The NCAA men's basketball tournament - popularly known as March Madness - begins next week. Millions of college basketball fans will be sharpening their pencils to predict the winning teams. 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, Jacobson created the BracketOdds website to assist fans filling in their brackets.
What is "bracketology"?
Bracketology has two phases. Phase I is the process of determining which teams will be selected to participate in March Madness. Phase II is determining which teams will win in each round and who will eventually be crowned national champion.
What are the odds of a person filling out a perfect bracket?
If you include the four "First Four" games, there are 67 games to be played. Assuming that each game is a tossup, the odds against this occurring are about 146 quintillion to one (that's 146 followed by 18 zeros). If you only consider the main bracket, which covers 63 games, the odds drop to about 9 quintillion to one. However, not all games are a tossup, so the odds are significantly less, but still quite large.
In your research, what factors have you found that could be indicative of a team's success in the tournament?
In the early rounds, having a high seed (seeds No. 1, 2 or 3) significantly increases your chance of surviving until the Sweet Sixteen. If a team has a double-digit seed (10 or more), seeds that avoid No. 1 the longest tend to survive longer. That means a No. 11 seeds can advance to the Sweet Sixteen by defeating a No. 6 and (potentially) a No. 3 seed, while a No. 10 seed can advance to the Sweet Sixteen by defeating a No. 7 and (potentially) a No. 2 seed. Once teams move beyond the Sweet Sixteen, the seeds become less predictive.
A lot of people rely on seeding to help them fill out their brackets. To what extent do seeds matter?
Seeds are everything early in the tournament (through the Sweet Sixteen). Upsets still occur. For example, No. 1 seeds do lose in the second round (about 12 percent of the time, on average). However, once teams reach the Elite Eight and beyond, seeds play a significantly diminished role in who will advance.
What do your statistical models say about upsets? Are a certain number of upsets probable?
Upsets are what make the tournament exciting. On average, almost four teams each tournament seeded No. 1, No. 2 or No. 3 do not advance to the Sweet Sixteen. On average, almost 1.5 teams each tournament seeded No. 11 or lower advance to the Sweet Sixteen. In fact, only four times since 1985 have no such seeds advanced to the Sweet Sixteen. The challenge is guessing which such teams they will be.
On our website, we have a section called "Help With Building Your Bracket" that highlights numerous observations to help people calibrate the right number of upsets in each round. For example, the 12-5 upset in the round of 64 is often discussed, yet the 11-6 upset is just as likely to occur.
What advice can you give to all those filling out brackets after Selection Sunday?
Create your bracket before Selection Sunday based on which seeds you wish to advance in each round. Since a bracket has four regions, four distinct regions are needed. Once the teams are announced, fill in your bracket accordingly. By focusing on the seeds, rather than the teams, any hidden biases are removed.