Optimal power of a boxing punch - how important is mass?

The important thing for knocking someone out is what kind of acceleration can boxer produce in opponents head for certain amount of time.

The force he exerts is basically immaterial. If his opponent would be quick enough to accelerate his own head to dodge the punch, the exerted force would be zero. But doing so, the opponents head acceleration can become so high, he would basically knock himself out, without the first boxer even exerting any force on him.

If the opponent gets very relaxed, even modest punch power can knock him out. That is because the whole force that boxer exerts on him is used to accelerate only head. If the opponent gets fully rigid, then the boxers punch will accelerate his whole body, not only his head and because $F=ma$, the acceleration would become proportionally smaller and this time, the boxer might fail to knock his opponent out.

The next thing to knock someone out is to keep this acceleration high for longer time. Imagine having very high acceleration for very short amount of time. Say, the whole punch will be done on the length of 0.1mm. If the acceleration is high enaugh, such punch would break the tissues in the impact area, but the broken tissues would not transfer gained momentum further to the brain and the opponent would not be knocked down. He might have hole in his face, but he would remain standing. The acceleration thus needs to be low enaugh so that tissues will hold and thus could transfer the momentum further into the body (that is the reason for wearing boxing gloves). But this transfer process takes time and if you stop the acceleration too soon, before the effect of the punch influences the brain, the punch is already over.

The higher the speed of the punch, the higher the initial acceleration produced by the punch. But because of the punch recoil (which is enhanced by boxing gloves) the punch might get decelerated too quickly to produce enough effect on the head. The boxer needs to keep the punch steady for as long as is needed and for this, he needs to back up the punch by enough force/inertia. That is why boxer needs to make himself as rigid as possible and stand in a good position - because this will back up the punch by whole bodies inertia and strength and the effect of recoil gets smaller. And that is why boxers are told that peak of the punch should not happen at the impact, but few centimeters behind it.

The impact force is not as important as keeping the arm in steady movement after the impact - and this is where power of the punch has advantage over speed.