They've actually done studies on how fast a person can initiate a movement (such as drawing a pistol).

Interestingly, a person who moved in response to a prompt (like their opponent drawing) were actually able to perform an action significantly faster than a person who simply decided when to move (the person who draws first).

The results suggest that in contests of speed, such as the prototypical western gunfight, it actually pays to wait until your opponent twitches.