## Statistics, probability and NCAA's "March Madness"

The NCAA men's basketball "March Madness" tournament may have just tipped off, but one academic is already thinking about the later rounds. Once the "Elite Eight" teams emerge, says Sheldon Jacobson, a professor of computer science and the director of the simulation and optimization laboratory at the University of Illinois at Urbana-Champaign, throw out a team's initial seeding—it's no better than flipping a coin to figure out their chances of winning.

For a study in the Journal of Gambling Business and Economics, Jacobson was trying to figure out whether the top three teams' seeding in each bracket at the beginning of the tournament is a good predictor of how far they will go in the tournament. Jacobson analyzed data from NCAA tournaments dating back to 1985, which ended with a classic game that saw Ed Pickney's Villanova Wildcats beat the heavily favored, Patrick Ewing-led Georgetown Hoyas.

His conclusion: "From the Elite Eight round and onward, you might as well pick names out of a hat."

Seeding does matter in the six-round men's Division 1 NCAA tournament's first three rounds, where a No. 16 seeded team has never beaten a No. 1 seed, Jacobson said in a statement.

The tournament's notorious unpredictability didn't stop Joel Sokol, a Georgia Tech operations research professor whose statistical model correctly selected last year's Final Four, championship game and overall tournament winner (the University of Kansas Jayhawks), from developing his own computer program. His picks? The University of North Carolina Tar Heels, University of Pittsburgh Panthers, University of Louisville Cardinals, and University of Memphis Tigers will make the Final Four, with the Tar Heels taking the championship, CNN reported earlier this week. (Michigan State and Oklahoma are ranked too high and due for an upset, statistically speaking, he added.)

Sokol's software uses Logistic Regression Markov Chain (LRMC), named for Russian mathematician Andrei Markov, which analyzes a variety of statistics to rank every Division 1 men's basketball team (with margin of victory being one of the most important factors).

Beyond the college tournament, the game of basketball itself relies heavily on probability, particularly when rebounding. In a study published a year ago in Nature Neuroscience, researchers at Rome's Sapienza University found that basketball players are nearly twice as good as sportswriters at predicting whether a shot will go in the basket, a predictive capability that helps the players put themselves in the proper position to grab a ball that clangs off the rim and start a fast break going the other way.

When the researchers showed a group of players from Italy's professional basketball league, coaches, journalists and college students video of a player shooting free throws, 70 percent of the time the players made the correct call, compared to 40 percent for the writers. (Read Scientific American.com's blog on the Sapienza study.)

For those nonplayers who still want to represent well in their office pools, but can't trust their gut instincts to get them through the later rounds, several Web sites have sprouted up to help these budding "bracketologists," including Poologic.com, TeamRankings.com and its BracketBrains prediction tool, and BracketScience.com.

Those whose brackets are in disarray after the first round, take heart, the start of the baseball season is just around the corner. (For more on the science of basketball, see Scientific American.com's in-depth report.)

Image ©iStockphoto.com/ Greg Cooper

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