# An Instant Analysis of the 2009 NCAA Tournament

Today’s guest post – and instant analysis of the 2009 NCAA Tournament (posted within minutes of the brackets being announced) — is yet another excellent offering from Erich Doerr .  Erich first contacted me prior to the 2006 NBA Draft with a statistical preview in hand.  Each subsequent year has seen improvement in the depth and breadth of his analysis. Outside of his basketball writing, Erich does consulting work for major software products by day and has started a fledgling sports-themed Open Source software initiative by night.

Back by popular demand, I have run the numbers on Selection Sunday and am here to offer WoW readers a bracket breakdown with a statistical bent.

Table One: NCAA Tournament based on Pomeroy Numbers

Table Two: NCAA Tournament based on Sagarin Numbers

Last year I employed the Monte Carlo method to generate probabilities. This year I have upgraded to calculate conditional probabilities.  Essentially, conditional probabilities produce the odds of a Monte Carlo simulation as the number of simulations increase toward infinity.

Just like in 2008, I am relying on the two strongest public NCAA metrics:  Sagarin Ratings and Ken Pomeroy‘s Pythagorean Ratings.  Statistics used by the Wages of Wins parallel Pomeroy’s approach, as both build off of offensive and defensive efficiency.

Table Three: Teams Probability

Since top seeds represent the best teams in the land, this approach will appear to heavily favor those teams due to their quality and favorable draw.  The final results here attempt to predict the statistically most probable brackets, which are not necessarily the picks most likely to win an office pool.

By the numbers, who has the right to gripe?  Well, the best Pomeroy teams to miss the tournament include San Diego State, New Mexico, and Florida.  As for the teams that made it, an average #1 seed would make it through Louisville’s bracket 36% of the time while the same average #1 seed would only make 21% of potential final fours given Connecticut’s draw.  This discrepancy is by design as Louisville’s #1 overall seed should come with an easier path, though some may say a 15% disparity gives Connecticut a reason to complain.  Last, and probably least, Pittsburgh’s first round draw against East Tennessee State generates that elusive 16-over-1 upset 6 times out of 100, about twice as often as the other 1 vs 16 matchups.

Stepping back, both the Sagarin & Pomeroy brackets come out with the same predictions in 63 out of 64 matchups.  The lone difference comes from each rating’s national champion.  Pomeroy’s ratings prefer the Memphis Tigers over Sagarin’s favored Tar Heels.  This year’s statistically-not-a-surprise upsets appear to be #12 Wisconsin over Florida State and the #6 WVU Mountaineers run to reach the Elite 8.

The tables linked above also provide odds by conference, seed, and region.  The vaunted Big East takes home the title a third of the time, while the combined effort of the 7 Big Ten entrants comes up short of a 5% probability to win it all.  Looking for all the number 1 seeds to reach the Final Four?  That number checks in around 24%.  See the tables above and comment on your own favorite observation.

Finally, please note the Wages of Wins Journal does not condone gambling.  These picks are unlikely to be as successful as last year’s batch.  In general, an entry in a bracket pool has a 1/N chance of winning, where N = number of entries.  Due to the layout of the NCAA tournament, it is highly improbable that a good set of picks could raise the pre-ante odds to even 2/N.  Generally, there may be more gains to be had in shopping for the right office pool (i.e. the one containing the least informed participants) or game theory analysis if one was so interested in improving their office pool odds.  Always note that past returns do not guarantee future performance.

- Erich Doerr

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

Update:

Some people reported having trouble accessing the above tables.  If this is the case, please see NCAA and NIT Analysis from Erich Doerr

- DJ