Posted by Dr Fro 2:40 PM
Off topic:

March Madness….as you know, I have been busy with my other website during March (/early April) Madness. A few interesting thoughts on filling out brackets:

http://www.stat.auckland.ac.nz/%7Eiase/publications/1/10_49_kr.pdf

http://www.lionhrtpub.com/orms/orms-2-01/hoops.html

http://www.yaledailynews.com/article.asp?AID=15053

http://www.defectiveyeti.com/archives/000146.html

http://probasketball.about.com/library/weekly/bl_2003ncaatournamentstrategy.htm

One thought that is mentioned is some of these is that there is an incorrect notion out there that the odds of correctly picking a bracket perfectly (the very scenario CBS will pay you millions for) is 2^63, or 9.2 with 18 zeros. This is wrong. That is the correct calculation if all wins and losses were equally likely (like a coin toss).

Consider the simple case of 1 game. Do you believe the odds of guessing correctly is 50%? Surely if Kentucky plays FA&M, Kentucky will win 90% of the time (if not more). By using the strategy of always picking Kentucky, you will be right 90% of the time, not 50%. If you flip a coin to make your choice (heads, I pick UK, tails I pick FAM), then your odds (pre-coin flop) are 50% of picking the winner of the game. But you did not use a coin to make your decision, you used your head.

Thus, the odds of getting the bracket perfectly correct is better than 2^63. What is it? Hell if I know, but I know it is better than 2^63.

So, the way to maximize your chances of getting the bracket perfectly correct is to pick all favorites. Note that the “favorite” would not always be the lower seed, as Vegas has two “dogs” as being favored – Louisville and Western Michigan.

But that is the way to maximize your chances of having a perfect bracket. Interestingly, this decreases your chances of winning a pool. Consider a pool where 33 people enter. You pick all favorites. Each of the other 32 people pick exactly 1 first round upset (each one picking a different game, thus covering all 32 first round games) and otherwise have an identical bracket to you. As long as there is at least one first round upset, you are not in first place.

So, your only way of winning is to nail the first round perfectly. Which although you have a greater chance of nailing it perfectly than the others, it is still a very remote possibility.

This is the mathematical explanation for what most bracket veterans already know – you gotta pick some upsets, BABY!

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