The Bowl Championship Series: A Mathematical Review, vol 51, number 8

Introduction On February 29, 2004, the college football Bowl Championship Series (BCS) announced a proposal to add a fifth game to the “BCS bowls” to improve access for midmajor teams ordinarily denied invitations to these lucrative postseason games. Although still subject to final approval, this agreement is expected to be instituted with the new BCS contract just prior to the 2006 season. There aren’t too many ways that things could have gone worse this past college football season with the BCS Standings governing which teams play in the coveted BCS bowls. The controversy over USC’s absence from the BCS National Championship game, despite being #1 in both polls, garnered most of the media attention [12], but it is the yearly treatment received by the “non-BCS” midmajor schools that appears to have finally generated changes in the BCS system [15]. Created from an abstruse combination of polls, computer rankings, schedule strength, and quality wins, the BCS Standings befuddle most fans and sportswriters, as we repeatedly get “national championship” games between purported “#1” and “#2” teams in disagreement with the polls’ consensus. Meanwhile, the top non-BCS squads have never been invited to a BCS bowl. Predictably, some have placed blame for such predicaments squarely on the “computer nerds” whose ranking algorithms form part of the BCS formula [7], [14]. Although we have no part in the BCS system and the moniker may be accurate in our personal cases, we provide here a mathematically inclined review of the BCS. We briefly discuss its individual components, compare it with a simple algorithm defined by random walks on a biased graph, attempt to predict whether the proposed changes will truly lead to increased BCS bowl access for non-BCS schools, and conclude by arguing that the true problem with the BCS Standings lies not in the computer algorithms but rather in misguided addition.