Defining accuracy & precision

I posted this a while ago on M4:

Ask someone how "accurate" they want their rifle to be, and generally you will hear a response of something about "1 MOA", "Sub-MOA", or "nothing over 2 MOA", depending on application.

First things first: Accuracy vs Precision

There is a difference between "accuracy" and the size of a group (commonly called "precision").
For the moment, let's stick with the conventional lingo for this part.
In the simplest perspective, accuracy is simply hitting a target of a specified size.
Precision (in this context) refers to group size (more on that later).
This pic does a decent job of simplifying the concept:
http://cdn.antarcticglaciers.org/wp-...n_accuracy.png
So, you can be accurate, but not precise, and precise but not accurate.

Now, to get in the weeds about this, linking group size to precision is less descriptive than simply discussing "dispersion", that is, the distance between each point of impact. So, for the rest of this, I will be mostly discussing dispersion.

What is 1 MOA?

In the simplest terms possible, 1 Minute of Angle (MOA) is 1.047" at 100 yards, measured from the end of the muzzle.
This distance increases in direct proportion to distance: 2.094" at 200 yards, 10.47" at 1,000 yards, 3.42" at 327 yards, etc.
We, being lazy, tend to round this number to 1" per every 100 yards of distance. Frankly, it doesn't matter a whole lot, but it does let the guy that shoots a 1" group at 100 truthfully say that he shot a sub-MOA group, which makes people feel good about themselves.
If you want to know more about Minute of Angle (Minute of Arc, semi-technically), the world of Google is a click away.
Be warned: it's super boring, and won't help you shoot any better.

What is a 1 MOA group?

Well, the first question that you didn't ask is: by what measuring convention?
Your reply to the question you didn't ask is most likely something about the distance between the two furthest away shots in a group.
That is the most common approach to measuring groups, and is called "Extreme Spread".
(Note: that is also the nickname of my high-school best friend's sister)

ES is good in the aspect that it is very easy to measure.
ES is bad in that it doesn't really tell you much about the group.
How so?

Let's look at these two groups I happened to have readily available:
http://i296.photobucket.com/albums/m...202010127c.jpghttp://i296.photobucket.com/albums/m...f97758054a.jpg
Which is the best group?

Most would consider the one on the left/top (depending on browser display) to be the "better" group, and would attribute the high shot to an ammunition or shooter issue, which it very well may be, but they will then discard that shot from the data set, which is not good at all. There is no point in gathering data and then throwing out the bits that you don't like. Now, if the shooter called the shot as off, BEFORE SEEING THE IMPACT, then it isn't such a problem to dismiss the shot. That said, something that far out would be readily apparent to the shooter if at magnification.

Anyway, if you are using ES as your sole data point for group comparison, the right/bottom (depending on browser display) side group would be better, at around 0.95 MOA, with the left group at around 1.55 MOA, even though 4 of the rounds are in a .5 MOA cluster.

Is there a better way?
One could use Average Mean Radius (aka Average to Center) as a method to discuss group sizes.
The concept is that instead of talking about the extremes of the group, we discuss the average distance from the center of the group to the individual holes. AMR minimizes anomalies, but can be misleading when talking to someone that is thinking in ES.
Molon has written up the "hows" and "whys" of this pretty well, and of course, Google is your friend for learning more about it.
Short story: if you get the "On Target" software, you can do this fairly easily at home, but you need a computer and some savviness to do it.
ES is pretty easily done with just a ruler.
So, is AMR better than ES?
No, it's just different. But better. Kind of.

Here is what On Target will give you:
http://i296.photobucket.com/albums/m...p/ACCEX1OT.png
Max is ES, ATC is AMR

Moving on.

So what criteria makes for a "1 MOA" gun?
Lots of dudes will go out to the range, shoot a bunch of groups, find the one that looks the smallest, measure it, and declare that they have a "sub-MOA" gun.
Of course, they disregard all of the 1.5-2.5 MOA groups that they shot before and after that group. While they very well may have a 1 MOA gun/ammo combination, they do not have the data to support that claim.

If they have a rifle that shoots 9 groups that measure 0.9", but 1 of 1.9", is that a "Minute Gun"? Sure, it might average 1 MOA, but is that really in accord with the impression given when one claims that they have a 1 MOA rifle?

Groups Shift.

Yup, they do. Get over it.
Where a bullet will go when fired through a cold, clean bore will be different than where shot 529 will go.
How much the Point of Impact (POI) will shift will be greatly linked to the condition of the bore and temperature of the barrel.
Steel expands when heated and contracts when cooled. Shooting faster will push more heat into the barrel steel.
Copper and fouling will change how the bullet interacts with the bore, and how much the jacket is deformed.
Every shot taken through a barrel is unique.

