Mathematicians find that the odds connected to a successful "March Madness" bracket are downright overwhelming. Video courtesy: Inside Science News Service / Ivanhoe
Like many sports fans across the country, five groups of physicists at the University of Maryland are filling out their brackets to predict the winners and losers in the NCAA men's basketball tournament. While most people use a strategy to guide their picks — such as relying on advanced basketball knowledge or identifying the cutest mascot — this Maryland method relies on quantum physics.
David Hucul, a graduate student, came up with the idea. Last year, his quantum picks performed surprisingly well against picks from other people in the laboratory.
"It almost won," Susan Clark, a post-doctoral researcher who works with Hucul. "It was kind of scary."
Both Hucul and Clark work in the lab of Chris Monroe, usually on problems related to quantum computing and building quantum networks. They use ions of the element ytterbium, a metal that's smack dab in the middle of the periodic table. Everyday research in the lab is dedicated to making connections between submicroscopic objects, across distances much longer than typical quantum interactions, such as a few yards instead of smaller than an atom.
When used to assist in picking basketball games, the team uses a phenomenon called superposition. They coax the ytterbium ion to act a bit like a coin. In the same way that flipping a fair coin yields a random result of heads or tails, superposition allows the physicists to prepare the ion to have a 50-50 chance of ending up in state A or state B. It's possible that, based on the way a coin is flipped, the result isn't always truly random. But by using quantum phenomena, in which the location or state of an object is based on probability, the result is truly random.
Ion picks the Panthers
Hucul and Clark create an ion that is simultaneously in those two states. They assign one state to each basketball team, and then record the ion's verdict for each game of the tournament. The ion's picks suggested that the University of Pittsburgh, the No. 8 seed in the West Region, will win this year's tournament. The New York Times' Nate Silver pegged the Panthers' chances of winning the whole thing at about 0.8 percent — making them about the 13th most likely champ, his analysis indicated.
The trouble with the ion technique, if you want to have the best chance of predicting the winner of the tournament, is that in many games the two competing teams do not really have an equal chance of winning.
However, research also shows that people — even knowledgeable basketball fans — are not very good at predicting the real result of the tournament. A 2010 study in the Journal of Applied Social Psychology showed that sometimes the best bet is always to pick the higher seed, because even though upsets will occur, picking the right one is difficult.
Speaking of difficult, the odds of generating a perfect bracket for all 63 contests that kick-off with Thursday's games is astronomical. If the predictions of game winners were based on coin flips, the odds of a perfectly correct bracket are one in over 9 quintillion — that's the number 9 followed by 18 zeroes — said Jeff Bergen, a mathematician at DePaul University in Chicago.
Odds of a perfect bracket
Bergen also projected how likely it is that someone who knows a bit about basketball would generate a perfect bracket. By estimating the probabilities that No. 1 seeds beat No. 16 seeds, and No. 2 seeds beat No. 15 seeds, and so on, he found that there's a roughly 1-in-17,000 chance of predicting a perfect first round of the tournament. With a couple of additional assumptions, he made the rough calculation that for an entire tournament, about one out of 128 billion brackets would be perfect.
"Certainly, one could make different assumptions, but the 128 billion is not a bad approximation," said Bergen.
That means that if each person in the U.S. knew a bit about basketball and filled in a bracket, there's about a 1-in-400 chance that one person would pick every game correctly.
The physicists might be able to simulate this. Clark said they could weight the ion's choice by creating an "unequal superposition," which would allow them to create a probability unequal to 50-50. In this way, they might be able to account for the type of basketball knowledge Bergen referred to, and reduce the odds of the ion producing a perfect bracket.
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Chris Gorski is a writer and editor for Inside Science News Service. This report was originally published on Inside Science as "A Quantum Leap for Basketball Bracketology." Copyright 2013 American Institute of Physics. Reprinted with permission.