Most people tend to punch with a loose hand to the top of the head: this simultaneously increases the chance of breaking their hand; reduces the impact force; and, strikes one of the most insensitive & hardest parts of the body (the skull). Trained fighters are targeting an untucked chin with a short high acceleration punch (jab, uppercut), with a tight fist. It is technically very challenging to do this, even for professionals.

In general: use your sneakers; if necessary, push opponents away with with your palms and tightly held fingers.