The Math of March Madness

With the opening round of March Madness (a.k.a. the NCAA Men’s basketball tournament) getting underway Thursday, the mathematicians are out in force. If you’re still looking for additional help with your bracketology, Lab Notes is here to help.


Among the more interesting picks is the computer ranking system devised by researchers at the Georgia Institute of Technology. Called LRMC (Logistic Regression Markov Chain), it was developed by Joel Sokol, Paul Kvam and George Nemhauser based on results during the season, which teams are competing, home court advantage and margin of victory. Last year, LRMC correctly predicted all of the Final Four and picked Kansas to defeat Memphis in the championship game.


And this year? The Georgia trio has University of North Carolina (number 1 in the South) vs. the University of Pittsburgh (number 1 in the East) and the University of Memphis (number 2 in the West) vs. the University of Louisville (number 1 in the Midwest) in the final four, North Carolina against Memphis in the championship game, and North Carolina coming away with the crown. Granted, the LRMC system deviates in only one place from the NCAA seedings, which have the University of Connecticut (number 1 in the West) rather than Memphis in the Final Four, but 1 in 4 is significant.


In earlier rounds, the LRMC system identifies Michigan State, Boston College and Utah State as potential upsets. You can find the LRMC rankings and analysis here.


If you prefer you pick your games one at a time, try to get whoever you’re betting against to re-open the wager at halftime. According to a new paper by Jonah Berger and Devin Pope of the Wharton School at the University of Pennsylvania, “being slightly behind can motivate people to work harder, and consequently, lead to increased success,” Berger tells me. Their analysis of 6,572 NCAA basketball games from 2005 to 2008 shows that being slightly behind at halftime increases a team’s chance of winning by 5.5 to 7.7 percentage points—half the home-court advantage. And compared to teams that are slightly ahead, teams that are slightly behind at halftime are more likely to win.


In general, if you’re ahead in a competition you are more likely to win, something that holds for sports or for groups of employees competing for a contract. “In hockey, the team behind after the first period wins fewer than 33 percent of the games,” Berger and Pope write in The New York Times. “In baseball, the team losing after three innings wins less than 20 percent of the time. Basketball is no different. N.C.A.A. teams across all divisions that fall behind in games tend to lose, and more so as the deficit increases. Teams down by 4 at halftime lose about 60 percent of games. Teams down by 8 lose about 80 percent of the time.”


Losing, though, can sometimes lead to winning. Teams behind by a single point at halftime win more often than teams ahead by one, the researchers report in an upcoming paper. They attribute that to motivation: being close but behind causes a competitor to bear down and try harder.

But be careful how you use this nugget of wisdom. “Every two points better a team is doing relative to its opponent at halftime is associated with an approximately 8 percentage point increase in the probability of winning,” the researchers write. It’s only when the halftime margin is as close as it can be—a single point—that expectations flip. Teams that are behind by 1 point are more likely to win, emerging victorious in 51.3% of games. If you think that 1-point halftime margins are too rare to bother with, refresh your memory of the 2006 NCAA tournament. Duke led North Carolina by 1 at the half—and lost 83-76.
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