*Here’s how Standard Deviation calculations can figure in ammo decisions (or not…) READ MORE…*

*Glen Zediker*

*Seems like the last couple of articles on load testing and velocity data got some pretty good responses and attention, and so that means there’s more! Of course there is…*

As said, Standard Deviation (SD) plotted out forms a bell curve. A bell curve indicates the “probability density” of the normal distribution, or range, for something like velocity consistencies. For our purposes that’s the likely speed of the next shot.

Chances are outstanding that running all the numbers gotten from a chronograph session will plot into what’s called a “normal curve.” Like any normal bell curve, it gets divided into three segments and values, and these divisions are the “standard deviations.” And remember it is “a” standard deviation.

(I’ve said many a time that I’m sho no mathematician, and I am aware that there’s more and different ways to apply and model a curve, and to manipulate standard deviation results for different applications, but I’m trying to keep it more simple and use this “normal curve” for examples, it’s also called “population standard deviation.”)

**We’ve been working with the right-respectable SD example of 12.**

Assuming that normal curve, the distribution of “some number” of shots is forecasted like so: some 68 percent will lie within 1 standard deviation of the mean, about 95 percent lie within 2, and over 99 percent lie within 3 standard deviations. Again, since our SD is 12, then about 68 percent (approx. 2 out of 3) of all “next shots” will be +/- 12 feet per second. Since, though, the curve is in threes, that means that a scant number of the shots pose a chance for +/- 24 and some much (much) smaller chance remains for some shots to go to +/- 36. SD estimates how likely it is for those “head-scratchers” to show up, and also what might be the most realistic extreme any shot can deviate.

Data is a record of numbers and I do know that there’s 100-percent chance that the highest and lowest velocities collected for an SD calculation did, in fact, happen. To me, that’s what matters. No matter what the collected shot results calculated into for an SD, those were the two that represent the highest and lowest prints on the target.

It’s mathematically not possible for an SD to be higher than the greatest single measured deviant, and an SD can sho be lower than any single “bad” shot. Given how it’s calculated, along with how many samples contributed to the calculation, it’s plain that the nearer the majority are to themselves the less impact a bad one or more has. The more input the better.

Many of us have heard or read the frequently-sung “…seen good accuracy with high SDs…” And we’ve probably also all decided that can’t be taken at literal value. Well, it can’t. Three things: what is “good accuracy” to this fellow, at which distance were the groups printed, and what’s he say is “high,” because without knowing these things there’s no accounting for the accuracy, believability, or interpretative definitiveness of what’s being said. So I say it’s 12. A 12 should not be responsible for a points loss, also considering the edge limits of usual group size. Getting into more and more numbers derived from more and more “what if’s” plotting out bullet trajectories and wind drift amounts, and, always assuming a consistent bullet ballistic coefficient demonstration (also not likely) running “12” through all these mathematical-hypothetical scenarios will show that 12 doesn’t lose many, if any, points.

One last that isn’t really a strong point, but is a point… If we’re shooting something like a .223 Rem. then a half-grain is about 40 feet per second. If that 12 SD shows its worst and pops one out +36 feet per second, to me that represents something akin to a pressure spike (logic dictates that more velocity had something to do with more pressure). I know my loads are running a tad amount edgy, and seeing a small velocity variation is likewise a tad amount more reassuring that a primer won’t go over the edge.

**TESTING TIP**

If you’re testing much beyond 200 yards, and especially beyond 300, pay no mind to the left and right, but keep a close watch on the up and down. In ideal conditions, groups are supposed to be round (I’m convinced they’re actually square, but there’s no need to go into that). If there’s any wind, don’t even try to correct for it (as long as impacts are on the target). I honestly don’t need a chronograph to confirm load consistency if I’m seeing small vertical dispersions. I’ll already have speed-checked the load I’m down on the mat with, and, again, I’m just wanting to see how level I get my perforations. If I come out with a 600-yard group that’s a foot wide but only three inches tall, I’m happy.

