Posted: March 15, 2017, 7:20pm
This is how you pick your NCAA bracket when you’re an engineer and don’t know anything about college basketball. Below is a picture of my bracket, filled out according to a computer program that I wrote a few minutes ago. The program takes inputs of each team’s seed number and uses it to calculate a probability of winning for each team. A random is chosen and compared to the probability and a winner is chosen and perpetrated through to the next round. Repeat until a winner is chosen!
A number “x” seed has probability (1 – x/(x + y)) of winning against a number “y” seed. So a number one seed is 16 times more likely to beat a seed 16 seed than the other way around. Makes sense, that rarely happens.
Except everyone knows that upsets do happen. It’s a huge part of March Madness — hence the “madness” part of the name. So I added a “risk aversion” non-dimensional parameter, RA (0 < RA < 1), such that when RA = 1 the top team always win (i.e. complete risk aversion) and when RA = 0 the underdog always win (i.e. “I’m feeling lucky”).
Here’s my bracket for RA = 0.55, with a total of 6 upsets across all rounds. Maybe I’ll win big — but then do I have to split the winnings with my computer?