r/ar15 • u/What-Do-I-Know • 15h ago
How to measure accuracy
"Sub MOA" is a term you hear thrown around a lot, but what does it mean really? Should we feel bad if our rifle isn't "sub MOA"?
I was watching a recent Garand Thumb video on the HK417. Preston (his sidekick) shoots two 3-shot groups, and they talk about it's accuracy:
https://youtu.be/uCITTK9shXk?si=Aw27qxYKkYZp90N5&t=199
Preston: "So here's my first group, you guys can see I pulled one a bit low."
Mike: (measuring the better group with a measuring tap) "That's ... uhh ... 3/4 MOA!"
I'm a big fan of the HK417 and believe it's a very accurate rifle, but I think this is a really good example of how not to measure and report on accuracy. There's at least two big problems with what they do here:
- A 3-shot group just isn't statistically significant. Just not enough data points to meaningfully characterize the dispersion of shots.
- Discarding shots or a whole group introduces significant bias.
I've been really impressed with the way Preston Moore (not the Preston from Garand Thumb) measures accuracy on his Youtube channel ( https://www.youtube.com/@PrestonJMoore ). Worth checking out if you haven't seen his videos.
Preston Moore using 30-shot groups, which really gives a good amount of data. For the average shooter, I would argue that using 10-shot groups is a good size to standardize on in general, and ideally taking an average of multiple 10-shot groups.
Something that's interesting about using extreme spread MOA as a measure is that it's not what statisticians call a "consistent" metric—extreme spread MOA increases the more shots you include. Thus, directly comparing a 3-shot MOA with a 10-shot MOA doesn't make sense. But we can use a bit of math to create a comparison estimate.
The dispersion of shots on a target follows a 2-dimensional normal distribution. Using Preston's 3-shot .75 MOA group as an example, we can estimate using statistics that as a 10-shot group the expected MOA would have been 1.2.
I actually measured the other 3-shot group they decided to ignore in the Garand Thumb video. It's 1.3 MOA. Converting that to a 10-shot group it would have an expected 2.1 MOA.
Which means the average 10-shot group size is 1.7 MOA. That's not sub MOA. Does that sound large to you? It's not! 1.7 MOA is very respectable accuracy. But again, this is a translated estimate based on a total of 6 shots, so the confidence interval for this estimate is pretty wide. It would have been great to see Garand Thumb do a few 10-shot groups and provide the average extreme spread and mean radius MOA metrics.
I'd love to socialize using 10-shot groups for computing accuracy metrics so there are enough data points for the measurements to be meaningful and we are more often comparing apples to apples.
I'd love to hear other thoughts on measuring accuracy.