Blake pointed out another interesting contest where you put in a probability of each team winning for each game, and points are computed according to a non-linear scoring function. I'm not sure where they got the scoring function (it's not a log). They make the dubious and unsupported claim that their function makes it optimal to select the "true" probabilities, a claim which is bound to rankle those with some knowledge of decision theory. But it still looks like a fun idea...maybe next year.
UPDATE: UConn won, and so did I! I even got pretty close on predicting the final score (I predicted 80-70, the final score was 82-73).