When our hop-ups were properly set we consistently experienced higher FPS than when they were backed off. I'm not going to claim that every gun is gonna react this way, but all of ours did.
As for the beer can analogy, that's not even close the physics of what's happening. Throwing a solid object at a solid object is not the same as having a sphere pass by a soft surface giving it enough backspin to increase its trajectory 2x, 3x, 4x, etc.
To be fair, I just ran a test on my gun.
PTW M4 CQB, X-Cortech 3500 Chrono, BB Bastard 0.20g
Hop-up ON: 396.29
Hop-up OFF: 390.87
PTW M4 CQB, X-Cortech 3500 Chrono, Elite Force 0.28g
Hop-up ON: 334.08
Hop-up OFF: 340.35
So oddly enough, using a 0.20g I'd get a consistent 5 FPS or more increase with hop-up and the exact opposite with 0.28g. I'd be interested to see what anyone else gets.
ďREALITY IS LIKE A STONE. TO MANY ITíS HARD AND COLD, THEY CANíT HUG IT OR EAT IT, IT ONLY FRUSTERATES THEM AND DOESNíT DO THEM MUCH GOOD. TO OTHERS ITíS STRONG AND DEPENDABLE, YOU CAN BUILD WITH IT, BUILD UPON IT, OR WORK WITH IT, ALSO USE IT TO SMASH PEOPLE IN THE FACE.Ē