The reason recoil applied to the shooter decreases is that the amount of energy absorbed by the pad is turned into the heat of compression, and is not conveyed to the shooter.
Also, lengthening the time of collision spreads the same energy pulse over a longer time.
So the peak is lower for the same energy input.
A somewhat fascinating comparison is the difference of a very light weight person, and a very solidly built person shooting the same load, it is easier for the gun to accelerate the lithsome person in reverse, further decreasing the felt recoil because of the length of time involved.
All quite academic, because all we really need to know is, yes they work, and do you like how they look?
Thanks for the right answer! Of course the recoil pad absorbs some of the energy, and the better the pad, the more it absorbs and the less that hits your shoulder.
I think everyone understands this instinctively if you will just think about it. If you want to really reduce the recoil, use a much better "pad." The best one I've found is an old horsecollar style life jacket. It's several inches thick and constructed in a way that it's easy to fit it between the gun and shoulder if you have to do a lot of stationary shooting with high recoil shells. I have used one when testing turkey loads and it reduces the recoil to almost nothing. The life jacket is absorbing recoil and also spreading what remains over a wider area. Arecoil pad isn't as good as the old life jacket, but I've been surprised by how good some are.