Group size: Moving towards using 10 shot ATC instead of ES

[P2000]

Exploring the idea of how to relate this new standard of measurement to the existing standard of using ES to estimate rifle/shooter/ammunition combination accuracy...

It is difficult to compare ATC to existing ES numbers. Some in the posts above have suggested doubling the ATC will yield a quantity that is more closely related to the ES numbers currently thrown around for comparing accuracy. I think this is a step in the right direction, but perhaps adding another factor in the mix will give a more complete story when relating this metric to others.

The ATC is a measure of the standard deviation of each shot from the center of a group. Another way of saying this is that it is also the length of the mean radius; an average of the lengths of the radii from the center of the group to each shot. Well, as a collection of radii, these also have a standard deviation themselves. I think that adding the ATC quantity to 2x the standard deviation of the radii themselves, then doubling that entire quantity would give a metric which more accurately measures overall accuracy, yet more closely indicates the largest possible group the rifle/shooter/ammo will produce (corresponding more closely to ES measurement).

What this number is, effectively, is the diameter of a circle which 95.4% of all shots taken by a shooter using a given rifle and ammunition combination will fall into. 95.4% comes from using two standard deviations of the average-to-center radius length.

Good idea, or am I over-complicating this? The reason for all this is that I think this number is more comparable to our traditional ES numbers, and gives a better idea than ATC alone of what we'd measure on a given day if we took a caliper to a group of shots on our targets.

Illustrated below...

That is a pretty awesome use of statistics! However, I think it serves a different purpose and is too cumbersome to simply measure precision. Using your method a statistician could make statements like "Under x conditions, a 1 foot diameter circle could be hit 87% of the time at 800m", giving soldiers an idea of what their equipment is really capable of. Pretty neat, but I would have no use for it. Trying to hit targets is another issue, with far more variables than just inherent precision of your equipment.

Part of the appeal of using the ontarget.com software and a 10 shot ATC is that it is very easy to do, and it is in my opinion the minimum necessary to evaluate precision. I think the role of this measurement is to do things like load development, comparing brand x ammo to brand y ammo, seeing if your new SPR is more accurate than your other rifle, see if your barrel really is starting to group poorly ect. That is it, just a simple tool to answer a question.

[twadsw01]

I agree with you, P2k, on the basis of simplicity-of-measurement. I think that if you're using the ATC on your own (in a world of people who talk about accuracy using ES as their chief metric) as a way to compare ammunition, your rifle's track record over time w/ regards to accuracy, and the like, then there's no need for the extra calculation I described. Simply plug photos of targets into the software, easy as it gets, and you have a more meaningful indicator of "accuracy" than ES.

I think I was simply trying to figure out a way that our numbers figured using the ATC method could be put in terms that are more comparable to ES numbers people typically quote to describe their rifle's accuracy, their shooting ability, and/or their handload's accuracy. As some have pointed out, for people who have always measured groups by using ES, the ATC numbers don't really have any meaning until they've spent time own their own measuring their own targets this way. That way, they build up a little bit of an intuition around how ATC corresponds to ES.

All I've described in the above posts is pretty much a scaling-factor to apply to ATC to get something corresponding better with ES, although a little more informed than simply multiplying ATC by two. So, it's really no less useful than describing accuracy in terms of ATC - just more intuitive for people used to ES measurements. That's all. Still describes accuracy of the rifle/shooter/ammo combination, like ES and regular ATC do.

Biggest thing, as shootist said earlier, is that all of this is wayyy too complicated for people who don't want to photograph targets and import the photos into software for measurement. If that's off the table, then ES wins every time because of its simplicity.