Working out the math in college football can be a little daunting. Unlike other college sports, National Collegiate Athletic Association (NCAA) football does not hold a national tournament at the end of the season to determine which team is the year’s national champion. Instead, a total of 25 bowl games are held throughout the country, pitting teams with winning records against each other. The Bowl Championship Series (BCS) consists of four of these bowl games: the Orange Bowl, the Fiesta Bowl, the Sugar Bowl, and the Rose Bowl. These four bowl games feature eight of the highest rated teams of the year, and each year a different bowl game is designated as the national championship game. An invitation to any BCS game guarantees that a school will receive a hefty sum of money at the end of the year. Winning a BCS game could bring in millions of dollars.

Lets look further into the math in college football. The mathematical formula used to figure out which teams make it to the BCS games (and which two teams will fight to be crowned the national champions) turns out to be a rather complicated application of statistical analysis; but algebra provides the backbone of the entire operation. Across the country every week, each team’s BCS ratings are updated according to four major factors:

  • Computer rankings
  • the difficulty of the team’s schedule
  • opinion polls, and
  • the team’s total number of losses.

Each of these four components yields a numerical value. The computer rankings, for one, are determined by complex computer programs created by statisticians. Computer ranking programs crunch an enormous amount of statistical data, including numerical values representing a multitude of factors ranging from the score of the game, the number of turnovers, and each team’s total yardage, to the location of the game and the effects of weather. The difficulty of a team’s schedule is also determined by algebraic equations with terms accounting for the difficulty of the team’s own schedule and the difficulty of the schedules of the teams that they will play throughout the season.

There are two separate opinions polls:

  • one involving national sports writers and broadcasters, and
  • one involving a select group of football coaches.

Each poll results in a numerical ranking for all of the teams. For each team, an average of a these two rankings determines their national opinion poll ranking A team’s number of losses is the most straightforward factor. The number of losses is figured directly into the general mathematical model, and each loss throughout the season has a large effect on a team’s overall ranking. The four numerical values are added together to calculate the team’s national ranking.

The top two teams at the end of the regular season are invited to the national championship BCS game. However, the selection of the six teams that are invited to the other three BCS games is not as straight forward. These other six teams are selected from the top 12 teams across the nation (excluding the top two that are automatically invited to the championship game). How these 12 teams are narrowed to six depends mainly on which teams are expected to attract the most attention and, therefore, create the most profits for the hosting institution, the television and radio stations that broadcast the game, and the various sponsors. These financial considerations are also modeled using algebraic formulas. As you can see, the math in college football is a rather complicated affair.