the old hype button
Almost anything you add to a stick dampens vibration. The rubber pad at the back of the butt does indeed have an effect on overall vibration and harmonics. It also increases dwell time of the tip on the cue ball. Any added weight will do that.
Now for the real question: What do we gain? We gain rear weight on the cue, a dubious advantage. We gain some dwell time of the tip on the cue ball. This could be a real benefit if it was enough to be significant, my bet is that it isn't. We dampen vibrations.(harmonics) I have no idea of the speed at which the harmonics pass back and forth through a cue stick but this may or may not matter. The primary harmonics pass back and forth through a rifle barrel several times before the bullet leaves the barrel making tuning the harmonics tremendously effective to increase accuracy. I have seen rifle accuracy increase tenfold by tuning harmonics. If, and this is a very large IF in my mind, the limbsaver dampens harmonics while the tip is still in contact with the cue ball this could be of benefit not by increasing accuracy but more efficient transfer of forces between the stick and cue ball.
The possible improvements are better transfer of forces between the stick and cue ball, a change of balance point, and a change in the feel of the hit that some players may prefer.
The possible losses are moving the balance point back on a cue that is well balanced now and changing to a less desirable feel. Also I don't see how much it weighs and adding only a few ounces of weight to a cue usually changes how it plays a huge amount even without changing the balance. Then there is the final negative: Unless you play better than Efren, everyone in the place including me, is gonna laugh at that thing more than the pink glove some guy is wearing!
I think that the limbsaver is hokum on a pool cue. On the other hand, a door knob on the end of a rimfire rifle barrel can work miracles. Some of us will have to pay to find out. You won't find me anywhere near the front of that line!
Hu