Tuesday, March 24, 2009

Sweet Sixteen Predictions by Simulation

Now that I've taken a day to recover from watching some 40+ hours of basketball over the weekend, let's revisit the predictions made by my NCAA Tournament Simulator. Here's a link to bracket that I picked based on the highest number of average wins in the tournament. As you can see, the picks did pretty well, landing in the 72nd percentile overall on ESPN. Thirteen of the sweet Sixteen teams were picked correctly, and the bracket lost zero Elite Eight teams over the first weekend of play. The three most notable exceptions were West Virginia, UCLA and Wake Forest. The simulation could not have taken into account how absolutely uninspired these teams would play. It also missed the Western Kentucky over Illinois, since the simulation didn't know about the injury to Chester Frazier.

West Virginia did replace Michigan State in the Most Likely Elite Eight according to the one million simulations. How likely was the first round overall? I wrote a script to count the number of times the simulation predicted the exact first round results in each region:

West = YES! 41733 times!
Midwest = YES! 2325 times!
East = YES! 84894 times!
South = YES! 13648 times!
Overall = Nope. 0 matches.

Upsets of Wake Forest, Utah, and West Virginia at the same time in the Midwest region rarely occurred in the same simulation, and when they did, that simulation did not get one of the other regions correct. In fact, in my pool of 1 million simulations, just 66 produced the correct first round results in three of the four regions. It seems that even if I could have entered all one million simulations, it would not be enough to win Yahoo's Perfect Bracket $1 million. Oh well.

So what do the Pomeroy ratings tell us about the Sweet Sixteen and beyond? To answer that I have two different approaches. One is to simply report the results of the final simulation from Sunday night, the results of which can be found in the data and graphs in this post. Those results are based on the Pythagorean Winning Percentages posted before the first round of the tournament. Four days and forty-eight games (not counting NIT games) later, the rankings are a bit different. How does the added information enhance or suppress the national title chances of each team left in the tournament?

Elite Eight Chances (Click for Chart)
Final Four Chances (Click for Chart)
Championship Game Chances (Click for Chart)
National Title Chances (Click for Chart)

Basically, the inclusion of all the statistics from the tournament games has improved the chances of Connecticut and Memphis winning the national championship, and hurt the chances for nearly everyone else. For Thursday and Friday's games, the teams that most improved were Connecticut (+8.2%), Villanova (+5.5%), North Carolina (+4.5%), and Kansas (+4%). Predictably, the teams that were most hurt by the newer statistics were the immediate opponents of those four teams. UNC-Gonzaga has gone from a tossup (51%-49%) to a more solid favoring of the top seed (55%-45%). The closest game of the Sweet Sixteen now projects to be Oklahoma-Syracuse, with the third-seeded Orange winning 52% of the time.

In the Final Four, Connecticut has actually seen its chances decrease, due to a much higher proportion alocated to Memphis and Missouri, but the Huskies still win the West region in 35% of the one million simulations. From the Midwest, Louisville is still the favorite with a slight edge over Kansas; Michigan State saw a drop in their chances with the inclusion of the new stats. The South is just as open as it was to start the tournament, but Syracuse maintains a healthy advantage, followed by Oklahoma. There is then a huge dropoff between those two and North Carolina and Gonzaga. Finally, the East regional still projects a showdown between Pittsburgh and Duke, with the Blue Devils giving an ever so slight edge (29.00% to 28.28% for Pitt).

The updated stats say that the national title game is less likely to have a representative from the East region, compared with pre-Tourney stats. This is because the four remaining South regional teams all improved their title-game chances, while Duke had the biggest drop of all the teams (from 17.01% to 14.82%). The other half of the title game is still most likely to come from the West, which had Connecticut, Memphis, and Missouri all increase their chances with the inclusion of new stats.

It has, so far, been a tournament small on upsets. The simulator predicts that this trend will continue, with one small exception (#3 Syracuse over #2 Oklahoma), although many of the games project to be very close. One thing that could be improved in the model is the log5 predictions for teams with such similar Pythagorean Winning Percentages. This is one of the things I will be taking a look at in the offseason. In the meantime, it's only two more days until things get kicked off in Glendale, Arizona. Hooray basketball!

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