Esoteric Dissertations from a One-Track Mind

March 22, 2008

March Madness Craziness: Part One

Filed under: programming — Tags: , — codesmithy @ 8:23 am

So, it is that time of the year again. The NCAA Men’s Basketball tournament is upon us. Raymond Chen has his predictions up. In years past, he has used seating capacity of the arena or the length the President/Chancellor of the University has been in charge. When filling out my own predictions, I try to pick some of the more likely upsets based on record, whether or not I feel the conference the team is from is overrated, or the team is overrated, impression of how I feel the coach has done in the tournament in the past and whether I feel they can achieve that level of success again. It is very unscientific and subjective.

I also find myself somewhat flabbergasted that Chen managed to pick Sienna, Villanova, Kansas St. and San Diego (and a little bit jealous). So, maybe he is on to something.

In addition, I feel that I have to pick some upsets because I know there are going to be upsets. However, I never really sat down and determined if that was actually a rational thing to do.

First of all, let’s talk about what is definitely irrational: random picking based on weights. I noticed a bracket simulator that assigned picks basically by picking a random number after assigning each team a relative likelihood of winning. It gives you an interesting bracket, but the strategy is not in fact rational. If you were interested in maximizing your chances of winning you’d pick the team with the best chance of winning every time. Or would you?

Let’s assume the NCAA selection committee is totally unbiased and correctly assigning seeds. Knowing the majority of people follow the NCAA’s recommendation, does it make sense to make a suboptimal bracket that virtually guarantees an exclusive victory?  I don’t know, let’s figure it out.

To determine a rational strategy, we have to start off with scoring. We’ll ignore the first game between the two 16 seeds because they aren’t included in most Pick ’ems. Generally, the scoring is based on correctly picking a winner multiplied by 2 raised what round the game was played (starting the count at 0 as is the want of computer scientists). Also, most Pick’ ems require a consistent bracket, that is a bracket where only the winners are allowed to play in the next round. I actually don’t know if would make sense to pick a team to lose in the first round, only to resurrect them later, but alas it is disallowed.

Definition of the NCAA Selection picker: Pick the team that is a lower seed. If two teams are the same seed from different regions, randomly pick one to be the winner with equal weighting.

Next time: how this selection algorithm actually performs against tournaments of the past.

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