A Penalized Maximum Likelihood Approach for the Ranking of College Football Teams Independent of Victory Margins

By Mease, David | The American Statistician, November 2003 | Go to article overview

A Penalized Maximum Likelihood Approach for the Ranking of College Football Teams Independent of Victory Margins


Mease, David, The American Statistician


1. INTRODUCTION

Prior to 1998, the national championship of U.S. Division 1-A college football was based solely on two opinion polls, commonly referred to as the Coaches and the AP (Associated Press) polls. The ranking of the teams in these two polls is determined by coaches and sports writers, respectively, who vote weekly for the top 25 teams based on the teams' performances in all games played. Up until 1998, the team that finished the year in the number one position in both polls was deemed to be the national champion. In cases in which the two polls did not agree on the choice of the top team, the two teams involved shared the title of national champion, which occurred most recently in 1997 with Michigan and Nebraska.

With the 1998 season came the inception of a new system under which the top two teams at the end of the season would play one final game for the championship, thereby eliminating the possibility of a shared title. This new system was called the Bowl Championship Series, or BCS. The BCS system employed rankings produced by a number of computer models in addition to the rankings of the AP and Coaches polls in order to determine the top two teams. The purpose of these computer models was to lessen dependence on the AP and Coaches polls which, although historically trusted as representing expert opinion, have often been criticized on the following two accounts. First, the human pollsters are not objective observers and may have biases toward certain schools based on regional loyalty, historical perception, and so on. Second, it is impossible for a human pollster to recall all outcomes of all games involving the 117 Division 1-A teams over the course of an 11- to 14-week season, even if he or she had witnessed or read about every game.

Although the computer models employed by the BCS do not have any such bias and are able to consider the outcomes of all games played, they have also proven to be extremely controversial as a result of many instances in which they produced nonintuitive rankings which differed significantly from the AP and Coaches polls. For instance, in 2001 the University of Oregon, which finished second in both the AP and Coaches polls, finished eighth in one of the eight BCS computer models, and finished seventh in two of the others. The low ranking of Oregon in these three computer polls was thought to be attributable to their many victories by narrow point margins, since the four BCS computer models that did not use margin of victory ranked Oregon no lower than third. This was not the first time that controversy resulted from the computers polls weighing margin of victory much more heavily than public opinion, and as a result it was mandated that all computer polls either ignore margin of victory or be excluded from the BCS system beginning in 2002. The idea was that by forcing computers to ignore margin of victory, the resulting rankings would be more consistent with the public's opinion, which tends to be more a function of a team's winning percentage and quality of opposition than a function of the point margins. Furthermore, this would remove any incentive for a team to "run up the score" in a game that is a foregone conclusion, which is universally considered to be bad sportsmanship.

It should be noted that the belief that the BCS computer models are more influenced by margin of victory than public opinion is not shared by everyone. Some people, including the creators of some of these computer models, would argue the human pollsters themselves can be highly influenced by large victory margins, citing examples in which a team that wins by a large margin climbs higher in the polls than a team that wins by a small margin. Although it is in fact possible for human pollsters to be influenced in such a way, a number of instances similar to the one involving Oregon described above were enough to convince the BCS that the computer polls tended to weigh margin of victory too heavily (even after a restriction was made limiting the maximum margin to 21 points). …

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A Penalized Maximum Likelihood Approach for the Ranking of College Football Teams Independent of Victory Margins
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