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Rifles, Reloading, Optics, Equipment
Rifles, Bullets, Barrels & Ballistics
# of Shots per Group and MOA - Results
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<blockquote data-quote="speedengineer" data-source="post: 1940561" data-attributes="member: 112986"><p>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. </p><p></p><p>All of us know that including more shots per group provides a more accurate estimate of the rifle/shooter accuracy...but how much so?</p><p></p><p>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:</p><p>[ATTACH=full]203233[/ATTACH]</p><p>^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. </p><p></p><p></p><p>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:</p><p>[ATTACH=full]203241[/ATTACH]</p><p></p><p></p><p>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:</p><p>[ATTACH=full]203235[/ATTACH]</p><p>^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. </p><p></p><p></p><p>For kicks, here is that plot again, but using 5-shot groups. There are way more possible 5-shot combinations, 6188 in fact. </p><p>[ATTACH=full]203236[/ATTACH]</p><p>^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. </p><p></p><p></p><p>And, here it is for 10-shot groups. 19,488 possible combinations on this one.</p><p>[ATTACH=full]203237[/ATTACH]</p><p></p><p></p><p></p><p>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. </p><p>[ATTACH=full]203238[/ATTACH]</p><p></p><p>[ATTACH=full]203240[/ATTACH]</p><p></p><ul> <li data-xf-list-type="ul">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. </li> <li data-xf-list-type="ul">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. </li> <li data-xf-list-type="ul">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...</li> </ul><p></p><p>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?</p><p></p><p>Oh, and also....Will someone please tell me what MOA my rifle shoots? <img src="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" class="smilie smilie--sprite smilie--sprite2" alt=";)" title="Wink ;)" loading="lazy" data-shortname=";)" /></p></blockquote><p></p>
[QUOTE="speedengineer, post: 1940561, member: 112986"] 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: [ATTACH type="full" alt="17 shot group.png"]203233[/ATTACH] ^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: [ATTACH type="full" alt="3 shot group.png"]203241[/ATTACH] 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: [ATTACH type="full" alt="3-shot Histogram.png"]203235[/ATTACH] ^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. [ATTACH type="full" alt="5-shot Histogram.png"]203236[/ATTACH] ^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. [ATTACH type="full" alt="10-shot Histogram.png"]203237[/ATTACH] 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. [ATTACH type="full" alt="Average.png"]203238[/ATTACH] [ATTACH type="full" alt="Minimum.png"]203240[/ATTACH] [LIST] [*]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... [/LIST] 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? ;) [/QUOTE]
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# of Shots per Group and MOA - Results
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