Browse through shooting forums and you will see claims of incredible accuracy from a wide assortment of firearms. Typically, these claims say that the rifle is a “X-MOA” gun. Bonus points are awarded if it shoots a certain level of precision “all day long” especially “if I do my part”. However, this claim tells us very little about the group size, number of rounds per group, whether fliers were removed, and a whole host of other variables. This system of measurement is imprecise and is inefficient at measuring precision in a rifle system.
Disclaimer
First of all, I must to add a disclaimer. I am guilty of using MOA as a metric in common banter as well as in some of my articles. There are several reasons for this. For one, extreme spread is easy to measure. Secondly, the shooting industry has used the extreme spread for so long that it has become entrenched as the standard by which we compare rifles. Finally, I do use more sophisticated measurements for measuring the precision of my rifles. However, I rarely discuss them with other shooters because most won’t know what I am talking about. With that out of the way, let’s look at some different measures of accuracy.
Extreme Spread
Extreme spread, or more commonly group size, is easily the most common measure of precision. The main reason for this is it is very easy to measure. Extreme spread also has a lot of momentum as the firearms industry has been using it as the standard for a long time now. However, extreme spread is a very inefficient metric.
For one, it can only grow larger. The larger the number of shots in your group the larger your group will be. In comparison, some of the other metrics we will look at will converge on the true value as the sample size grows larger. The other main drawback is that extreme spread only uses information from two of the shots. This is discarding a lot of good data.
Rayleighs Distribution – Sigma
The most efficient and accurate measure of a rifle’s precision is the sigma of it’s Rayleigh Distribution. However, it is mathematically complex and above the ability for your average layman to compute and understand. I will try to break down the concept into layman’s terms so that one can have a conceptual understanding of the ideas. For the more mathematically inclined, Ballistipedia has a fantastic article on the mathematics and real world implications of the distribution.
The basic idea is that the more shots we fire the larger the group will get. Even though the group will get larger, the impacts will be more concentrated near the middle of the target than right around the edge.
Imagine our target was an x-y graph we could measure how far each miss was off horizontally and vertically. We could then plot the size of our misses and we would get a two bell curves (normal distributions). One curve would show horizontal dispersion and the other vertical. The shape of the bell curves can be measured as a number and can tell us how accurate the rifle is.
That said, the Rayleigh Distribution is too complex for everyday use, so let’s look at another measurement.
Mean Radius
The mean readius is essentially the distance of the average shot from the center of the group. This is a better metric than extreme spread because it uses information from all of the shots in a group. Mean radius falls somewhere in the middle of extreme spread and the Rayleigh Distribution as far as computational difficulty. For a long time the additional math has hindered people from using mean radius to evaluate accuracy. Another benefit of mean radius is the more you shoot, the more accurate your estimate becomes because it can get smaller as well as larger.
Nowadays, the invention of mobile apps that analyze group size eliminate the need for shooters to calculate mean radius. Simply snap a picture of the group and your phone will do the math for you. This allows shooters to utilize the benefits of mean radius without putting up with the extra computation time. In my opinion, this is a convenient alternative that is more accurate than extreme spread but much simpler to calculate than a full statistical model.
Advice for Measuring Accuracy
Finally, here are some tips for those measuring the precision of a rifle system. Everyone wants to have a great shooting rifle to brag to your friends about. Don’t let your bias get in the way of good data collection.
Stop Eliminating Fliers
Far to many shots that are a bit out of a group are labeled as fliers and eliminated. Oddly, I’ve yet to see someone say “Ah I might have pulled that one a bit”, then crossing the shot off when it went through the bullseye. My policy is I will only eliminate a flier if I call the flier before I’ve seen the target and I also correctly called where I pulled it.
Shoot from Stable Positions
Accuracy testing your rifle system is not the time to work on positional shooting. If you want to shoot off of a barricade or unsupported go wild, but those groups are you and not the gun. Accuracy testing for a rifle system should be off of a bench with a rear bag or prone with front (or bipod) and rear bags.
Use all Data Points
Don’t cherry pick your data to improve the results. Include all your groups in your analysis, even the poor ones. Furthermore, decide how many shots are going to be in a group before you shoot it. We all have an urge to hold the fifth shot when we have a great four-shot group. Don’t alter your data collection to preserve desirable results.
Concluding Thoughts
In closing, coming from a statistics background I see a lot of misunderstanding of measuring rifle precision on forums online. There is a lot of unscientific data collection out there. Furthermore, I think that this is compounded by an inflated perception of what real-world accuracy actually is. Hopefully this article will help shooters think critically about their data collection and improve their processes.