There are I know many out there with more mathamatical abilities than I. However it is my understanding a normal bbl time for a shotgun is on the order of .003 sec. Assume a 1 1/8oz charge with a combined shot & wad weight of 60 grains, fired from a 7lb gun. During that .003 second while the charge travels the length of a 218" bbl the gun will have moved (If in Free Recoil) approx 5/16" & attained it's recoil velocity. The rest of it's movement is from inertia. Personaly, I am extremely thankful that I am so totally insensitive, that from the same gun acheiving the same ballistics I can't tell if it's using Pink dot, Purple dot, & has ½" or 5½" cones.
I simply do not have the means of proving it one way or the other, but am extremely confident that such things as recoil pads, hydro-coils, gas operated autos etc which acheive lower "Felt Recoil" do so by spreading it out over a longer time frame than that .003 sec, or they are still working in the "Inertia Stage".