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Dear Labby Explains Standard Deviation

The Statistician’s Friend: The Bell Shaped Curve.

Will you please explain what Standard Deviation is and why I should care?  It just seems like another useless bit of information.  What is its role in predicting accuracy?

I think the importance of Standard Deviation is probably overestimated as a predictor of accuracy, especially at normal hunting ranges.  It is simply the application of statistics to analyze values within a relatively narrow range by using multiple data points.  For shooters using Standard Deviation as a measuring stick, this means comparing a number of shots that were all supposed to be the same velocity.

Perhaps a shooter making loads for 600 yard competition plans to shoot three groups consisting of three shots apiece to test a load in the final stages of accuracy testing.  By chronographing those nine shots, our shooter can also measure Standard Deviation to examine the quality of their loads.  Nine shots is a pretty narrow predictor statistically, but it is a realistic one in real world practice.  The mathematics aren’t something you would care to do in your head while testing loads, but luckily most chronographs offer the analysis at the end of each shot string.  It is the ready availability of this data, I think, that makes it seem so important to shooters.

At the end of a string of shots, the computer will probably offer up information that looks something like this:  Ave=2700 fps, SD= 10″.  But what is really being said?

Understanding your chronograph’s output takes a little intellectual leg work.  It is providing data that references the statistician’s friend, the Bell Shaped Curve and a statistical model called the 68-95-99.7 Rule.

In this model, the first Standard Deviation represents 68% of the samples taken, or in our case, 68% of shots fired.  In a shot-string with an SD of 10 fps, 68% of shots fired will fall within 10 fps of the average velocity.  This first grouping, in a velocity range between 2690 fps and 2710 fps represents the first Standard Deviation.

Two Standard Deviations statistically encompasses 95% percent of the shots fired in the sample by picking up the less commonly occurring outlying velocities.  In a bell curve these shots would begin to represent the flaring bottom end of the bell and become much less common as they move further from the average velocity.  The velocity range would be from 2680 fps on the low side and 2720 fps on the high side.

Three Standard Deviations represent 99.7 percent of the shots fired, suggesting that all but .3 percent of shots fired should show a velocity variation less than 30 fps faster or slower than the average velocity.  Beyond that, over many, many samples, outlying velocities less than 2,670 and greater than 2,730 fps might be encountered but only from .3% of shots fired.

Is this Information Useful?
Let’s summarize this conclusion in the language of Tarzan: Unk, Bo-mon-gony.  Big number bad.  Little number good.”

If your benchrest ammunition, has a Standard Deviation of 120 fps, perhaps it is time to take up golf.  The last batch of Hornady factory ammunition I shot with a sample size of 20 shots came in with an SD of a bit more than 12 fps.  This is very good, especially for factory ammunition.  Bragging rights among the benchrest crowd begins at anything less than 10 fps and reaches a low end SD running around 5 fps.

So yes, Standard Deviation does provide an important reference regarding the consistency of ammunition.  As ranges increase even small variations in the bullet’s launch velocity will impact group size.  Ammunition with a low Standard Deviation offers a promising indication that those launch velocities will be consistent.

Remember what Tarzan taught you.  Big number bad.  Small number (especially under 10 fps) good.