speedengineer
Well-Known Member
I just did a bunch of math to understand how group size depends on the number of shots per group. I found the results interesting and wanted to share in case some here find it interesting as well.
All of us know that including more shots per group provides a more accurate estimate of the rifle/shooter accuracy...but how much so?
I went to the 100 yard range and shot 17 rounds, each at a different black dot on the target. I used calipers and recorded the X and Y coordinates for each shot. Plotting those coordinates gives me a group that looks like this:
^Pretty much exactly 1 MOA. I was happy with the results, but was wondering what the group sizes would have been if I had shot a bunch of 3-shot groups instead of 17. If I use my actual shots in the order I fired them, and split them into five 3-shot groups (and throw away the last two), each group would have had these MOA values: 0.65, 0.26. 1.0, 0.84, 0.72. Clearly I wouldn't call this a 0.26MOA rifle, but one of my 3-shot groups would have been that small.
If I take 3 of the 17 shots at random and plot them, they will make a group of equal or smaller size. Here is an example:
We can take this process a step further. For 17 shots, there are actually 680 possible combinations of 3-shot groups. I calculated the group size in MOA for each one of these programmatically. The distribution of group size for these 680 groups looks like this:
^Clearly most of the 3-shot groups would have had a diameter between say 0.4 and 0.9 MOA. But, the smallest group possible from my data was actually 0.15 MOA. Obviously, the maximum 3-shot group MOA will equal the full 17-shot group size, since it will contain the worst 2 or 3 shots.
For kicks, here is that plot again, but using 5-shot groups. There are way more possible 5-shot combinations, 6188 in fact.
^Including 5 shots removes most of the possibility of getting crazy small group sizes. Most groups would have ranged between 0.6 and 1 MOA.
And, here it is for 10-shot groups. 19,488 possible combinations on this one.
I ran this program for every shot count from 2-shots per group up to 16-shots per group. Below are the average and minimum group sizes observed as a function of shots per group.
Hopefully I explained my thoughts in a way that is at least slightly clearer than mud. Let me know what you think. What method do you all employ when you label a rifle as "x" MOA?
Oh, and also....Will someone please tell me what MOA my rifle shoots?
All of us know that including more shots per group provides a more accurate estimate of the rifle/shooter accuracy...but how much so?
I went to the 100 yard range and shot 17 rounds, each at a different black dot on the target. I used calipers and recorded the X and Y coordinates for each shot. Plotting those coordinates gives me a group that looks like this:
^Pretty much exactly 1 MOA. I was happy with the results, but was wondering what the group sizes would have been if I had shot a bunch of 3-shot groups instead of 17. If I use my actual shots in the order I fired them, and split them into five 3-shot groups (and throw away the last two), each group would have had these MOA values: 0.65, 0.26. 1.0, 0.84, 0.72. Clearly I wouldn't call this a 0.26MOA rifle, but one of my 3-shot groups would have been that small.
If I take 3 of the 17 shots at random and plot them, they will make a group of equal or smaller size. Here is an example:
We can take this process a step further. For 17 shots, there are actually 680 possible combinations of 3-shot groups. I calculated the group size in MOA for each one of these programmatically. The distribution of group size for these 680 groups looks like this:
^Clearly most of the 3-shot groups would have had a diameter between say 0.4 and 0.9 MOA. But, the smallest group possible from my data was actually 0.15 MOA. Obviously, the maximum 3-shot group MOA will equal the full 17-shot group size, since it will contain the worst 2 or 3 shots.
For kicks, here is that plot again, but using 5-shot groups. There are way more possible 5-shot combinations, 6188 in fact.
^Including 5 shots removes most of the possibility of getting crazy small group sizes. Most groups would have ranged between 0.6 and 1 MOA.
And, here it is for 10-shot groups. 19,488 possible combinations on this one.
I ran this program for every shot count from 2-shots per group up to 16-shots per group. Below are the average and minimum group sizes observed as a function of shots per group.
- Basically, it looks like if you want to shoot small numbers of shots per group, then you'll want to shoot several groups and take the largest group size to be your rifle/shooter accuracy.
- If you want to shoot single groups containing more shots, then once you get up to 6 or 7 shots, you've recorded (on average) ~80% of your rifle's true group size. Well, true 17-shot group size, anyway.
- Looking at the minimum plot - If you shoot only a single group, then it is possible that you could be deceiving yourself unless that single group has a lot of shots in it. Maybe for future work, I'll calculate the probability of this happening...
Hopefully I explained my thoughts in a way that is at least slightly clearer than mud. Let me know what you think. What method do you all employ when you label a rifle as "x" MOA?
Oh, and also....Will someone please tell me what MOA my rifle shoots?
