The writer teaches math at Davidson College. Three weeks ago he wrote about his student March Madness exercise. Today, after Duke’s victory over Butler in the NCAA basketball championship, he shares the results.
By TIM CHARTIER
This year’s March Madness was easily maddening for many of us who created brackets. The many upsets in the NCAA men’s basketball tournament created an exciting whirlwind of results.
That was also the case for with the mathematically generated brackets by students in the math modeling class at Davidson College. (We played for high stakes: The winner would receive a Davidson basketball T-shirt and coupons for free cones from Ben and Jerry’s.)
Students’ brackets performed well in the first round, with all but one performing in the top 90th percentile of the close to 5 million brackets submitted to the ESPN Tournament Challenge. (Put another way, these brackets based on mathematical modeling beat 90 percent of the picks submitted to the ESPN competition.) The lowest in the class was a 72nd percentile.
Stephen Curry, 27th percentile
President Barack Obama, 51st percentile
Dick Vitale, 21st percentile
LeBron James, 64th percentile
Given the constraints of the class, we learned one ranking method, though we had many to choose from. Students learned how to reward momentum during the season. With this knowledge, each student could produce a personalized bracket from individual modeling decisions.
This created variability in the students’ predictions, but the overlap in the underlying method was evident, as most picked Kansas as the likely overall winner. Given Kansas’s early loss to Northern Iowa, one might expect that the brackets performed poorly after the second round of the tournament. But that wasn’t the case. After the Sweet 16 round, almost a dozen students’ brackets were in the 98th percentile (some even in the 99th percentile).
After the Elite 8 and Kentucky’s loss to West Virginia, many student brackets remained in the 94th percentile. However, only two stood to gain additional points in Final Four games.
Amid all the games, sweat, and athleticism, our class pool came down to two brackets and the result of one of the semifinal games:
If West Virginia won, Chuck Wessell, a graduate student from North Carolina State University who visited Davidson for a month and aided and taught in the modeling class, would win the pool.
If Duke won, Daniel Martin, a junior math and physics double major, would win.
The rest of the class, with brackets ranking in the 90th percentile, was left wondering how the games’ results would affect their overall standings.
In the end, of course, Daniel won the pool and will enjoy the fruits of his mathematical modeling. His class-winning bracket was in the 90.9th percentile and ranked 435,169th.
Surprisingly, a second bracket he created, using another variation of the method, did even better. (The students were allowed to submit only one entry.) That bracket also chose Duke as the overall winner and along with its other predictions ranked in the 99.9th percentile and ranked 5,170th out of approximately 5 million submissions.
Another memorable note: Chuck Wessell actually tried to create a bracket that would lose. He randomized the weighting of games’ importance. Instead of losing, he had one of the best brackets. Very funny! Given the surprises in this year’s tournament, it’s no wonder he did so well.
Quite a mathematical journey through the madness of March and the inherent unpredictability of sport.
March 19, 2010, “Can math beat your March Madness bracket? Yep”by