In this way you are not so concerned with the hits or the beats, its when you or your opponent uses those hits or beats that mean anything to you. Now comes those half beats, you use the half-beat on your opponent after you can keep count of his timing. That would be hitting on his half-beat. You should not try to establish a rhythm until you can recognize any rhythms you have already established by training. It's only after you can recognize your established rhythms that you should concern yourself with either braking those rhythms or trying to establish new ones.
Some people just try to count punches and that is where they make their mistake.