March Madness victors
For those who like to play the odds, the annual National Collegiate Athletic Association (NCAA) men's basketball championship tournament is like the Superbowl.
Dubbed March Madness, the contest inspires hordes of hopeful bettors to wager billions in pools in offices, bars and on the Internet to predict the winner of the 63 game tournament. But scoring the jackpot isn't easy -- there are a staggering 9.22 billion billion (quintillion, to the mathematicians) possible outcomes, points out Edward H. Kaplan, the William N. and Marie A. Beach Professor of Management Sciences at the Yale School of Management.
Kaplan, a long-time loser of March Madness pools, is betting that he can improve his chances this year by applying his expertise in statistical modeling. An operations researcher widely recognized for his accurate predictions of the spread of AIDS, Kaplan and his colleague, Yale SOM deputy dean Stanley J. Garstka -- an expert on bankruptcy -- set out to tackle the problem last summer. "We decided we'd like to win once in a while," confesses Kaplan.
Working mainly in hotel rooms in Rome and Jerusalem while attending conferences, Kaplan mapped out a model that incorporated estimates of the probability that any team would win the game it played in each round and the specific point rules for the pool. The goal in a pool is to garner the highest number of points for correct predictions. Kaplan notes that the simplest case is when pools offer one point for each correct winning prediction. In this case the object is just to pick as many winners as possible. However, many pools are more complex, offering bonus points for upsets, or "depth" points for predicting correctly as the tournament rounds proceed.
When the data are combined using a technique known as dynamic programming, the model produces a slate of predictions. "This is complex, since you have to consider all possible opponents, as well as the chance for all teams to advance to all rounds," Kaplan admits. "Nonetheless it can be computed. The basketball problem is data rich, and the tournament structure is, from a mathematical point of view, beautiful to model."
In preparation for the March 2000 frenzy, the Yale researchers put their model through a "dry run" by testing it with the data available at the beginning of the 1998 and 1999 NCAA tournaments. The model considered such information as regular season performance, professional sports rankings and Las Vegas betting odds. It achieved an overall prediction accuracy of about 58%, a significant edge over the 30% you would expect by making selections randomly.
Kaplan found that the model did better in pools with more complicated points structures. "In contests where the goal is simply to pick as many winners as possible, we did not really do any better than just picking the seeds. For a more complex pool that we found on the Internet with both bonus points and depth points, our models actually would have garnered more points than the person who won," he says.
Even without a powerful computer model, there are some ways players can optimize their chances of winning, says Kaplan. For example, suppose you believe that should two teams, say "A" and "B," play head-to-head, A has a 60% chance of beating B. Also, suppose that in determining a slate of predictions, you actually arrive at a juncture in a downstream round where you have forecast A to play against B. It is not necessarily the right decision to choose A over B in this case, says Kaplan. "Just because you pick A and B to make it to a game in a downstream round does not mean that they will. You should take into account the chance that you may be wrong in the earlier rounds," he notes.
It is also important to keep in mind that every single game in a single-elimination tournament can be viewed as the "championship" of a "subtournament" that concludes in that game, says Kaplan. The subtournaments that end in any round are all completely unrelated. "What happens in one has no bearing on what happens in any other," he says.
Kaplan suggests that players will do better by making their selections by starting at the end. Most people, he says, fill the brackets out from start to finish, basing each round on their selections in the preceding one. "It is a much better strategy to work backwards," he says. "First decide who you really think is going to win the entire tournament. Once you have made that choice, then that team must also win in all earlier rounds." Next, decide who you think will lose in the final. Whatever team that will be, it also must win all earlier rounds. And so forth.
As of now, the Yale model is taking its final exam. Kaplan doesn't believe the model will prevail in the larger pools, such as ESPN, which attract more than 500,000 entrants. In last years's ESPN tournament, the model would have garnered 1,050 points out of a maximum of 1,680 points. But the actual winner scored 1,470. "Chance alone suggests that the tournament outcome will more closely match someone else's picks," he says. Instead, "we are actively looking for pools with complex point structures."
Kaplan plans to reveal his scores in a paper titled "March Madness & the Office Pool" at the national convention of the Institute for Operations Research and the Management Sciences on May 2 in Salt Lake City. He will also present a distinguished lecture "Policy Modeling for Better Decisions -- The Case of HIV Prevention."
Win or lose, Kaplan says his work on the far more complex problem of predicting the toll of AIDS is what is most important to him. With AIDS, "the stakes are life and death as opposed to a reputation for calling games correctly and winning a few beers or a few bucks," he notes.
-- By Alan Hall,
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