As you know, the NCAA Selection Committee uses highly scientific methods to distill each team down to a numerical "seed".  This seed can be applied to any number of highly accurate prediction methodologies practiced by bracketologists for ESPN, Sports Illustrated, and the Harvard School for Applied Bracketology.  We will start by illustrating the predictive power of a simple first-order approximation.  More advanced lessons in advanced factoring, numerical integration, and complex numbers will be in future chapters.

Probabilities reflect the uncertainty of future outcomes.  The classic example is a heads or tails coin flip.  Probability theory dictates that the chances of a heads or tails flip are equal; i.e., 50%.  In a first-order bracketological solution to the NCAA tournament, the seeding is used to apply probabilities to given outcomes.  There are different theories on how to convert seed matchups into outcome probabilities.  What I present here is a solution that attempts to take into account historical results as well as maximizing predictive capabilities of the model.

The most controversial aspect of the Craft Bracketological Solution, or CBS, is the result of the 1 vs. 16 seed matchup.  Historical evidence indicates that 92 out of 92 1 seeds have defeated their 16th seeded counterparts.  However, it is clear to even first-year bracketology studies majors that, given enough time, a 1 seed will lose their opening round game.  However, because the CBS is based on historical evidence, it places the odds of a 1 seed losing to a 16th seed at 0%. 

Here, then, is the formula used for determining the probabilities of each matchup:

y = 0.5 - (1/30)*x  where y is the probability of victory for the lower ranked team and x value of the difference between the seeds.

For example, equal seeded teams facing each other (1 vs. 1, 2 vs. 2) will each have a 50% probability of victory.  A 1 vs. 16 matchup will result in a 100% chance of victory for the top seed.  Now, I will apply this formula to the bracket for March Madness 2008.  The next 3 weeks of games will help determine the efficacy of the CBS.  What follows is my commentary as I fill out my bracket.  I will use a random number generator to resolve the probabilities into predicted winners.

EAST BRACKET

George Mason, the Cinderella Final Four team from two years ago, makes another run to the Sweet 16 before being wiped out by North Carolina.

A #1 vs. #2 matchup for a spot in the Final Four between North Carolina and Tennessee ends with North Carolina headed for San Antonio.  I double-check the randomizing circuits on my random number generator before continuing.

MIDWEST BRACKET

Albany hometown favorite Siena comes through with an upset in its first round game, but doesn't make it to the second weekend.

Kansas St. makes a Sweet 16 run behind presumptive first overall NBA pick Michael Beasley.

In another #1 vs. #2 matchup, Georgetown upsets Kansas for the Final Four ticket.

SOUTH BRACKET

Hilariously named Oral Roberts falls to Temple in the second round, but the clock strikes for Temple against a team I like to call the Memphis Paper Tigers.

In yet another goddamn 1 vs. 2 matchup, the Memphis Paper Tigers claw their way past the Texas Longhorns. 

WEST BRACKET

Duke haters everywhere rejoice as they fall to 15 seed Belmont in their first-round matchup.

Our first 1 vs. 3 matchup for a final four spot ends predictably, with UCLA going to the final four.  (Since UCLA would actually be my pick based on, you know, basketball, to win it all, if they had not made it I would have thrown this manuscript against the wall in a fit.)

FINAL FOUR

Georgetowns "Cinderalla" run to the finals ends at the hands of North Carolina.

The Memphis Paper Tigers finally show their true stripes (more tiger puns!) against UCLA, who advances to the finals.

UCLA over North Carolina for the championship.