before fouling takes over and makes chrony data worthless. Even so I strongly agree with our asteamed moderator all we need to know is going to come within the first few shots especially when fouling's not the issue

If I am loading to a power factor and working up a load, a single shot is all I need to tell me if I am still too low on my powder charge and need to keep going up.

If I have a load I really like and just curious as to what it’s doing I might chronograph a few groups.

You can infer a lot about any given load without a chronograph you can know a bit more with one.

denton said:

So if you shoot 5 rounds and the SD of the sample is 25 FPS, then the Standard Error is 25/(square root 5) = 11.2. You basically know the true mean within plus or minus 22.4 FPS.

Those are typical real numbers for most rifle loads. There isn't much practical reason to need numbers more precise than that

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In 6 creed, a difference in mean velocity of 44fps is a 7” shift at 1,000.

I have a practical reason to need numbers more precise than that.

460Shooter said:

I really enjoyed using it. The one thing to remember is you need to take about 2 seconds between shots. I missed a few rounds because I got a little too rambunctious.

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I do this all the time. I think I warned you about this too!!! I have been shooting the speed sports over the last couple of years, so it is hard for me to be patient! I want to blast away!

460Shooter asked:
"...how many shots do you consider relevant?"

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It depends what I am trying to determine.

For load development, my home-made data sheet includes a blank table for recording 20 shots.

SD & ES , l love benchrest shooting with my Rem 700 308 . I don't own a chronograph but I do work up loads that are accurate . Knowing speeds using the Chrono is the purpose of the unit finding how accurate your loads are and knowing what velocity is accurate to duplicate that load . I shoot 3 ten shot groups for testing at 200 yards , my groups are tight but the only way to see how really tight the groups are the shooter has to be out of the test . How are you steadying the rifle , I know when I pull a shot but it's so hard to repeat every hold an stay perfectly dead on every time . I would love to shoot that one hole group once you find that perfect load . Is there a system that is used for accuracy like a random rest in a hand gun . Would be nice to see how really accurate the rifle shoots without us screwing up the group.

I'm not a statistician and have no expertise in the field. I will usually run a full revolver over the chronograph a minimum of 3x with 5x or more being better. I would think 20+ to 50 rounds would supply me with the best data.

With a rifle I usually send a string of 10 shots over the chronograph and I'm happy with that. (the string limit of my inexpensive chrono)

cw308 said:

SD & ES , l love benchrest shooting with my Rem 700 308 . I don't own a chronograph but I do work up loads that are accurate . Knowing speeds using the Chrono is the purpose of the unit finding how accurate your loads are and knowing what velocity is accurate to duplicate that load . I shoot 3 ten shot groups for testing at 200 yards , my groups are tight but the only way to see how really tight the groups are the shooter has to be out of the test . How are you steadying the rifle , I know when I pull a shot but it's so hard to repeat every hold an stay perfectly dead on every time . I would love to shoot that one hole group once you find that perfect load . Is there a system that is used for accuracy like a random rest in a hand gun . Would be nice to see how really accurate the rifle shoots without us screwing up the group.

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Measuring group size is a whole 'nuther thing.

Group size is a measure of variation, and variation is much harder to pin down than where the center of the data is (average MV for example).

denton said:

Measuring group size is a whole 'nuther thing.

Group size is a measure of variation, and variation is much harder to pin down than where the center of the data is (average MV for example).

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Not harder at all. You can use many of the same statistical analysis tools. It just two dimensional (X & Y) instead of one dimensional (V).

When knowing SD & ES is the purpose finding the accurate load for that barrel ? I'm getting 1/2" groups an I shot through a friend's Chrono , he said it's running slow , should goose up your load alittle

I see different types of units , some attach to the barrel others .. shooting through a wire V on a stand . Would think the one on the barrel would change how the rifle shoots . What made you buy a chronograph .

Sorry , I didn't intend to go off topic . Gathering data is new to me .

The August Guns & Ammo has an article on ES and SD. Essentially concludes that if you shoot pistol, you probably don't care (short distances, slow bullets). If you shoot precision long-range, yes, lower extreme spread and standard deviation makes a huge difference in consistent groups.

berettaprofessor said:

The August Guns & Ammo has an article on ES and SD. Essentially concludes that if you shoot pistol, you probably don't care (short distances, slow bullets). If you shoot precision long-range, yes, lower extreme spread and standard deviation makes a huge difference in consistent groups.

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For pistol loads <25 yards, I only care about the SD and ES as I think it is a good indication of how a powder is performing. For instance, position sensitivity in 38spl and 357mag (powder forward effect). I've seen a ES of 300fps with some powders, so I would not consider using that powder for that application, as I would be afraid I might end up sticking a bullet in the barrel.

mcb said:

Not harder at all. You can use many of the same statistical analysis tools. It just two dimensional (X & Y) instead of one dimensional (V).

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Hmmm.....

Measures of central tendency (means, medians) converge pretty quickly as you add samples. So after a relatively small number of samples, you have a pretty good idea where the center of your group is (assuming you're shooting a decent firearm) for a two dimensional example, or what your average muzzle velocity is as a one dimensional example.

Measures of dispersion require much larger samples, and are uglier to handle.

The statistical tools aren't hard to come by, but measures of dispersion require quite a bit more data to get decent precision. That's what I meant.

As an example, suppose you shoot a sample of 5 rounds from your rifle and get the following muzzle velocities in FPS:

2782
2819
2800
2798
2820

You can be pretty sure that your true average MV is between 2784 and 2823. That's probably close enough to discourage taking much larger samples for most of us.

But we only have the Standard Deviation (a measure of dispersion) nailed down to between 9.55 and 45.8. Group size, mean deviation from center, etc. all have the same problem, plus there are some other uglies in the works.