For this year’s NCAA March Madness tournament, Quicken Loans and billionaire Warren Buffett have offered $1 billion for a perfect bracket. Will anyone claim the prize? In an interview with News Bureau physical sciences editor Liz Ahlberg, computer science professor Sheldon H. Jacobson discusses the mathematics behind “bracketology” and shares his insights. Working with U. of I. students, he also created the BracketOdds website to assist fans when creating their brackets.
You have been researching bracketology for some time. What has some of your research shown about which team makes it to the championship?
Obviously, survival in the early rounds is critical to having a chance to win the national championship. The reason more teams seeded No. 1 win the national championship is that they survive the early rounds at a higher rate than teams seeded No. 2, who in turn survive the early rounds at a higher rate than teams seeded No. 3.
So being highly seeded is important in the early rounds. Yet the biggest obstacle to a perfect bracket is predicting upsets. What have you found about upsets?
The number of upsets that occur is quite predictable, based on the seeds of teams. For example, in the round of 64, the 5-12 upset gets a great deal of attention. In the 29 tournaments from 1985 through 2013, the No. 12 seeds had a 41-75 record. What gets less attention is the 6-11 upset. In the 29 tournaments from 1985 through 2013, the No. 11 seeds had a 39-77 record. Moreover, in 11 of the past 29 tournaments, two, three or all four No. 11 seeds advanced to the round of 32. Collectively, an average of 4.45 teams seeded No. 11 or lower advanced to the round of 32. However, an average of 1.69 teams seeded No. 13 or lower have won in this round, so picking one or two such upsets is prudent.
A team seeded No. 16 has never won a game. Using our models, the odds against one or more No. 16 seeds reaching the Final Four is 679 to 1, which is quite a long shot.
What have you found about upsets in the round of 32 and the Sweet Sixteen?
In the round of 32, teams seeded No. 7 and lower continue to advance. In 25 of the past 29 tournaments, two or more of these teams have reached the Sweet Sixteen, with an average of 3.41 of these teams reaching this round. In fact, only once (1995) in the past 29 tournaments has a team seeded No. 7 or lower reached the Sweet Sixteen. Moreover, in 25 of the past 29 tournaments, one or more teams seeded No. 11 or lower reached the Sweet Sixteen, with an average of 1.51. Among highly seeded teams, in 19 of the past 29 tournaments, eight or fewer teams seeded No. 1, No. 2 or No. 3 reached the Sweet Sixteen.
The Final Four draws the most attention. What have you found about the seeds in that round?
Here is where people often make errors, since it is difficult to imagine teams seeded No. 1 losing. Our research compared the performance of teams seeded No. 1, No. 2 and No. 3, and showed that once these teams reach the Elite Eight, their performance against each other is statistically indistinguishable. It is more than eight times more likely that no teams seeded No. 1 reach the Final Four than all four teams seeded No. 1 reaching the Final Four. Also, the probability that Final Four contains exactly one or two teams seeded No. 1 is about 0.70.
Will anyone win the Billion Dollar Bracket Challenge, sponsored by Quicken Loans and Warren Buffett?
Absolutely not. Quicken Loans and Warren Buffett have deep pockets, but this challenge will do nothing to empty them. The odds against someone randomly picking a perfect 68 teams bracket are more than 147 quintillion (147 followed by 18 zeroes) to one. Even when taking into account the “sure wins,” the odds against picking a perfect bracket are still on the order of 1 trillion to one. Moreover, it is highly unlikely that anyone will even pick all the winners through the First Four and the Round of 64.
