Accuracy Analysis

I’m going to start posting results of range sessions once or twice a month as we get our accuracy analysis up to speed. Right now the plan for a given weapon is 3 10-shot groups, so 30 shots total. Time between shots 30 to 60 seconds, 100 yards, mild conditions (hopefully), and the 3 10-shot groups will be taken with no scope adjustments so that they can be compiled into a single 30-shot group. Time between groups could be 5 to 30 minutes and is not deemed relevant, except that the barrel will have had a chance for substantial cool down.

The following image indicates what I hope to produce for these updates, which will be used to characterize a given barrel and weapon:

 

That 100 yard 10-shot group is just an example as I’m still working on presentation. The group was shot with one of our 18″ .223 Fulcrum barrels with 77gr Federal Gold Medal Match ammunition. In the future I plan to measure bullet velocity with with my LabRadar unit. The Sigma values  above indicate that this rifle and ammo combination is no worse than low Class 5, and probably Class 3. This is as much information as can be gleaned from 10 shots, which is one reason why 3-shot and 5-shot groups are dubious for gleaning weapon accuracy. I took 15 other shots with Hornady 75 grain match ammo and when both groups are centered and combined, just for example to get more shots in the group, I get the following retults:

 

In this case the Sigma value over a 95% confidence range tighten up from [.221, .433] to [.265, .397]. This indicates the rifle is no worse than Class 4, and could reasonably be Class 3 (especially given that I was the shooter and I’m not particularly good). Class 3 is realistically as good as auto-loading rifles get so this is the target, so to speak, for a competition gun like this one. For grins we can separate the two different groups and overlay to see how the different ammo shot:

I didn’t measure muzzle velocity of any of the shots, but that is planned for future analysis. In the future we can tag any given shot with a muzzle velocity and then analyze the results.

The important takeaway is that it takes a lot of shots to properly characterize weapon accuracy, and that even with a lot of shots, the accuracy potential of the weapon is hard to nail down with a lot of precision. Still, were confident that we can back up our Class 5 guarantee on our products, and that we’ll be able to zero-in on that number a lot better with more data.

Truth in Accuracy

Countless times I am asked and have asked the question that arguably troubles rifle shooters more than anything: “How accurate is my rifle?” Most shooters, myself included, have settled on 3 or 5 shot groups, and the expected extreme spread of that group. We like to buy rifles that promise groups that are 1 inch or 1 MOA. We take our shiny new weapons to the range and put the manufacturer’s guarantee to the test.

The after-action report finds us sometimes pleased and sometimes not. We all know a single bad range trip can be due to lack of sleep, too much coffee, a bad batch of ammunition, ammunition the weapon simply doesn’t like, or one of many other excuses. These excuses might be legitimate, but there’s no way to know. Adjustments are made, bullet seating depth is changed, different ammo is selected. The next range trip might produce a couple groups in the MOA to sub MOA range and we are then pleased that our rifle is indeed a shooter and we pack up happy until next time.

Then we get really sophisticated, especially if we are hand loading our ammunition. 50 rounds, in a blue plastic box, the first 5 sets of 5 rounds varying powder charge by a few tenths of a grain, the second varying bullet seating depth. We shoot our 10 groups and look for trends, and we see the groups open up or close down in a manner that appears to vary proportional to the change in the parameter of interest. And who doesn’t love a good looking target after a trip to the range.

I’d seen some interesting measurements of group statistics that got me thinking. Extreme spread was never completely satisfying from a practical point of view, and achieving a small extreme spread had become more like winning a football game than providing meaningful feedback about the outcome of a shooting session. Here’s where things could have gone one of a couple different directions. If I were to keep on keeping on, business as usual, keep chasing MOA and sub-MOA 5-shot groups with extreme spread as the metric, I start to run the risk of fooling myself. Fliers are the shooters equivalent of Mulligans in golf, and we use “called fliers” as a means to tighten up the group size. I find called fliers very unsatisfying and if the group didn’t stay together, it didn’t stay together and that was that. Still, not enough useful information.

Not surprisingly, all these shooting sessions, all this data, and it’s clear there’s more meaningful information. The problem of measuring shooting accuracy clearly has a statistical nature, and concepts like mean and standard deviation, already long in use when thinking about muzzle velocity, must be applicable in some way. The internet knows everything and Bing searches quickly lead to Ballistipedia. Go there and you will find the application of some serious statistical expertise to the problem of thinking about and measuring rifle accuracy. The problem turns out to be a lot more complicated and nuanced than I thought.

Once I got through my five stages of grief, having given up the old and beloved way of thinking about accuracy, serious study of the proper way to analyze the measurements of little holes in paper began. It took me a couple months of part time study, but I finally gained a good understanding of the statistics of measuring rifle accuracy. The problem is complicated and I think the subject is not one that is suitable to most shooters who just want to know the practical accuracy of their weapons so they can be aware of what shots are reasonable for them to take, and what is the probability of a given outcome.

Getting back to the beginning of this post, as a company that sells rifle barrels and components, we want to be able to tell our customers what level of accuracy they can expect from our products. Now we know there is no meaningful answer to the question “Will my rifle shoot MOA groups?” The hope is for a sea-change in the way rifle accuracy enthusiasts think about and discuss their topic. The methods presented at Ballistipedia are correct but not generally accessible, and the practical implications of the results of detailed statistical analysis of shooting data are hard to discern. A system is needed that boils down the results of the statistical analysis of a sample of shooting data into different classes of performance. Once a weapon and ammunition combination has been classified, the shooter can easily assess the likelihood of a particular outcome of a hypothetical scenario. The shooter can know how likely they are to shoot a 5-shot group with MOA or better extreme spread. They can also know the probability of any given shot being within 1/2″ from the true point of aim. They can also know how many shots are needed to get a good estimate of the true point of aim of their weapon so that they can achieve a good zero for their scope.

To this end, Bison Armory has worked with Ballistipedia.com to create the Ballistic Accuracy Classification system.

We are still working to classify our barrels, upper assemblies, and rifles, but to start we guarantee that our products are at least Class 5 as defined in the BAC system. In practical terms, this means a shooter can expect at least 39% of their shots to fall within 1/2″ of the true point of aim, 9% of 5-shot groups to measure 1″ or better extreme spread, and 35% of 3-shot groups will achieve this measure. Our data indicates that our products are probably typically Class 4 but we’ve not gathered enough data yet to make a guarantee i this regard. For Class 4, a shooter can expect 54% of their shots to fall within 1/2″ of the true point of aim, and 26% of 5 shot groups will have a mean radius of 1″ or smaller, and 57% of 3-shot groups will be this small.

Our match grade, heavy barreled, and Fulcrum products should approach or achieve Class 3 status with the right ammunition. Of course, the true classification of a given barrel in practice will depend on the quality of the build, the ammunition used and its suitability to the weapon, the setup and performance of the shooter, the trigger, the total weight of the weapon, the quality of the optics, the tightness of the fit between upper and lower receiver, and other factors.

Once you know the class for your weapon, you can know with confidence important metrics like the probability of hitting a given target at a given range with a single shot.
No other rifle manufacturer we know of goes to these lengths to give a meaningful accuracy guarantee for their products. It takes time, it takes commitment to the truth above marketing, and it takes dedication to rifle shooting as a discipline. Don’t be fooled by phony accuracy guarantees. Demand the truth, embrace the truth, and then every shot will count.