In a gunfight, said this BBC story the other day, thinking is slower than reacting. Drawing first could kill you. Andrew Welchman did the research at Birmingham University (there really is a university in Birmingham), saying that hardwired responses are quicker and dirtier than cognitive ones. Niels Bohr did some similar work in Copenhagen after watching loads of movies where the reacter wins.
In The New Thinking Man's Guide to Pro Football, by Paul Zimmerman, we meet little, slow, old* linebacker Larry Grantham, who should not be able to regularly make the plays he makes. He says:
Well, there's something to this being old ... [you learn to understand what a player will do by how he sets up] ... You've got to look for that first movement, and that's the time you react - not your brain, but your legs. Your brain catches on later. I look at one man, but I'm actually seeing about five. And there's absolutely no waiting involved
* These are relative terms