### Sportscasters misunderstanding probability

March Madness is upon us, so it's time for more "sportscasters misunderstanding probability" fun. Here is one I hear a lot:

Let's say that every single year, one of the four 14-seeds beats one of the four 3-seeds. Pundits will say, "Well, because one of the 14-seeds always wins, you should pick one to upset a 3."

No: unless you have some special knowledge as to which 14-seed will win, you should pick all four 3s. Then, you will get 3 of the 4 games right. But if you pick (at random) a 14-seed to win, one time out of four you will get four right, but three times out of four you will get two wrong. That's an expected 1 and 1/2 wrong, as opposed to a certain one wrong by picking all the 3s.

1. This should be a TV show: "America's Least Probable Sportscasters"

2. One of the announcers on CBS just mentioned how, "When you fill out your bracket, you always have to figure out which 12 will beat a 5."

3. It's like a ratings difference in chess. If your rating is 200 points higher than mine and we play a 6 game match you should bet on a score of 5 to 1.

1. But one isn't betting on *how many* 12s will advance! You have to *pick one of them*. And that means you should pick none.

2. I am pointing out his confusion. You should expect a one in a million event to happen once in a million events, not zero, but in any particular instance you should bet against it.
I always bet for you to beat MF, for exactly this reason, and exactly these odds.

3. Yes, got it.