{"id":1620,"date":"2019-12-27T11:49:31","date_gmt":"2019-12-27T16:49:31","guid":{"rendered":"https:\/\/david.bookstaber.com\/Interests\/?p=1620"},"modified":"2023-12-28T16:56:46","modified_gmt":"2023-12-28T21:56:46","slug":"understanding-gun-precision","status":"publish","type":"post","link":"https:\/\/david.bookstaber.com\/Interests\/2019\/12\/understanding-gun-precision\/","title":{"rendered":"Understanding Gun Precision"},"content":{"rendered":"

I’ve written a number of posts over the years in which I test the precision of various firearms<\/a>. Some readers have asked about the particular methodology I use.<\/p>\n

When testing guns for accuracy it is common practice to look at the Extreme Spread<\/a> of a group of 3 or 5 test shots. I will explain why this is a statistically bad measure on a statistically weak sample. Then I will explain why serious shooters and statisticians look instead at some variation of circular error probable<\/a> (CEP) when assessing precision.<\/p>\n

It is easy to fool yourself with Extreme Spread, and it\u2019s even easier to fool others.<\/strong><\/i><\/center><\/p>\n

First, note that even the most precise rail gun will occasionally print a \u201cflier.\u201d If 99 out of 100 shots nestle into a dime group, but one breaks away by an inch, would you characterize the accuracy of that gun as shooting one-inch groups? Now pick up a rifle, pop in a 100-round beta mag, close your eyes, and empty it from the hip. There\u2019s a decent chance that some 3 of those shots will be touching at 100 yards. But does that tell you anything about the precision of the rifle? The answer to both questions is \u201cof course not.\u201d And it gets worse: Why not crop one of those cloverleaf shot-from-the-hip groups and share it online. Then tell everyone your rifle shoots like that \u201call day long.\u201d Well not you<\/em>, of course.<\/p>\n

You probably want to test your mettle and your gun\u2019s metal and really figure out how precisely you can shoot. Maybe your manufacturer gave you a \u201c1-MOA guarantee,\u201d by which they (typically) mean that your gun will shoot a 3-shot group into 1\u201d at 100 yards with quality ammo. So you hit the range, tighten your scope, and fire three shots at the same point. Bingo: You don\u2019t need calipers to see that they\u2019re within an inch of each other. You\u2019ve really got a sub-MOA<\/a> rifle!<\/p>\n

Well you\u2019ve got a full box of ammo, so why not knock the center out of that pretty little group? You take another shot and, damnit, it goes wide. (You\u2019ll have to crop that group pretty tightly to show it off now!) But everyone knows you can call fliers, so you take a breath and try some more. Before you\u2019re through with the box you will probably notice something unfortunate:<\/p>\n

The more shots you take, the wider your group tends to get.<\/strong><\/i><\/center>Here’s a real-world target showing 20 shots at the same point of aim:
\n\"20-shot<\/a><\/p>\n

Now something doesn\u2019t add up here. The manufacturer guaranteed your rifle would shoot three shots within 1 MOA. But neither they, nor you, nor your gun could predict which order the shots in that group would appear. If your gun is really sub-MOA you should be able to pick any three at random as your \u201cgroup\u201d and it should measure under 1 MOA. You\u2019ve just discovered one of the industry\u2019s inside jokes: Accuracy guarantees expressed in terms of finite shots are either impossible or meaningless.*<\/sup><\/p>\n

You\u2019ve also discovered one of the problems with the Extreme Spread: It all depends on the number of shots you take. Worse yet, it doesn\u2019t differentiate between a target where most of the shots are in a tight group and there\u2019s a lone \u201cflier,\u201d and one with the same Extreme Spread but with every shot scattered about the same distance from the center.<\/p>\n

If you kept your sight zeroed and logged every shot taken with a given rifle and lot of ammunition, after 1000 shots your aggregated target would look something like this:<\/p>\n

\"1000<\/p>\n

(Here the dots represent the center of each hit, not the size of the holes cut by the bullet.) We\u2019ll call this picture a sample \u201cdistribution<\/a>\u201d of shots. It doesn\u2019t matter how accurate or inaccurate your gun: the mathematical distribution of its shots is the same as the one that produced this sample. The only thing that varies with accuracy is how large or small this cluster is. The red circle is drawn around the center of the distribution and contains exactly half of the shots in the picture. The radius of that red circle is called the Circular Error Probable (CEP), and that single value is sufficient to characterize the accuracy of a gun. Some real-world CEP values:<\/p>\n