Bill,
I've seen so many matches lost because golfer 1 was watching and focusing on golfer 2.
You have to play the hole, first and foremost, but with an awareness of your opponent.
Hale Irwin told me, always expect your opponent to make the shot that you don't want him to make, that way you're emotionally prepared if he makes it and satisfied if he doesn't. Whereas, if you don't expect him to make it and he does, it can shake you up.
I've seen guys 15 feet from the hole in two and their opponent 30 yards or more off the green in two, then they either hit it "gimme" close or scuff it to 50 feet then drain the putt and the guy 15 feet 3 putts and loses the hole.
Expect the unexpected but be aware.
Then again, your opponent just might play better and deserve to win.