Indeed -- as number of groups goes to infinity, the outliers will be 3MOA and 1MOA, but the average "should" be as stated. This thread is a fascinating example of everybody being right, but in different ways, and talking "past" each other.

All of that, of course, assumes that the deviations are truly random (and thus, evenly distributed). They probably aren't, since there are certain phenomena that create these deviations. The result will likely not be random. I would guess that some of the deviations, such as a wobbling hold or inconsistent cheekweld, "tend" to produce linear deviations (rather than "planar", if that distinction communicates) such that you might well approach the "extreme case" of 3MOA more often than root-mean-square indicates.

Nevertheless, 3MOA is a "worst case" given the conditions. Math IS awesome, especially since it includes probability and statistics

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