Originally Posted by bermuda
Certain patches do affect the sound somewhat, but they were originally intended for protection where the beater strikes.
Back in the day, a piece of moleskin was used to help protect the head. Ss harder beaters and harder playing became more prevalent, more resilient synthetic patches became popular.
There are a few tricks involving 'patches' that do noticeable affect the sound though. One is to take a piece of a separate head, and tape it where the beater strikes so that there's about a 1/4" gap between the piece and the batter. This creates a nice slap without affecting how the pedal feels. Another trick involves taping a thin piece of wood or a coin (a US 50¢ piece when they were readily available) to get extra attack and 'cut', both acoustically and in the studio.
I use a Dr. Scholl's moleskin patch that's about 2x3 inches with a vintage soft Ludwig beater (wool?). It adds fantastic punch and warmth - it was EXACTLY what I was looking for.