You see it there on the left. A guy in the outfield (where this tradition proudly reigns) catches a ball. The fans cheer. And the player acknowledges the applause with the Finger of Thank you.
Mostly, it's the top version that you see -- the Limp Finger of Thank You. Note how the Finger in the top photo is not fully extended, as if it's some sort of half-gesture. That's the usual way the Finger is used. In effect, it's like a pointing index finger that fainted along the way. "Meh," I say to all the Fingers.
Any other opinions out there?