Sports Rankings

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As the college football season continues, team rankings get more important – and controversial. Some mathematicians are trying to make the rankings fairer.


Making sports rankings more sporting. I'm Bob Hirshon and this is Science Update.

Sports rankings, like those used for college football, often make players and fans cry foul. That’s why mathematicians at the Rochester Institute of Technology are suggesting changes to the ranking systems. Project leader Darren Narayan (nah-RY-an) says the goal is to factor in head-to-head competition. Right now, college football rankings are based on two polls and a computer-generated ranking.


Head-to-head play isn’t incorporated in there directly. Obviously it’s going to impact the votes. But there still opens the door for a situation where 3 beats number 2.

That happened four years ago, when third-ranked Colorado beat second-ranked Nebraska, but still got shut out of the championship game. I'm Bob Hirshon, for AAAS, the science society.

Making Sense of the Research

In professional sports leagues like the NFL and the NBA, it’s relatively easy to pick a champion every year, using the playoff system. Even the NCAA has a straightforward playoff. But in college football, where an enormous number of teams play relatively few games in a limited season, it’s a lot harder to say who’s number one.

That’s how the Bowl Championship Series (BCS) came to be. It’s not just a bunch of football games, but a key part of an extraordinarily complex statistical system. There are dozens of Bowls at the end of the season, but only four – the Nokia Sugar Bowl, the AT&T Rose Bowl, the FedEx Orange Bowl, and the Tostitos Fiesta Bowl –feature the best teams. Each year, one of these bowls is designated the official championship game, winner take all.

But how do you get into the top bowl? You get ranked #1 or #2 in the country, and that’s where all the statistics come in. The rankings, which are updated every week, are determined by four main factors:

  1. Opinon Polls: actually the average of two polls, one of sports writers and broadcasters, the other of coaches.
  2. Computer ranking: actually the average of eight independent computer rankings, with the lowest ranking dropped. Each of these eight rankings takes into account a different combination of factors, which may include a team’s number of wins, the total number of points they scored, how many points they won each game by, how tough their opponents were, and other issues. Some of the rankings even make adjustments for having the home-field advantage, and one system actually penalizes teams for running up the score in a blowout victory. As you can imagine, translating subjective issues like these into numerical values is a challenge in itself.
  3. The strength of a team’s schedule: a mathematical formula that determines how tough the team’s opponents were, and therefore, how impressive their victories are.
  4. Number of losses: an important factor that weighs in heavily after the three issues above have been integrated.

What a project! You would think that after doing all this work, the rankings would be fair, but that’s really impossible to know, since there’s no absolute measure of who the best team is. (If there were, we wouldn’t need this system!) However, there are times when the system just seems blatantly wrong, as in the Colorado-Nebraska game mentioned above. Why shouldn’t Colorado outrank Nebraska after they just beat them? Now that you know how the BCS works, you can see how it happened.

Narayan isn’t suggesting getting rid of the BCS. His team is just trying to refine the statistical system to take head-to-head play into account more strongly. Their goal is to eliminate controversial situations like the Colorado-Nebraska problem.

But is even head-to-head play a fair way to judge teams? After all, the old football saying says that any team can beat any other team on any given Sunday. We all know that weaker teams beat stronger teams once in a while, and that many a World Series, Super Bowl, or NCAA Championship has been won by a team that wasn’t necessarily the best in the league. The advantage of head-to-head play, though, is that while it isn’t necessarily fair, it’s clear: one team wins, one team loses. That’s why other leagues rely on playoffs to settle the score. The contrast between the Superbowl playoffs and the BCS shows that sometimes, the harder you work to make statistics fair and accurate, the more controversial they become.

Now try and answer these questions:

  1. Why is Narayan trying to improve the BCS rankings?
  2. How are the BCS rankings currently determined? Do you agree with this system? Why or why not?
  3. “The harder you work to make statistics fair and accurate, the more controversial they become.” Explain this statement, and how it applies to the BCS.
  4. What factors do you think should be taken into account when determining football rankings? Which would you leave out? Why?

For Educators

In the Illuminations lesson Will the Best Candidate Win?, students explore alternative voting methods. They discover what advantages and disadvantages each method offers, and also see that each fails, in some way, to satisfy some desirable properties.

To experiment with their own rankings systems, students can access sports statistics at ESPN.com and SportsIllustrated.com.

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