I'm not any sort of basketball expert. For that I defer to my colleagues at Basketball Prospectus.
What I can do, however, is adulterate the hard work of others.
Specifically, what I can do is the following:
1. Take any of several power ratings. This requires nothing other than a search engine. The four power rankings that I like, in rough order of preference, are:
a) The Pomeroy RPI ratings.
b) The Sagarin ratings ('Predictor' version)
c) The Greenfield Predictive Power ratings;
d) And the Massey ratings.
In the interest of time, I'm not going to go into great length about the differences between these various systems. They're far more similar than they are different, with the partial exception of the Massey ratings, which do not account for margin of victory in their calculations and are probably inferior for that reason, but can be useful in providing something of a hedge against the more aggressive systems.
2. Translate the power ratings into winning percentages. For instance, if Louisville has a rating of X, and Ohio State has a rating of Y, I want to know how often Louisville will beat Ohio State. In fact, we want to develop a whole matrix, knowing how often any team in the tournament field is expected to beat any other team. The Pomeroy ratings, fortunately, are specifically designed for this purpose. For the other systems, I first 'map' them to the Pomeroy ratings by running a regression, and then proceed.
3. Use a Markov prcess to chain together the probabilities and play out the tournament an infinite number of times based on these head-to-head matchups.
This sounds fancy, but it really isn't; all I'm doing is taking the power ratings and translating them into probabilities, through a process that ultimately requires nothing more than addition, subtraction, multiplication and division. To the extent there's much value-add, it's not so much in picking the winners, but in adapting the system to the peculiar scoring rules that your tourney pool might have. In one pool I'm in, for example, which heavily rewards picking lower seeds, I have a final four of Memphis (a #2 seed), Gonzaga (#4), West Virginia and UCLA (both #6s). In another, which doesn't reward picking upsets at all, I play it much safer: Memphis and then the three number one seeds: North Carolina, Louisville and Pittsburgh (which happens to match the president's bracket).
So without further ado -- and since the tourney is about to tip off in 5 minutes -- here is what my numbers show this year. The first chart is the probability of each team reaching the Final Four from any of the four regions. Separate derivations are provided for each of the four power rating systems that I evaluated, as well as a composite rating that averages the four.
And here are the probabilities of winning it all. Get your money in now on Tennessee-Chattanooga, which is a mere 114,853,003-to-1 underdog.