Stan, IMO, uou have communicated a good question very accurately! The answer is a qualified "Yes." I say qualified because the calculation is not simple, not at all. The reason is that patterns never have a uniform distribution of shot. The pattern always exhibits a Rayleigh distribution; the same distribution as governs bomb patterns, artillery fire, and rifle fire. It is fair to think of a shot pattern as a "bunch of rifle bullets all fired at the same time." Rifle fire would make a smaller pattern, but the distribution within the pattern would be the same 'ole Rayleigh distribution.
We can make a passable SWAG (note that this is not the real statistical calculation, but it will do for illustration) by saying that the .410 will have about 11/18 (11/16 / (18/16)), that is 61%, of the effective area of the 12 bore. Lets say, for grins, that at the distance and with desired choke, the 12 has a 24" effective diameter; that is 452 square inches. The .410, then, has 61% of 452 = 276 square inches. The radius for 276 is the square root of 88, which is 9.4 inches. So, the diameter is 2 X 9.4 = 18.8". Note that your aiming error with the .410 must be not worse than 78% of aiming error with the 12 bore. As you can see, the situation for the .410 is not as bad as is often presumed.
Hope that helps. BTW, post back if you need more detail with the math.
DDA
Last edited by Rocketman; 03/06/13 11:46 PM.
