Final Four

 ...and I was worried when my bracket didn't have any number 1 seeds going to the final four.

UCONN at the moment has the best chance of the teams left, and I'm not just saying that because of how the seeds worked out.  The dice chose UCONN.  Which means they have always had the best chance of winning the tourney.

The dice also choose to form impossible shapes

In all seriousness, I've been thinking that maybe this whole method is not actually as good as I want it to be.  The NCAA is really bad at choosing seeds.  I mean, sure you can get some information out of the seeds, but really the seeding makes some teams just have an easier path towards the end of the tournament.  Given the assumption that a three seed (like UCONN) is just as good as a one seed (i.e. each has a 50/50 chance in winning...which is an assumption I made), the only thing that makes a difference is the path that the teams take to get to the championship.  UCONN is going to be facing better teams earlier than, say, Ohio State did.

 Furthermore, the sheer number of possible outcomes makes it so that it is nigh impossible to get a bracket which is good (on the other hand, the sheer number of people making brackets makes it so that somebody is going to have a good bracket *wink*).  Think about it this way...instead of playing basketball, each team decided to flip a coin to determine the winner.  The model should be pretty clear...each team is going to have a 50/50 chance in winning.  Given that there are five rounds of play, the probability that you pick the correct winning team is (1/2)^6, or 1/64.  The problem here is that all of these probabilities are being multiplied together.

Warhammer fans should be familiar with this decay; a space marine squad rapid firing into another space marine squad has 2/3 chances to hit, 1/2 chances to wound, and then 1/3 chance for the opponent's armor to fail.  These aren't awful odds for this situation, but when you multiply it all out, you're only expecting 1/9 shot to wound.  That means that on average, from 20 shots, you're killing 2 marines a turn.  Not exactly stellar odds, but because three things need to happen for you to kill a marine, you're multiplying all these numbers together which are less than one, and they get small quickly*.  So no matter what the odds are for a 1 seed to win the championship, the probability is very slim that it will happen because of the layers of events which need to happen in succession.  Oh, and unlike Warhammer, you only get one shot at this one.

U Newbie!!  I kill you!!...Or...maybe not....

Now the interesting question becomes...can you do better than the average bloke will with a bracket rolled with dice?


*Side note: this is why things like Fortune, Feel No Pain, Ghosthelms vs Perils attacks, etc. are so freaking good....they add more dice which need to be rolled to kill your guys.  This is also why power weapons and other armor-ignoring weapons are so fantastically good...they subtract the number of dice which need to be rolled to kill other guys.