I tend to prefer barrels and complete systems that show the least amount of group to group shift after fouling.
Kinda showing my hand here, but I would rather have a 1.5 MOA gun with 0.5 inches of shift than a 0.5 MOA gun with 1.5 inches of shift.
I'll let you ruminate on that before addressing it directly.

How much shift happens?
With one particular adopted Army sniper system, the specified allowable shift is 1.1" at 100 yards over 4 groups.

So what?
The only way to know what the gun actually shoots is to compare numerous groups.
The single most important aspect is the center of the group, and where your statistical center lies in relation to your desired point of impact at a stated distance.
Why?
Because each group is unique, and represents a very small data point when it comes to really knowing what the gun shoots. That is, until it is time to use that rifle in the defense of life.
What the individual group sizes are is almost irrelevant. Any of those individual groups could have any of the others' ES or AMR, and those numbers mean nothing practically if they don't go where you need them.

How many rounds to shoot in a group?
There are pros and cons to 5 and 10 round groups.
3 round groups tell you pretty much nothing useful unless you overlay around 10 of them, and frankly are too limited to really give a good indication of group center, which means that it gets harder to accurately track group shift from POA.

10 round groups are good, in fact I used to prefer them, and still do for non-precision low recoil guns. They get a little tiresome after the first 3 or 4, and can start showing heat effect more than baseline precision and shift. Shooter error with 10-round groups usually isn't a big deal right out of the gate, but when you get into the 200 round area shooter fatigue becomes more of a thing.

For dispersion and group-center shift, I prefer 5-round groups. A single 5-round group on its own is indeed a data point, but that data needs to be populated with several (at least 4) groups to accurately indicate anything usable.

This comes around to zeroing.
After my initial zero, I won't touch the turrets until I have at least 4 groups from which to determine actual group center.
If the group center isn't consistent with regard to point of aim, I want to check heat, and will generally shoot 4X 5-round groups, with enough time between strings to allow the barrel to cool.
If the group centers become more consistent, I do a heat work-up, shooting 40 to 50 rounds in 5-round groups with only enough time between groups to ensure good natural point of aim and correct position/NPA.
If the group to group dispersion does not improve, I at least know that the issue is probably something other than heat.

When it comes to data collection, I am more interested in group centers in relation to the POA than I am in individual group size. After shooting the gun for a while, I know what the groups should look like, and anything weird (large) gets noted

So what is a 1 MOA gun?
A true 1 MOA rifle would be capable of consistently placing the center of every round fired within 0.5" of the intended point of impact at 100 yards, for multiple groups, with the same POA for all groups, with the only changes to POI being made by environmental factors.

Like I have said before: there aren't too many of those rifles in the world.

In the end, I don't really care about claiming to have "sub-minute" guns. I expect on-demand performance.
A 1.5" gun (no group size over 1.5" ES, or no shots further from the center of any individual group than 1") with group to group shift of less than 0.5" is an exceptional performer, and frankly, of higher performance than most "sniper" rifles. This combination ensures that as long as I do my job, I will hit a 2" circle at 100 yards every...single...time.
This translates to a 12" target at 600 yards. Think of 100% success on a chest plate at 600.

Lets talk about that "0.5 MOA" gun with 1.5 MOA of shift:

It encourages a shooter to "chase zero". In this situation, the shooter puts out a nice group, and assumes that he did everything right, and therefore adjusts the optic to bring the group to the center of the target. He/she then shoots another group, and sees another good group, but outside the center of the target. So what do they do? Yup, crank away on the turrets again. Had that shooter simply fired 4 or more groups of 5 rounds and compared those group centers to the point of aim, he would be able to determine if the aiming device actually needed to be adjusted (group center average was not within 60% of a single click value) or if he is simply seeing the inherent group shift.

Most critically, is that it becomes very easy to overestimate performance potential, and wind up taking shots that the gun doesn't fully support. Shooter takes gun to range, shoots a bunch of the above .5 MOA groups and by chance happens to get his final group exactly where it's supposed to be. When it's time to take that .5 MOA shot, the group shift puts the projectile 1.5 MOA away from the intended impact point. Successive shots go around the same place, leading the shooter to adjust the optic/point of aim to achieve hits. Data for drop/wind (and truing) gets entered under the assumption that those variables, rather than inherent group shift, are responsible for the needed adjustment, which throws off the entire data set. This issue will continue to affect the data set (during following live-fire sessions) until sufficient data is accumulated and scrutinized with a careful and analytical eye.

All because you shot a 0.5" group that one time...