BCS stands for Bowl Championship Series. It turns out to be one of the most complex statistical systems that we can encounter in daily life. Unlike other National Collegiate Athletic Association (NCAA) sports, college football does not have an end-of-season tournament or playoff series. Instead, any Division I-A team with a winning record can play in a post-season competition called a bowl game. These games bring publicity and money to the colleges and universities that participate in them. But with winners of 25 different bowls all claiming to be the number one, it's been hard to call any one team the "National Champion." In 1998, the Bowl Championship Series debuted and promised to solve this problem. The BCS divides the glut of post-season games into two groups:
  1. The BCS bowl games - These four games consist of the Nokia Sugar Bowl, the AT&T Rose Bowl, the FedEx Orange Bowl, and the Tostitos Fiesta Bowl. Each year, one of these contests is designated as the national championship game. These are the premier games that feature only the top-ranked teams. Getting into one of these games guarantees that a school will receive a lot of money from bowl sponsors. Winning one of these games can be like hitting the lottery. This year's Fiesta Bowl, which isn't even the National Championship game, pays the victor and their athletic conference $13.5 million.

  2. All other bowl games - The remaining games are now considered minor bowls. Any team with a 6-5 record can be picked to play in one of these games, but their prestige and the monetary rewards for playing in them are much lower than the BCS games.
Teams compete throughout the year to participate in one of the four high-profile BCS games. To figure out who gets to play, a complex, mathematical formula is used to rank the top 25 teams throughout the season. Each Monday, the BCS ratings are updated based on the teams' performances during the previous week. At the end of the regular season, the top two teams in the ratings play each other for the national championship. The calculations performed by a small number of mathematicians and statisticians off the field are more important to a team's chances of being in the final game than their efforts on the field. No college football fan can deny how important mathematics is to everyday life after seeing this formula.

Math and Football:
A Long History

Opinion polls have topped the sports page since the Associated Press college football ratings appeared in 1936. But the very first widely known poll was actually a mathematical system, just like the BCS rankings. This ranking was designed in 1926 by an economics professor at the University of Illinois.

The competitors for the other three bowl games are chosen from teams who end up in the top 12 of the final ranking. These bowls don't pair off No. 3 vs. No. 4, No. 5 vs. No. 6, and No. 7 vs No. 8, because bowl organizers also factor in regional considerations, like what conference a team comes from. They want to pick a team that will attract a lot of fans and advertising dollars to their game. Once again, math plays a role in these financial forecasts.

What counts in the BCS ratings?
Here is a closer look at how the math that produces the BCS rating works. There are four components that contribute to a team's rank.

  1. Subjective polls
  2. Computer rankings
  3. Strength of a team's schedule
  4. Number of Losses
Each of these factors is represented by a numerical value. Teams are assigned a certain number of points for their performance in each category. These four values are then totaled to produce a team's final score. The team with the lowest point total gets the number one spot for the week.

The Four Variables Explained
The Associated Press (AP) and USA Today/ESPN Coaches Poll Ratings
Two subjective polls, The Associated Press ranking and USA Today/ESPN Coaches Poll make up the first variable. Both of these polls have been around for many years and have an established track record. Both of these are personal choice polls. They are called this because members of both groups cast their votes based on what they think about a team's performance. Both groups also know a whole lot about football. A national board of sports writers and broadcasters participate in the AP poll, and a select group of football coaches determines the USA Today ratings. The BCS incorporates their input by averaging team rankings from these polls. For example, a team ranked No. 3 in one poll and No. 5 in the other would get four points in this category.

Computer ranking
There are eight computer-generated rankings that make up this variable. The rankings are actually the output of computer programs that crunch weekly game statistics. Most of these programs were designed by people with backgrounds in math or statistics. Their formulas factor in an eclectic mix of variables, from who won to where a game was played.

To get a team's point total, the lowest ranking is dropped, and the remaining seven are averaged to produce the team's score. This prevents any one computer's results from ruining a team's chances at No. 1 or 2. For example, if a team is ranked 1, 1, 1, 1, 4, 2, 2, 1, the fourth place finish will be dropped. A team's final computer ranking would then be 

( 1 + 1 + 1 + 1 + 2 + 2 + 1 ) / 7 = 9 / 7 = 1.29

rather than what they would have scored with all eight included 

( 1 + 1 + 1 + 1 + 2 + 2 + 1 + 4) / 8= 13 / 8 = 1.63

Some of the teams at the top of the BCS ranking can be separated by tenths of points, so a difference of 0.34 points is no small matter!

Computer Ranking Run by Important variable
Billingsley Report Richard Billingsley, businessman Strength of opponent, final score, won-lost records of teams (before and after the game)
Dunkel Index John Duck, statistician Strength of schedule, won-lost record, the upset factor
Massey Ratings Kenneth Massey, mathematics graduate student Overall team rating, offense and defense specific ratings, strength of schedule, home-field advantage
New York Times (NYT) Marjorie Connelly, editor of NYT surveying department Margin of victory, strength of schedule, recent performance
Rothman David Rothman, retired mathematician Number of wins, margin of victory, quality of opponent
Sagarin's USA Today Jeff Sagarin, mathematician and MBA Margin of victory, strength of schedule, location of game
Scripps-Howard Herman Matthews, mathematics and computer science professor Game score, penalty for running up score, strength of schedule
Seattle Times Jeff Anderson, political science graduate student
and Chris Hester, sportswriter and broadcaster		 Quality of opponent, strength of schedule

Strength of a Team's Schedule
Another computer program helps to determine the third variable -- how a team's strength of schedule compares to other teams nationally. The cumulative win/loss record of not only the team's opponents, but their opponents' opponents are included in this calculation. This makes teams think twice about lining up a bunch of teams they know that they can crush on the field. It also makes coaches and athletic directors once again jump into the world of statistics. They have to plan their schedule in advance, meaning that they have to predict how well their opposition will do in the future as well as who they are likely to play.

The computer program produces a numerical value representing the strength of the opponents schedule (So) and one for the opponents' opponents (Soo). A team's overall strength of schedule (St) is then calculated using these numbers. The opponent's scheduled strength is worth twice as much as their opponents' schedule. Let's put it in the form of an equation:

2 * So + Soo= St

The resulting number, St, is used in ranking a team's schedule relative to all other 115 Division I schools. Once they have been placed in order, this list is then subdivided into quartiles (1-25, 25-50, 50-75, and so on). Their rank is then converted back to a point total by multiplying it by 0.04. This allows teams to be rated based on their placement within a given quartile.

Here's an example: A team's schedule strength is ranked No. 30 in the nation. Multiplying 30 by 0.04 gives you their point total for this category, 1.2. The 1 tells you that they placed in the second quartile, and the 2 tells you approximately where they placed within that group.

Number of Losses
The final category, number of losses, can really sound the death knell for a team. Each loss equals one point, and is added directly to a team's total score. Remember, a lower point total means a higher ranking. One loss often means the difference between playing in the national championship game and hoping to be chosen for one of the other BCS bowls. If you think about it, that's fair. This is the one place where what happens on the field matters far more than mathematical models.

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