Every year the National Collegiate Athletic Association holds a
64 (65 this year) team bastketball tournament for the men's and womens
division 1 schools. Since the tournament runs through the month of
march, it is known as "march madness." It provides an excuse for,
among other things, the premption of TV shows, a derth of
betting on the actions of college students (kids), heated water
cooler arguments about schools most people can't find (Xavier? Holy
Cross? McNeese St.?), Grown men with jobs in offices will talk
about "seeding" as though they plan on plowing the back 40 after
they get home from their engineering jobs at applied dynamics
corp., and finally the tournament gives an excuse for people
who didn't go to college to take an active interest in college athletics.
Now, During the tournament, the teams are broken into brackets of
16. These are the South, East, West, and Midwest. (Apparently
"North" didn't get adequate protection under affirmative action
coverage.) These brackets consist of 16 teams, and have nothing to
do with geographic locations. (Utah and Indiana, for instance,
played in the "South" region, while Boston University and Cinncinnati
played in the "West." Up yours Rand Mcnally.) As the teams "come
down to the wire" (read: eliminate each other in wild mismatches for
the first two rounds. Example: Winthrop played perrenial powerhouse
Duke in round one. The Christians had a better chance against the
Lions.) (Actual lions, not the Detroit Lions.) (Your Average
Christian could defeat the Detroit Lions, with or without playing a
decent run defense.)
Here's the Mathematics part. There are 64 teams playing. each team
can only win or lose. By my math that leaves 2^64 possible
combinations for the bracket, or 18,446,744,073,709,551,616
possible permutations for the bracket. But, that doesn't count that
in each round, a set of teams gets eliminated. A more accurate (I
think) set of computations would work back from the final game. In
the championship game, there can be one of two winners, team a or
team b. so you get 2^1. in the round before, there are 4 possible
out comes. Team a beats team d, team d beats team a, team b beats
team c, or team c beats team b. So we get 2^2. double this to move
back a bracket for 2^4, then 2^8, 2^16, then 2^32. Add the sum of
these squares and you get 4,295,033,110. that should be the
most accurate number of outcomes for a tournament bracket.
So how did I do? At the bottom of the page is a scanned picture of
the bracket I filled out. Take my word for it, I filled it out
around march 12th, the day of this years "play in" game. (a chance
for two very small schools play each other for the right to be fed
to the top seeded team in the east region.) In round 1, of a
possible 32 games, I was correct on 21 of the games. Not bad, but
round 1 is easy. Very few 16th seed teams will beat a number 1 seed
(although it has happened twice in the last three years.) For round
2, I managed only 10 of 16 games, but since there were teams I had
chosen to advance into round 2 that didn't make it out of round 1,
this isn't as bad as it seems. Round three left me with only 4 of 8
(Damn you Alabama and Miami.) Round four upped me to 3 of 4, and in
the championship game, only one of the two teams was one I had
chosen, the eventual tournament champion, The University of
Maryland.
Below is a link to the bracket itself, which may give you a better
idea of what I'm talking about. You'll notice the two blurred out
areas. Advertisers be damned.
The tournement
bracket
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