# An Instant Analysis of the NCAA Tournament

The following is a quick guest post from WoW Journal reader Erich Doerr. Erich used the Win Score metric to investigate the top prospects for the 2007 NBA Draft. He also provided similar analysis in a first glance at the 2008 draft.  In this post, Erich provides an analysis of who should be the favorites in the Big Dance.

Now that the seeds have been given, what are the odds on a national championship?  One way to assess probabilities is to simulate the tournament, using basketball statistics.  Given 10,000 simulations, a Monte Carlo method, we can generate a plausible list of championship odds for each tournament entrant.

The two strongest public NCAA metrics are the Sagarin Ratings and Ken Pomeroy‘s Pythagorean Ratings.  Statistics used by the Wages of Wins are parallel to Pomeroy’s approach, as both incorporate offensive and defensive efficiency.  Individual game outcomes can be modeled via methods like log5 analysis and Sean Foreman’s Sagarin approach.

With this approach, we should expect to see favorites generally prevail, and given enough trials, we’ll see a low seed team go all the way.

Which #1 got the easiest bracket?  This analysis suggests Kansas has the easiest path by either metric.  Sagarin seems to show UCLA got the toughest draw while Pomeroy’s stats believe North Carolina received the toughest draw.

The following tables report my analysis:

Table One: The Path to the Final Four

Table Two: Projecting the National Champ

Outside of statistics, there is another approach I find very fruitful. I enjoy following the prediction markets and their National Championship expectations. One example of this is at http://www.tradesports.com. If we average the bid & the ask prices, we can get an assumed percentage chance of winning.

As of writing this, the tradesports.com prediction market has Kansas trading at around 13, which indicates the market believes they have a 13% chance of winning the tournament.

The prediction market can also answer one other question. Who’s tournament chances improved given their seeding? For this question, I look at the Change column, indicating the price swing for today (Selection Sunday). The biggest winners & losers are as follows:

Team Last Trade Change
North Carolina 16.0 +1.6
UCLA 14.0 +1.5
Kansas 13.0 +1.2
Pittsburgh 1.7 +0.8
Georgetown 4.5 -0.8
Tennessee 4.9 -1.7
Duke 5.6 -2.0

Given the Sagarin, Pomeroy, and prediction market information, you have three powerful tools to approach your bracket game decisions. Enjoy, and keep your eyes on the prediction markets and this comment thread for updates throughout the tournament.

Update: With the results from a Monte Carlo analysis, we can construct the model bracket for each statistical measure.  These brackets will advance the team that appeared most in each game situation.  The numbers by the school name indicate number of advancements out of 10,000 iterations. (Numbers may differ from table as these statistics have been updated for Sunday’s games)

NCAA Brackets based on KenPom Simulation

NCAA Brackets based on Sagarin Simulation

– Erich Doerr

Notes:
Sagarin stats are as of March 16
Pomeroy stats are as of March 15
For simplicity I assumed Coppin State would lose in the play-in game

Monte Carlo
http://en.wikipedia.org/wiki/Monte_Carlo_method
Sean Foreman on Sagarin Stats and Monte Carlo Simulation
http://www.sju.edu/~sforman/research/talks/NCAA/
Sean Foreman’s current day job
http://www.baseball-reference.com/
Ken Pomeroy on Log5 and his statistics
Math behind Log5
http://www.diamond-mind.com/articles/playoff2002.htm
Ken Pomeroy’s Day Job