RELOADERS CORNER: Standard Deviation

Improving longer-range accuracy has a lot to with consistent bullet velocities. First comes understanding it! Here’s a start on it… KEEP READING


Glen Zediker

It’s springtime (finally) and one of the things on your list might be working up a load for a new rifle, or new bullet. I’ve talked about testing processes and procedures, and also some about those bullets, and especially those with higher ballistic coefficients. The more aerodynamic bullet, by itself, is no guarantee of a smaller group (and whether you’re shooting one shot or 20 shots, you’re always shooting a group…).

To make the “magic” of a high-BC bullet come to life, they all need to be arriving at the destination at really close to the same speed. On target, that’s all about elevation consistency. It’s pretty commonly accepted among long-range competitive shooters that points losses come more from errant high and low impacts than from missed wind calls. High-BC bullets traveling at more consistent speeds reduces dispersions in all directions. But only if they’re traveling at consistent velocities!

The first step to improving velocity consistency is getting a good way to measure it. That there would be a chronograph. Nowadays especially, there are a number of simple-to-use and inexpensive chronographs available, that are accurate. Some have more features, which mostly revolve around providing printouts, digital records, and calculations, but what matters most (to me at least) is one that lets me easily read the velocity of each shot.

Check Misdouth offerings HERE

The newer barrel-mounted electro-magnetic chronographs make it really easy. I like the idea of being able to chronograph from shooting position, not just from a benchrest. This is a MagnetoSpeed.

So. What’s next is understanding the terms associated with this area of data-gathering.

“Standard deviation” (SD) is the most common measure of shot-to-shot consistency. It reflects on the SD reflects on the anticipated consistency of bullet velocities (some number of recorded velocities). The “standard” part reflects on a sort of an average of the rounds tested.

[Phrases like “sort of” upset mathematically-oriented folks, so here’s the actual definition: SD is the square root of the mean of the squares of the deviations. More in a bit.]

I pay less attention than many to standard deviation because: I don’t think standard deviation is near as important as is the “range,” which is the lowest and highest speeds recorded. Another that matters is “extreme spread,” which, by definition, is the difference between this shot and the next shot. I watch the speed on each shot. I compare this one to the next one and to the last one, and, as said, find the highest and the lowest.

Why? Well because that’s how I shoot tournament rounds. This one, then another, and another. A low velocity difference means that the accuracy of my judgment of my own wind call has some support.

standard deviation
Standard deviation calculation forms a bell curve. The steeper and narrower the apex of the bell, the narrower the fluctuations were. But there’s always a bell to a bell curve and the greatest deviations from desired standard are reflected in this portion of the plot. Depending on the number of shots that went into the SD calculation, these deviations may be more or less notable than the SD figure suggests. So? Watch each shot. That’s the way to know how a load performs with respect to velocity consistency. SD allows you to estimate how likely it is for “outliers” to show up.

A load that exhibits a low SD is not automatically going to group small, just because a low SD. I’ve had Benchrest competitors tell me that sometimes their best groups don’t come with a low-SD load, but do not apply that to greater distance! At 100 yards a bullet’s time of flight and speed loss are both so relatively small that even what some might call a big variation in bullet velocities (+/-25 fps or so) isn’t going to harm a group, not even the tiny groups it takes to be competitive in that sport. On downrange, though, it really starts to matter. (And keep in mind that “it” is a reference to velocity consistency, whether denoted by SD or otherwise.)

For an example from my notes: Sierra 190gr .308 MatchKing. Its 2600 fps muzzle velocity becomes 2450 at 100 yards and 1750 at 600 yards. (These numbers are rounded but serve for a example.)

If we’re working with a just awful 100 fps muzzle velocity change, that means one bullet goes out at 2550 and the next leaves at 2650, in the worst-case. The first drifts about 28 inches (let’s make it a constant full-value 10-mph wind to keep it simple) and the next slides 26 inches. But! Drop… That is THE factor, and here’s where inconsistent velocities really hurt. With this 190, drop amounts over a 100 fps range are about three times as great as drift amounts. This bullet at 2600 muzzle velocity hits 5-6 inches higher or lower for each 50 fps muzzle velocity difference. That’s going to cost on target, big time. And it gets way, way (way) worse at 1000 yards. Velocity-caused errors compound on top of “normal” group dispersion (which would be group size given perfect velocity consistency). Now, it’s unusual for a wind to be full-value and dead constant, so on-target left and right displacement is even relatively less — but elevation displacement is consistent regardless.