**6 TIPS FOR LOWER SDs**

Aside from finding the perfect and magical load combination, ha, there are a few things that do seem to help tighten shot-to-shot velocity deviations. They’ve all be talked all the way through and back again in this space in other articles, but, considered ultimately that this is the overall effect they have, here they are again:

**One.** Primer seating: fully seated onto a flat pocket bottom.

**Two.** Consistent propellant charge: weigh the charges if metering isn’t dead-on.

**Three.** Ignition efficiency: consider trying that inside flash hole deburring routine…

**Four.** Consistent case neck sizing, and, believe it or not, about 0.003 worth of “tension.” Don’t go too light…

**Five.** Temperature insensitivity: choose propellants that exhibit stability under extremes.

**Six.** Balance: strive to find a propellant that fills the case, but “loosely” (no compressed charges); even more, avoid an overage of air space. These both allow too much variance in ignition pattern.

*This article is adapted from Glen’s books, Handloading For Competition and Top-Grade Ammo, available at Midsouth HERE. For more information about other books by Glen, visit ZedikerPublishing.com*

I’ve heard or read lots of folks spouting that SD is irrelevant and one should look (only) to ES. Can’t tell if the author is one of them.

I couldn’t disagree more. Start with the fact that all three, five, ten or however many shots in a string don’t have exactly the same velocity. That tells us that uncontrolled factors are at play (what we call “residuals”). To some extent, these uncontrolled factors affect every shot in the string, some more than others.

Our goal is (or should be) to gain some sense of how significant the effect of the uncontrolled factors will be in the future. ES doesn’t tell us that, because by definition ES tells us only about the impact of uncontrolled factors on one (actually, two) of the shots. But, if we accept that the underlying relationship (here, charge weight to instrument velocity) is normal, then SD tells us something–indeed, a lot–about how the uncontrolled factors will affect a future string, set of strings, or shooting lifetime.

Second comment: I hear (and sometimes read) statements to the effect that a “good” SD is X. This is meaningless, for the simple reason that the unit of SD is feet per second. An SD of X has vastly different meanings for a round whose mean MV is 850 versus a round with a mean MV of 3,000. What I counsel folks is to divide SD by mean MV (actually, instrument velocity), a task that produces “Coefficient of Variability,” usually displayed as a percentage. Suddenly it will become obvious that an SD of X (fps) is more than three times less “good” for the rifle round than for the pistol round.

Third (and, mercifully last) comment: I hear (and read) many times the observation that a given load ” is accurate” despite a “bad” SD — a comment usually intoned with some consternation. The fact of the matter is that we assume that vertical stringing is solely a factor of variability of muzzle velocity, and that simply isn’t true. At least one uncontrolled factor is the component of wind that is parallel to bullet track (i.e.., headwind or tailwind). This affects the coefficient of drag, which in turn affects time of flight. Time of flight affects vertical stringing directly. At any significant target distance, wind is both unmeasurable over the course of bullet flight and constantly changing. Bottom line: we can have loads with “bad” SDs that seem to be “as accurate” as loads with “good” SDs, but all other things equal, the better the SD, the less the effect on vertical stringing that is caused by variability in MV. Simple physics.

All of the foregoing said, I love these articles, want to see them keep coming, and should not be construed as being “critical” is the colloquial sense (just picking nits).

Another very good article, but I think one area needs a bit of amplification. Probability theory and the normal distribution curve are based on experiments in which there are a large number of observations, such as manufacturing processes. Ie. Hornady only has to measure a very small percentage of bullets to have thousands of observations. For a small sample experiment, such as we are talking about, one can only get a certain “level of confidence” in the results, which depends on the number of shots measured. It is mathematically possible to calculate the average and standard deviation from three shots, but there would not be much confidence in the results. I showed the calculations in my comment on Part 1, but it requires measuring at least ten shots before any reasonable level of confidence can be developed.