Simulated Simians Pick Best Football Teams As Well As Pros
According to lore, during a debate in 1860, evolutionist and agnostic Thomas Huxley argued that six immortal monkeys working at six infallible typewriters given an unlimited supply of paper and ink one day could bang out the entire works of William Shakespeare.
Tricky? Absolutely. But it helped him defend his point at the time, which was that it didn't take an omniscient and enigmatic God to create man -- only time and evolution.
Now an undergraduate researcher in Georgia Tech's School of Mathematics - and his two faculty advisers - say that a team of monkeys tossing coins and picking their favorite football teams could come up with the same championship teams as the almost-omniscient and definitely enigmatic NCAA Division I-A Bowl Championship Series (BCS) ranking system.
And they've developed calculations that demonstrate it.
Georgia Tech junior Thomas Callaghan, working alongside Assistant Professor Peter Mucha and Visiting Assistant Professor Mason Porter, scratched his head while pouring over the befuddling BCS rankings this past summer and wondered: Could a bunch of monkeys rank the top Division I-A football teams at least as well as the expert coaches, professional sportswriters and complicated statistical ranking algorithms in the BCS system?
It turns out that they can, at least in theory. Callaghan tested the hypothesis using simulated monkeys - the actual, mathematical term is "random walkers" - and a list of the 117 teams playing in Division I-A.
"Each of our virtual monkeys got a single vote to cast for the best team in the nation, making their decision based on only one, simple guideline - they periodically look up the win-loss outcome of a single game played by their favorite team, and they flip a weighted coin to determine whether to change their allegiance to the other team when making their vote," Callaghan said.
The "weighted coin" is the key, Callaghan said. In this hypothesis, the monkey's coin toss is meant to imitate what happens in the real world, when there's a better-than-50-percent chance that the winning team -- say, "heads"-- is the better team. But the weighted coin toss also allows the losing team -- or "tails," with a less-than-50-percent chance of winning - to still be considered the better team by voters, thus regarding the game as an upset. The monkey simply casts its vote according to the outcome of the coin toss, Callaghan said.
This system, of course, is far less complex than the labyrinthine BCS system, which looks at much more than a team's win-loss record. [See details below.]That system takes into account such things as the strength of an opposing team, when a game is played in a season, a team's poll averages and the sometimes-secretive computer rankings given to Division I-A teams by several formulas.
Callaghan's Monkey Ranking System, however, looks only at wins and losses. A monkey starts voting for a randomly chosen team in Division I-A. Then, the monkey meanders around a "network" of the other teams, randomly changing his vote for his favorite team each time a game is played. Again, the monkey bases his vote decision on a weighted coin toss.
"We let the monkeys change their minds over and over again, but the total number of votes cast for each football team quickly stabilizes," Mucha said. "We thereby obtain rankings each week of the season and, at the end of the season, by looking at the fraction of monkeys that have voted for each team."
Under this system, winning a game is directly rewarded and the strength of a team's schedule is automatically incorporated into the rankings, because games played against highly ranked opponents lead to more monkeys inquiring about a team and making vote decisions based on the outcomes of those games.
The mathematicians took their system and compared the monkey rankings with the real rankings from the past 33 seasons of Division I-A football.
It turns out the monkeys do almost as well as the BCS system in picking the two teams that face off in the national championship. For example, at the end of the 2002 season, the monkeys picked Miami and Ohio State as the top two teams. In 2001, they picked Miami as the top team and, in 2000, they picked Oklahoma.
"Although an individual monkey never settles on an individual team, the collective behavior of all the monkeys after they all vote appears to give you a meaningful ranking of teams," Mucha said.
"We're not statisticians. We don't know anything about statistics," he said. "I mean, there are just some real freakish football fans out there that really get into this, and we're just doing this as a fun research topic. But I think we've proved our point."
And that is?
"One of the main things that comes up in this is its simplicity," Mucha said. "All our system does is take into account who beats who. Only by that, we come up with a ranking system that, in the end, is almost comparable to all the other systems used to rank teams today. All these other systems have all these arbitrary points of information. At the end of the day, if you take all that away, the monkeys often come up with the same championship competition."
The researchers are quick to point out, however, that they haven't come up with the best way to rank Division I-A football teams.
"Saying our system is better than the others - you're not going to win that argument," Mucha said. "This was about trying to make decisions in an environment where you have very little data. It has applications to many settings, especially in helping a student understand how to attack a problem with little data when you're forced to make a decision."
Callaghan is more succinct.
"I believe there should be a playoff system," he said.
This summer research experience was funded by the National Science Foundation through the three-year, $1.5 million VIGRE program, which aims to increase the number of Americans who pursue careers in the mathematical sciences. Porter's postdoctoral position at the Institute is another component of Georgia Tech's VIGRE award, which encourages research interactions with undergraduates like Callaghan.
"The projects are intended to involve students in the creative aspects of mathematics in a non-classroom setting, and they're also expected to enhance the development of student communication skills," Porter said, adding that Callaghan's project did all those things while examining a topic of real interest to scientists and football fans.
"All of this monkey ranking actually comes from who plays who. The idea is that we spent time looking at this football network. But there are networks all over the place," Porter said. "You can look at networks in Congress, or when looking at the power grid and, of course, when you're talking about the Internet. Each of those represents a network of some kind. This is a timely topic and it's not going away. That's what makes it beautiful for Thomas to pursue as a research project."
Gary Schuster, dean of Georgia Tech's College of Sciences, said the VIGRE grant opportunities in the School of Mathematics are among the many undergraduate research options available to students throughout the Institute.
"This is one of the features that distinguishes Georgia Tech from many other universities," Schuster said. "Our faculty members are dedicated to advancement of knowledge in their fields, and students at Georgia Tech have the opportunity to work with a wide variety of the world's leading scientists on projects that lead to exciting and meaningful discovery."
Callaghan said he'd heard about this research opportunity last year through Porter and Mucha, and it immediately caught his interest.
"[Mucha] told me about this idea and I said, 'Sign me up!' I just jumped on the project and started doing research on college ranking systems," he said. "There are statistical methodologies that are out there among sports enthusiasts and serious scientists, and there are all kinds of ranking systems employed."
Looking at the Division I-A system, Callaghan said he quickly realized that it might fit into a mathematical study of networks and systems.
"There's information in that system. Given that - and the controversy over the rankings - we thought this would make a great exercise," he said. "As a result, I get a lot out of this by being able to look at real-world problems and elegant ways to address them using mathematics. For example, I got to learn how to use mathematical computer programs out of it, and I'd had no experience with them before. I got very comfortable using them after this. I also had a chance to gain a better understanding of networks, discrete mathematics, applied mathematics - a whole range of topics."