So, my 100 fps example is extreme, but half of that, or a quarter of that, still blows up a score, or an important hit on a target.

propellant charge consistency
This is probably the most influential factor in improving SD: consistent propellant charge. It’s not only that each case has an identical powder load, though, because primer factors, and finding the right combination ultimately is why we do all the testing…

So what’s a tolerable SD? 12. There have been, rest assured, much calculation to lead  up to that answer. That’s the SD that “doesn’t matter” to accuracy, meaning it’s not going to be the leading factor in a miss. It’s more than I’ll accept for a tournament load, but for those I’m looking for an extreme spread never more than 10 fps (the range might be higher, but now we’re just mincing terms). More later…

The information in this article is from Glen’s newest book, Top-Grade Ammo, available HERE at Midsouth. Also check HERE for more information about this and other publications from Zediker Publishing.

5 thoughts on “RELOADERS CORNER: Standard Deviation”

  1. SD is very reliant on sample size. 5 rounds (samples) means nothing, 10 not much. 50 or more samples, and SD becomes mathematically meaningful. Holes in the target are meaningful, even with less than 100 samples.

  2. So, how does one reload to get consistent velocities? What are the factors that contribute to a round’s velocity? This is a problem I’ve always had with reloads, and I’ve wondered how to mitigate that.

  3. I think the unique harmonics of each rifle are the answer to the question about why good SD loads aren’t always tge most accurate. I believe now that we should also be looking for and loading to specific velocity ‘sweet spots’ that result in harmonic accuracy nodes.

    What I found by accident with my Ruger Precision Rifle, is that the most accurate loads seem to cluster around very specific Velocity ranges,. If a load happened to ‘land’ in one of these ranges, then its target accuracy better than loads with better SD that did not. So, I was doing some seating depth tests with a bullet that should have been a great performer but had given just so-so accuracy previously.

    I found the seating depth sweet spot and got the MV exactly on one that another load had shot one ragged hole at. This bullet now shot “bug holes” with that load at that velocity where previously 1” groups seemed the best it could do. I’ve got another bullet test series setup to find that MV/SD sweet spot combination and see if I can confirm what the data seems to be indicating. What it seems to show is at least two MV accuracy nodes, one around 2600 fps, another at 2780. There are indications another exists above 2900 fps, but that is harder than I want to push a 6.5 Creedmor with a 140 gr bullet.

    Fun, fun, fun…

  4. Good article! Something so many overlook as they think it is just too complex, but it is really the most important aspect., and the mean (average) is overly emphasized.

    I usually describe SD using “grandma” terms as how much on average the data is away from the average. (no offense to any grandmothers out there, it was a term my advanced stats instructor used and it stuck! He said his never graduated high school, so explain it in terms she could understand (if you do know stats – imagine trying to explain a Scheffe post hoc under those restrictions!)

    I wouldn’t recommend using “range” as much though, as that is susceptible to a single flyer. if you have 9 shots in the 3000-3100fps and one at 2800fps, your range is 300fps, even though your average is decent and SD would be decent. So in this case you should see if that one low round was a fluke or repeats every 10-20 rounds.

    One measure that is very useful is the confidence interval (usually 95%). So basically what can you expect 95% of the velocities to be in. (~same as 2 SDs) You can download free apps on your phone that will calculate all this now, or Excel has good statistics abilities (you just have go to FIle:Options:Add-Ins and check it so that it makes it available)

    Also – good pointing out that your variability matters varied upon range you are shooting! You can get away with more variability under 100 yards, just like a larger MOA, but as you go out it definitely matters mush more!

    I just wish we had more info on the variability in commercial rounds. It is a very good measure of the quality of the manufacturing.

  5. Since we have gone this far, I believe we should discuss how the comments made by Phlllp Tron and Terry are related and what they mean based on the numbers given by the author in the original article. As Terry states, 95% is a very common confidence level to use. The original article states that the author shoots for a range of 10, also called a confidence interval, also that a SD of 12 is the magic number. The formula for finding the sample size (N = number of shots for which velocity must be measured) for a given SD and interval at a 95% confidence level is N = (2*1.96*SD/Range)^2. Inserting the stated values: N = (2*1.96*12/10)^2 = 22.13 shots. Since that 1/8 of a shot would be a real trick, we have to round that up to 23 shots, which is quite a lot if a variety of loads are being tested. If one is willing to increase the range to 15, then the number of shots for 95% confidence drops to 10 and for a range of 20 it drops to 6. If one requires 99% confidence then the number 1.96 in the equation is replaced with 2.58 with the result that 1.73 times as many shots or 39 would be required for verification at the desired range of 10. If 90% confidence is acceptable then the number 1.65 is used and 0.71 times as many shots are required. I believe this is the point that Tron was trying to make; that it can require a large number of shots to have a high level of confidence that additional shots will fall within a reasonably small range. Note that the actual average velocity does not enter into these calculations. It is important for other reasons but not for determining the confidence that one can have that the velocity of the shots will fall within the desired range.

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