Rocketman, I do know that I have never missed a target or bird because the pattern was at fault! And I can prove that rigorously for anyone who wants to take me hunting.

After about a century or more of various experimenters endeavoring to mathmatically define performance of shotguns, chokes and their various shapes, shot sizes and composition plus duplexing, pressures, velocities, rates of acceleration,shot stringing, wadding with all it's variables, forcing cones with lengths and shapes, chamber dimension variation, weight to bore ratios, buffers, burn rates, priming compound brisance, bore condition, rifling straight or twisted, phases of the moon, northern or southern hemisphere vortex influence and sundry other real or imagined variables; the national budget could be fully consumed without resolve. So my flippant response above may actually be mankind's best shot at ever fully grasping effective shotgun performance. The answer is to be found in Mona Lisa's smile. It is what you believe it to be.