## Monday, March 12, 2012

### March Madness

Once again, America's favorite binary tree, the NCAA Men's National Championship Bracket. The tree seems to get more unbalanced every year. There are four regions, the East has the traditional 16 teams, the West and South have 18 teams each and the Midwest has 19 teams for a total of 68 teams. Single elimination starts tomorrow.

Many Americans participate in office pools where they fill out the bracket to predict which team wins each game. There's lots of math one can use for your bracket. But here is my advice: Pick the higher seeded teams to beat the lower seeded teams. Every time. There will be upsets but you can't predict where they will be so you have the best chances predicting none of them.

The most likely seeds to make the final four are two number 1's, a number 2 and a number 3, 3 times in the last 27 years. So why follow my advice which predicts four number 1's. Because there are 12 ways to get 11 2 3 and only one way to get 1 1 1 1 and you have to pick a specific combination when you fill out your bracket. The four first seeds all went to the final four only once in the last 27 years but given there's only one such combination that makes it more likely than any other possibility.

May the madness begin.

#### 3 comments:

1. This strategy may be correct when one is participating in a pool consisting of two people (i.e., competing with just one person), but is almost certainly wrong when one is participating in a pool consisting of a large number of people.

2. A single deviation from picking the higher seed has a small impact on your odds of winning. However, it should significantly decrease the chances multiple people used the same strategy, necessitating the splitting of the pool. Of course, if everybody follows that logic, then the optimal strategy is again available, so you should deviate from the 'pick the higher seed' strategy with some large-but-not-1 percent chance.

3. Agreed: Lance's strategy fails in a pool because it drives up collision probability.