The NCAA men's basketball tournament - popularly known as "March Madness" - begins next week. Millions of college basketball sports fans will be sharpening their pencils to create a winning bracket. 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 filling in their brackets.
The tournament is exciting for its upsets and seeming unpredictability. Yet your research has found distinct patterns. How can that help people trying to make sense of it all?
Each game in the tournament can be viewed as a random experiment, with a different probability for each game (or each pair of seeds pitted against each other). Our research suggests that in the Elite Eight and beyond, we can model the performance of how far seeds progress. An implication of such a model is that it is less important which teams are playing each other, but rather, which seeds are playing each other.
How does the BracketOdds site help aspiring bracketologists?
The site translates our model into a Web tool for anyone interested in assessing the seed combinations for their brackets in the Elite Eight and beyond. Let's take the Final Four, for example. The most likely Final Four seed combination is 1, 1, 2, 3. The odds against this occurring are about 16 to 1. It has occurred three times in the past 27 years. The odds against the four No. 1 seeds reaching the Final Four are about 48 to 1, just about three times less likely. This has occurred just once in the past 27 years.
The site can compute the odds against seed combinations occurring that have never been observed. For example, that odds against a 1, 1, 2, 4 Final Four is about 26-1, the highest odds Final Four that has yet to occur. The odds against one or more No. 16 seeds reaching the Final Four are about 791 to 1. The odds against all four No. 16 seeds reaching the Final Four are about 100 trillion to 1, which is just over six times the size of the national debt.
How should people interpret the odds that the site calculates?
The odds provide a measure of likelihood for a certain set of seed combinations to occur in a given round. Relative odds rather than absolute odds are the best way to use the information from the site. To illustrate this point, the odds against a 1 vs. 2 national finals is about 3.7 to 1, while the odds against a 2 vs. 3 national finals is about 13.6 to 1. This means that a 1 vs. 2 national final seed combination is just over three times more likely to occur than a 2 vs. 3 final combination. In other words, comparing the odds of different seed combinations can help people assess the likelihood of their bracket compared to other people's brackets.
Its seems so unlikely that a team seeded No. 11 could reach the Final Four, yet that is exactly what VCU did last year. How can you explain that?
The laws of probability can neither be ignored nor avoided. The odds against one or more teams seeded No. 10 through No. 16 reaching the Final Four is about 18 to 1, which is almost as likely as the most likely Final Four seed combination, 1, 1, 2, 3. In fact, there have been three such times that a team seeded No. 10 or worse has reached the Final Four. The hard part is predicting when it will occur, and that boils down to old-fashioned luck, plain and simple.
Are there any other insights you can share with the millions of people who will be filling out brackets after Selection Sunday?
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. In all but three of the past 27 tournaments, an average of just over 3 teams seeded No. 7 or lower have reached the Sweet Sixteen. As for upsets, in 18 of the past 27 tournaments, eight or fewer of teams seeded No. 1, 2 or 3 reached the Sweet Sixteen (in other words, four or more did not). On the other hand, for the risk averse, in 11 of the past 27 tournaments, only teams seeded No. 1 or 2 have reached the Final Four; the odds against this occurring are 6-1.