Thursday, March 11, 2010

One Million ACC Tournament Simulations

One year ago, we had some fun with spreadsheets and used a number of different methods to predict the ACC Tournament. Unfortunately, the raw numbers had no way of knowing the status of Ty Lawson's ankle, so the team predicted to win about 30% of the time grabbed the title, while UNC rested for bigger fish. In the past year the number of Pomeroy Disciples has grown, and so traditional "log5" predictions of the conference tournaments can be found all across teh internets (although this one in particular, from Basketball Prospectus, is a must read).

I like to find my little niche here at the Immaculate Inning, and that means simulating the hell out of things. The method is the same as for last years' ACC tournament. This year, I used raw offensive and defensive efficiencies that were tabulated here. This means that a team did not have their stats adjusted for home games or for the strength of opponent: the only values in the stat is points scored (or allowed) per possession. Via the Pythagorean Expectation Formula (with KenPom's exponent for unadjusted efficiencies = 8.5), I calculated a team's "expected winning percentage."

To determine the chances that team A beats team B, a form of Bayes Formula is applied, which in the stat-head world has come to be known as "The log5 Method." The method could be applied to any scenario where the probability of a single outcome is desired, given the prior probability for each of two alternatives. Here, we have two teams, each with an expected winning percentage, and can calculate the probability of a .900 team beating an .800 team. If we assume that the result of each game is independent, then we can multiply probabilities together to get a team's overall probability of making a certain round.

Personally I find the method rather deterministic, in what essentially is a stochastic process. Instead, I run the tournament 1 million times and calculate the percentage of simulations n which each team makes it to each round. The results of my simulations for the 2010 ACC Tournament are below:

The spreadsheet has two tabs, one for a simulation done using stats from all games, while the other is for ACC games only. The way to read it is that each team (row) won a certain number of games (0,1,2,3, or 4) in a certain percentage of the 1 million ACC tournaments I simulated. For the top four seeds, the maximum number of wins is 3, while the other 12 teams could potentially win four games and the tournament.

Duke's chances of winning the tournament is severely if stats from the entire season are used, and they go from a near 2-to-1 favorite to not even winning a majority of simulations. Part of this has to do with the raw nature of the efficiencies; accounting for Duke's tough schedule (and it was one of the toughest in the country by most any measure: KenPom, Sagarin, RPI) would probably account for most of the discrepancy.

On the other end of the spectrum is Miami, which gained an incredibly high percentage (from 0.1% to 3.4%) because they had a highly positive efficiency margin for all games, while it was highly negative in ACC games only. The Canes played very very well against a bunch of schools I've barely heard of, followed by getting clobbered in ACC play. Their adjusted efficiency margin is still decent due to the ACC games they played, but it's hard to give the full season stats much regard in this instance.

The numbers for the ACC-only simulations differ from those seen at Basketball Prospectus; I imagine most of the differences here also have to do with using raw efficiencies rather than Pomeroy's adjusted numbers. The adjusted numbers, Pomeroy claims, are the best for predicting "the chance of beating an average D-1 team on a neutral floor." The raw numbers, then, are skewed based on home-court advantage, schedule (remember, the ACC is no longer "balanced"), and the overall strength of offenses and defenses a team faces. In particular the predictions differ in that Maryland's chances are reduced, at the expense of better chances for FSU and VPI. Both methods agree that fifth-seed Wake has one hellish path towards an ACC title; much worse than sixth-seeded Clemson's chances. Overall, it will be interesting to see whether raw or adjusted efficiencies do a better job predicting the ACC tournament.

Another advantage that these simulations have is the amount of fun I can have with the results. Below I present the "Fan Anxiety Matrix." Each cell in the Matrix represents the chances that a team (in the rows) loses in the ACC tournament to a specific team (in the columns):

So, Duke's "Fan Anxiety Matrix" says that, in the 37% of simulations when they didn't win the whole thing, the most common opponent taking down the Blue Devils was Maryland (Using the ACC stats here). Perhaps no surprise there, but then there were still 8.3% of the simulations in which the Blue Devils fell in the semi-finals to Virginia Tech. Duke's first round game is against either Boston College or Virgina, and the combined percentage of simulations in which the Blue Devils' ACC run ended against those two teams was six percent. It should be of some comfort that UNC's chances of taking down Duke (this would have to be in the finals) clocked in at a tiny 0.029%.

Looking at the matrix, Clemson's path is an interesting one. The Tigers are seeded sixth and must at least pass through NCSU and FSU to get to the semifinals; the Matrix has them losing to these teams 22.5% and 37.1%, respectively. Maryland (22.4%) and Duke (10.1%) also appear in the double-digit percentages as Clemson's final ACC foe, with the remaining 3.2% speaking for Clemson's ACC title chances.

Virginia Tech's bubble position would certainly be helped with a win in their quarterfinal matchup; things are looking up according to the simulations, which have them falling to Duke in the semifinals 50% of the time. Wake Forest has a rough road to the ACC title, as they must win Thursday versus Miami (losing %: 30.5), Friday versus Virginia Tech (39.5%), Saturday versus (with 94% probability) Duke, who accounted for a further 25% of Wake's losses in the simulations.

For posterity's sake, here are the official Immaculate Inning ACC Tournament Predictions:

Thursday winners: Virginia, Wake Forest, Georgia Tech, Clemson
Friday winners: Duke, Virginia Tech, Maryland, Clemson
Saturday winners: Duke, Maryland
ACC Champion: Duke 75, Maryland 60

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