A Stochastic Model for Picking Winners in the NCAA Tournament

For people interested in this kind of analysis I recommend Mathletics by Wayne Winston. He's written a blog and a book about similar subjects.

The book itself is approachable with a basic knowledge of mathematics, probability, and statistics. It provides a good introduction to things like Sabermetrics (for baseball), and applications to the NBA and the NFL.

"In real life the probability of one team beating another team is independent of what happened in the past."

This sentence seems under-specified, but no matter how I slice it, it's not true. In sports, past performance is indicative of future results. Even in college you'll have correlations brought on by relatively stable (across decades in many cases) coaching staffs. The correlation isn't anywhere near perfect, but it isn't 0 either.

(In your statistics courses, everything is independent for your computational convenience. In the real world rather a lot of things are not independent.)

Consider what it would mean for past performance to say nothing about future results. It doesn't match reality.

I've wasted a lot of time on this kind of analysis for picking brackets. I estimated that the odds of a person picking a perfect bracket are 1 in 924 trillion: http://www.codeswimming.com/blog/2008/03/the-perfect-ncaa-br...

If you want a shortcut to estimate win probability instead of looking it up in a chart:

Prob Team 1 winning = Rank Team 2 / (Rank Team 1 + Rank Team 2)

That formula only breaks down at 1 vs. 16 and 1 vs. 2.

It's fun to postulate, but it won't really help in picking your bracket. What I do is look for teams highly rated by Sagarin or kenpom, but underrated by seeding. I have Wisconsin winning the whole thing in my bracket. You've gotta maximize the probability of occurance while also minimizing redundant picks with the rest of the pool. However, I've never done especially well in practice and regularly get beat by people who choose by jersey color. It's still fun though.

Some of the stats are kind of self-explanatory.

For example, "#8 seeds often upset higher ranked teams. In the four match-ups against #2 teams, #8 teams won twice. They have also beaten #4 and #5 seeds more often than they lost to them."

For an 8 to play a 2 (or 4, or 5) they'd have to have already beaten a 1. That's a pretty good 8. The typical 8 will have already lost to a 9 or 1.

Personally, I love Ken Pomeroy's rankings / predictive model (kenpom.com). It breaks games down into possessions and then builds a statistical model of each team from that. The predictions seem pretty accurate by the time February rolls around.

Of course, the biggest caveat of this kind of model is that it doesn't take into account extraordinary events. For example, a player gets injured or comes back from a suspension.

Not just critiquing this particular model, but at least a couple things that need to be improved upon in game prediction:

1. Need to take into account playing styles of the teams along with their seed. (eg. how do teams that rely on 3pt shots fare vs. teams that play very physical defense, and all other permutations)

2. As Locke pointed out, extraordinary events play a large part in games. There was an article in the NY Times on stat analysis where a team official (may have been Houston Rockets' Daryl Morey) lamented a lucky shot-clock-beating 3-pointer by the opposing team, saying those kind of instances significantly alter the game. It'd be interesting to see if some teams are better at creating these lucky instances, or if they're strictly random