If you want to win the NCAA College Basketball Tournament office pool and know nothing about basketball, the good news is you have just as much chance as devoted college basketball fans unless you get all crazy about it.
One solution is to try and play it safe by picking all the top seeds in the brackets to make it to the Final Four and then using a back-azimuth strategy to determine the winners among the early games. But upsets are almost a guarantee in the NCAA Tournament. So what is the optimum strategy for people without a clue?
If you know nothing, says an operations research analysis model developed by Sheldon H. Jacobson, a professor of computer science and the director of the simulation and optimization laboratory at the University of Illinois, you're better off picking a combination of two top-seeded teams, a No. 2 seed and a No. 3 seed.
Forget emotion, this is about winning the pool. Any number of websites offer assistance to budding 'bracketologists', such as game-by-game probabilities of certain match-ups or determining the spread on a given team reaching a particular point in the tournament. Jacobson's is the only one to look at collective groups of seeds within the brackets.
"What we do is use the power of analytics to uncover trends in 'bracketology.' It really is a mathematical science," he said. "What our model enables us to do is look at the likelihood or probability that a certain set of seed combinations will occur as we advance deeper into the tournament."
Illinois undergraduate students Ammar Rizwan and Emon Dai then developed the BracketOdds website to help March Madness fans determine the relative probability of their chosen team combinations appearing in the final rounds of the NCAA men's basketball tournament.
Jacobson's model is different in that it prognosticates not based on who the teams are, but on the seeds they hold. They team applied a statistical method called goodness-of-fit testing to NCAA tournament data from 1985 to 2010, identifying patterns in seed distribution in the Elite Eight, Final Four and national championship rounds. They found that the seeds themselves exhibit certain statistical patterns, independent of the team. They then fit the pattern to a stochastic model they can use to assess probabilities and odds.
For example, the probability of the Final Four comprising the four top-seeded teams is 0.026, or once every 39 years. Meanwhile, the probability of a Final Four of all No. 16 seeds – the lowest-seeded teams in the tournament – is so small that it has a frequency of happening once every eight hundred trillion years. Since the Milky Way contains an estimated one hundred billion stars, that means if every star was given a year, the years it would take for this to occur is 8,000 times all the stars in the galaxy.
So don't bet on all underdogs, though sets with long odds do happen. The most unlikely combination in the 26 years studied occurred in 2000, with a Final Four seed combination of 1, 5, 8 and 8. But such a bracket is only predicted to happen once every 32,000 years, so those filling out brackets at home shouldn't hope for a repeat.
So plan on upsets. For even the most probable Final Four combination of 1,1,2,3 to occur, two top-seeded schools have to lose.
"In fact, upsets occur with great frequency and great predictability. If you look statistically, there's a certain number of upsets that occur in each round. We just don't know which team they're going to be or when they're going to occur," Jacobson said.
After the 2011 tournament, and in years to come, Jacobson will integrate the new data into the model to continually refine its prediction power. For 2012, Jacobson, Rizwan and Dai hope to integrate a comparative probability feature into the website to allow users to calculate, for example, the probability of a particular set of Final Four seeds if the Elite Eight seeds are given.
Until then, users can find out how likely their picks really are, and compare them against friends' picks – or even sports commentators'.
"We're not here specifically to say 'Syracuse is going to beat Kentucky in the Elite Eight.' What we're saying is that the seed numbers have patterns," Jacobson said. "A 1, 1, 2, 3 is the most likely Final Four. I don't know which two 1's, I don't know which No. 2 and I don't know which No. 3. But I can tell you that if you want to go purely with the odds, choose a Final Four with seeds 1, 1, 2, 3."They describe model in a forthcoming paper in the journal Omega. Co-authors are Alex Nikolaev of the University of Buffalo, Adrian Lee, of CITERI (Central Illinois Technology and Education Research Institute) and Douglas King, a graduate student at Illinois.