The odds of picking the winner of a basketball game blindly (without knowing which team is better, more highly ranked) is 50%
The odds of picking (in advance) winners of a four-team tournament is 12.5%. You first have to guess right in the first two games, so you are at 25% there, and then also have picked in advance the winner of the final game.
Now with 8 teams, you have to pick four winners in the first round correctly. You have 1/16 of a chance to get that right. If you do, then you have a 1/4 chance of picking winners for the next round, and, again, a half and half chance of getting the final game right. So 1/16 x 1/4 x 1/2. I would guess, then, that with every round you add onto the tournament, you multiply the difficulty exponentially by 2 to the power of y, where y is the number of the round you added.