NCAA Tournament as a Math Problem: Mathematicians Saint Louis University Unlock Surprising Solutions
ST. LOUIS -- This Sunday, March Madness begins with the official release of the NCAA Tournament brackets. Two mathematicians at Saint Louis University have tackled the competition like a math problem, and their answers may surprise many pundits.
Come Monday, many people will pick the top seeds to win in their office pools. But Saint Louis University professors Bryan Clair, Ph.D., and David Letscher, Ph.D., have found that those who take the road less traveled may fare better than their cube-mates who choose the all favorites.
The professors have detailed their NCAA tournament math problem an academic article, “Optimal Strategies in Sports Betting Pools,” which currently is under review for publication.
The math duo began thinking about the problem in 2003, when Kentucky was picked to win the championship by more than 50 percent of entrants in a large, Internet pool. The Wildcats ended up being sent home in the fourth round. The professors also recalled the 1999 pool, when 70 percent picked favorite Duke, which lost a thrilling NCAA final at the buzzer.
“To us, those numbers seemed way too high,” Clair said. “Idle musings turned into serious research when we analyzed a few simple cases and realized how difficult and interesting the math turned out to be.”
According the professors, any good math problem usually involves a search for a balance between opposing forces. In the case of tournament pools, there are two major competing forces: the desire to pick good teams and the desire to pick differently from the rest of the pool. Good teams may win more often, but a less popular pick that turns out a winner offers a big advantage over the crowd.
The heart of the problem is how pool participants can strike a balance between picking favorites and underdogs, without going too far.
For the Saint Louis University math professors, making good picks is a problem of modeling and optimization. First, they created a mathematical model of a tournament pool.
“Once the model is created, finding the optimal picks simply comes down to pure mathematics,” Letscher said.
The math professors model each game in the tournament as a coin flip. The coins are weighted by the strengths of the teams. A massive group of researchers from around the country already are attempting to rate, rank or otherwise measure team strength. The SLU professors simply put these researchers’ results into their model.
But it’s not just the competition taking place on the court that’s important. The professors must model other players in the pool who are making picks. They also do this with weighted coin flips, using a basic view of human decision making that’s turned out to be fairly accurate, according to the professors.
Using this data, the professors formulated a strategy to find the picks that maximize the chances of winning a pool and then wrote a computer program to estimate the quality of a set of picks.
Although there are only four days between Sunday’s bracket selection and tournament tip-off, the math professors say that gives them enough time for them to gather data and make picks.
Clair and Letscher are quick to point out their system doesn’t guarantee a win, and the pair have never actually used it in a pool in which money is on the line.
And because probabilities only work after numerous trials and attempts, it likely would take years before pool participants would see a dramatic impact using the math professors’ methods.
However, during the last two years, the professors have noticed some patterns in their optimized picks and came up with the following basic tips:
- Try to figure out the teams that are being over- and under-picked for the Final Four. Those who put a good, but unpopular, team, in the Final Four and win will find they will score points that few other players in the pool do.
- Choose one of the top teams to not make the Final Four — it’s happened before (think Kentucky in 2003). Such Final Fours are as likely as those filled with the favorites and may keep players away from the most common picks.
- Pick better teams to win in the early rounds. While there may be a popular belief that players in a pool should pick a team seeded 12th to win in the first round — and there is some history to support these teams’ success early on — the professors say it’s better to take risks with the Final Four. The rest of the bracket won’t mean much for players whose unpopular Final Fours come true.
- The professors caution against picking underdogs for the finals.
- They add that the size of the pool matters. With just a few friends, pick the favorites to win; forget about upsets. Avoiding the crowd can be worth the risk as the size of the pool grows and players’ picks start to make a difference.
The professors’ paper in pre-print form and a public domain copy of their software are available at http://euler.slu.edu/~clair/pools.
EDITOR’S NOTE: To arrange an interview with the professors, call Clayton Berry at (314) 977-7117.
