Rethinking Rifle Accuracy: What is Mean Radius, and Why Should We Care?

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Group size, not mean radius, has been the dominant method used to describe a rifle’s precision capability for more than a hundred years. Ask a hunter how accurate their favorite rifle is, and “three-quarter-inch,” “one MOA,” or simply “It’s an inch-shooting gun” will often be the response. Some will brag on “half-inch guns,” though in reality, they aren’t nearly as common as you might think. Hunters and shooters place great value, and often pride, in how accurate their rifles are — or how accurate they believe them to be. In hunting and shooting applications, some of this matters, and some of it doesn’t. Still, most of us define or visualize and verbalize rifle accuracy in terms of group size, but is that the best way? Maybe not. In fact, the only thing that group size (extreme spread, or dispersion) tells us is how far apart our worst two shots of a group were. Is there a more useful way to quantify rifle accuracy? Mean radius might just be the answer. The Information Age Mean radius isn’t new, but like many other existing concepts that seem revolutionary, it just needed a voice. Like virtually every other shooter, I always defined accuracy by group size, and mean radius wasn’t on my radar. Over the past 18 months, Hornady has put out several very informative podcasts that challenge the average way of thinking about rifle accuracy and load development. The information, presented by Senior Ballistician Jayden Quinlan and Project Engineer Miles Neville, is based on real data from their testing of thousands upon thousands of rounds to examine different topics. Their findings have resonated with many shooters and, in my case, completely changed how I think about rifle accuracy and load development. I listened to their episode on mean radius several times, and I’m embarrassed to only now discover how useful it is. Mean Radius: Defining Our Terms To understand the benefits of considering mean radius in rifle precision, we need to know what it is, and how it differs from group size. We shooters are chronically guilty of throwing out terms and measurements, whether we understand them or not, and this often leads to confusion. Many of the most heated debates are hashed out to the point of exhaustion, with the participants not even arguing about the same things or considering things on the same terms. For example, one shooter might say their rifle shoots half-MOA. His watchful range buddy might argue that it’s actually a one-MOA rifle. The resolution of the argument depends on how each is defining their performance standards. Does the rifle shoot some half-MOA groups sometimes or all the time? Is the average group half-MOA, while the extreme limits of its dispersion are more like one MOA? Clearly defining our terms and what they mean is key to getting our point across, but also key to maximizing our understanding. That said, here are a few terms that you should know:  Dispersion: the pattern, spread, or distribution of bullet impacts from a rifle — how the shots are dispersed. Extreme Spread: As it pertains to dispersion, this is the group size, or outer limits of the group, defined by the centers of the two shots that impact farthest apart. Mean Point of Impact (POI): The mean, or average, point of impact of an array of shots. In simpler terms, the mathematical center of a given group of shots — aka your rifle’s zero. Radius: The distance from the center of any given shot to the mean POI or, the distance by which a given shot missed the mean POI. Mean Radius: The average of all radiuses in a group, or average distance by which shots miss the mean POI. What Doesn’t Extreme Spread Tell Us? Like most other shooters, my entire definition of rifle precision and accuracy has been extreme spread, or group size. When every rifle review that I have ever read quantifies or scores accuracy by listing a group size average or group sizes, it’s easy for me to visualize what that looks like and relate it to my own rifles. Lots of rifle companies have MOA or half-MOA or three-quarter-MOA guarantees for their guns, and even though they aren’t as meaningful as they seem, it gives the customer a quantification of how they should expect the gun to perform — that’s the idea anyway. But what are some of the shortcomings of only defining precision by group size?  The reality is that group size or extreme spread doesn’t tell us that much about our rifle’s dispersion, only how bad the worst two shots were. It is true that despite that, shooters have relied on group size with some success. My line of thinking was always that if a rifle could shoot consistent sub-MOA groups at 100, 200, or 300 yards, I ought to be able to hit an MOA-sized target out to 1,000 yards and beyond. I believed that it defined the outer limits of 3- or 5-shot samples, which I could use to predict future performance. Hunters use it to estimate their maximum effective distances and hit probability. This works to a point, but it’s a grainy, fuzzy picture of what you can expect from your rifle. You could load up sample sets of two different test loads with different bullets or powders, hoping to select the better option. Both loads might print equal-sized groups, but that doesn’t mean they’re equal. Sometimes the group with a slightly larger extreme spread might actually be more accurate. Imagine shooting two 10-shot groups. The first group measures one inch, with the ten shots spread evenly around a one-inch circle. The second group has 8 or 9 tightly clustered shots, and one or two that make the group measure 1.1 inches. Mathematically, the second group is better, and mean radius will tell you that — especially where the results aren’t as obvious. Extreme spread only tells you how bad your worst two shots were, not what your whole group did. The Advantage of Mean Radius The benefit of considering mean radius is that every shot plays a role, not just your two worst. Knowing your average miss distance gives you a much more informative picture of your dispersion than just the extreme spread. Consider a result of some recent in-depth load development experimenting that I recorded. My beat-up old Remington 710 printed a 30-shot group (an aggregate of 3- and 5-shot groups) with an extreme spread of 3.75 inches. Pretty bad huh. In the rifle’s defense, the point of the experimentation wasn’t to find the most accurate bullet/powder combo, I just picked a bullet and powder. No hunter would ever want to admit their rifle shoots nearly 4 MOA, but hey, sometimes the truth hurts. Is the rifle un-usable for hunting? Let’s look further. Since I shot a large enough sample size to calculate a meaningful mean radius (you want at least 20 shots), what does it tell me? The mean radius for that awful 3.75-inch group was .904 inches. What does that mean? It means that the average impact was less than an inch off its mark at 100 yards. Is it a tack driver? No, but it’s not as bad as the overall group size might indicate.  