How many teams will win the men's NCAA Basketball Tournament this year?
You may consider this a daunting question, but finding out the answer is not as difficult as you may think. First, let's take the 64-team field (the 63 regular teams and the winner of the play-in game). Since the NCAA tournament expanded to 64 schools in 1985 -- 19 years ago -- there have been 19 champions, meaning that there has been one champion for every 64 teams (19*64/19) that have played in the tournament since the expansion. Since we are given no reason to believe the trend will not continue, we will assume that a team in the tourney, chosen at random, has a one-in-64 chance of winning the NCAAs.
So. What is the chance that no team will win the tournament this year? Using basic probability theory, we take the chance that any individual team will not win -- 63/64 -- and take it to the power of the number of teams we don't want to win in the tournament -- 64. Thus, since (63/64)64 = about .365, there's about a 36.5 percent chance that no team will win the NCAA tourney this year.
Let's look at the chance of one team winning. Again, Using basic probability theory, we take the chance that any individual team will not win -- 63/64 -- and take it to the power of the number of teams we don't want to win in the tournament -- 63. Then we take that number a multiply it by the chance of one team winning (1/64) times the number of teams that could possibly win (64). Thus, since (63/64)63*(1/64)*64 = about .371, there's about a 37.1 percent chance that one team will win the NCAA tourney this year.
I'll spare you the arguments, but for more teams it ends up as:
2 winners: (63/64)62*(1/64)2*(64*63)/2 = 18.5 percent
3 winners: (63/64)61*(1/64)3*(64*63*62)/6 = 6.1 percent
4 winners: (63/64)60*(1/64)4*(64*63*62)/24 = 1.5 percent
5 or more winners: less than .5 percent
Let me know if this helps you with your tournament pool.
i sincerely do not know what you are doing here. are you lost? were you
looking for your delicate calico cat, and did you follow her up two flights of stairs
to this room? she is not here. she was here, yes. we gave her a warm bowl of milk, we talked with her about campaign finance reform for a time, and then she bid us good day. i believe she was
going to the post office two blocks down, but i don't quite recall.
for surely you did
not find your way from prinsiana, the least traveled site on
the internet. if you did, though, perhaps you are looking for humor. perhaps you are looking for profundity. perhaps you are looking for answers.
i'm sorry, but you shall go naught-for-three.
