A little bit of head movement can mean the difference between getting hit and not getting hit. In fact, it is one of the most important skills in boxing. The key is to hit without being hit. The skill to dodge punches is the key to extending your career and the life span of your brain. This is an indisputable fact. Head movement does not just mean moving your head, but also your body. Often times, proper head movement is pivoting your body and bending the legs. But even the untrained can benefit from trying to dodge punches.
Head movement makes you a much harder to touch target, and moving your head right after a combo allows you to avoid counter punches.