When comparing groups of the same size, trying to suss out details or decide which is best, a better mean radius tells you that more shots in the group hit closer to the center. Some shots that we would normally write off or exclude as “flyers” are simply on the outer fringes of our rifle’s normal dispersion pattern — we just have to shoot enough times to see the image develop. If one group has a significantly worse mean radius, that means that shots are generally more spread out within that outer dispersion, compared to a generally tight-shooting group with a sparsely-populated outer limit. Shooting larger sample sizes and using mean radius as a tool to evaluate a given rifle and ammunition gives value to every shot, and it’s useful for considering hit probability — whether that’s for your back-forty hunting rifle or a hot-rod ELR rig. It’s a powerful tool for load development, constructing a high-definition picture of how ammunition shoots, where only considering group size is like watching black-and-white TV. Using mean radius with valid sample sizes gives you more detailed, useful information that just extreme spread. Calculating Mean Radius The key to obtaining a valid mean radius is to shoot a valid sample size. You, me, and every other shooter have always shot 3-, 5-, or maybe even 10-shot groups, but the mean radius of those sample sizes will vary too much to calculate a reliable mean radius. Once you get 20 or 30 shots in a data set, it starts to become a meaningful, statistically significant number. Beyond 50 shots, it shouldn’t really change at all.  Step 1: Shoot Your Groups Shooting 20- or 30-shot groups doesn’t seem ideal for most people, but there’s a simple solution. You can shoot smaller 3- or 5- shot groups and correlate your points of aim to calculate the total dispersion and mean radius. If you do shoot 20 shots at the same aiming point, make sure you’re far enough away that you can plot every impact precisely, not just create a hole. The advantage of a single large group is that you can let software quickly do all the calculating for you. If you’d rather shoot smaller groups at different aiming points, that works too. Shoot strings at different but repeatable points of aim, letting your barrel cool between groups like you normally would. Then you can either measure by hand, or use the software on a group-analysis app like Ballistic X or Hornady 4DOF to plot your shots, your aiming points, and let it do the measuring for you. I’ve found that there is a small amount of error in using these digital measurements (group sizes usually end up about .005 to .010 inches larger than I measure them with calipers), but it’s worth the time they save. Step 2: Measure and Tabulate After shooting your groups, you’ll measure them manually or digitally, but what are you actually measuring? Your goal is to tabulate your results in “X” and “Y,” or horizontal and vertical measurements from your aiming point at (0,0). Here’s that middle-school math coming back to haunt you. Knowing the X and Y distances of each shot from the aiming point allows you to calculate your mean point of impact, which will be an average of your X values and an average of your Y values. The next step is to calculate the radius, or straight-line distance between the mean POI and each shot. These ballistic apps do that for you if you’re using a single group, or you can plug them into a spreadsheet such as Google Sheets or Excel to compute the result of multiple groups. Worst case, you could do it all manually by measuring the distance from your mean POI to the center of each shot with calipers. The Hornady 4DOF app’s group analysis feature will calculate mean POI and mean radius for individual groups. It will also give you (X,Y) coordinates if you want to compile larger samples with multiple groups. Once you tabulate the radius of every shot, simply average them, and that’s your mean radius.  The easiest way to do all this is to shoot 20- or 30-shot groups at 200 yards, plot your shots, and let the apps spit out your mean radius for you, but because I also want to see how a rifle prints 5-shot groups at 100 yards, I usually opt to use the app to give me my (X,Y) coordinates for each shot of a group, then tabulate the next group — doing my radius and mean radius calculations in Excel. Unfortunately the group-analysis apps don’t currently allow you to combine different groups fired at different aiming points. FAQ What is the mean radius measurement? The mean radius of a group of shots is the average distance between each shot and the mathematical center of the group. How is bullet spread measured? Most often, bullet spread, or extreme spread is measured between the center points of the two shots in a group that are farthest apart. Mean radius is a calculation that considers how far each shot is distributed from the center of the group. What does SD mean for guns? For guns, SD means “standard deviation,” which is usually used when referring to velocity — but not always. Standard deviation is the average difference between each individual shot fired and the average of all shots fired — whether it’s velocity or mean radius. Valid SD calculations can give you an idea of the variability you can expect from shot to shot.   Final Thoughts on Mean Radius At Outdoor Life, we are constantly striving to improve the quality and information value of our gun coverage, and rifle accuracy is a huge topic. In today’s world of more accurate guns and better-informed shooters and hunters, simply dishing out a few group sizes isn’t good enough anymore. I don’t think that every hunter who fires a couple rounds from the same box of ammo to check their deer rifle before each season needs to be as infatuated with mean radius as I have become. But you should understand what it is, and how to interpret it.  Mean radius is an incredibly valuable tool for really understanding how a rifle is shooting, and useful for hunters, reloaders, and competitive shooters alike. Mean radius is one of the metrics that is revolutionizing and enriching the way we consider rifle precision and accuracy and, ultimately, makes us more informed.