Abstract #301769

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JSM 2003 Abstract #301769
Activity Number: 411
Type: Contributed
Date/Time: Wednesday, August 6, 2003 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistics in Sports
Abstract - #301769
Title: We're Number One!: A Comparison of Two Common Ranking Models for the 2002-2003 NCAA Division I Football Season
Author(s): David H. Annis*+
Companies: Purdue University
Address: Mathematical Science Building, West Lafayette, IN, 47907-2067,
Keywords: paired comparison ; ranking ; Bradley-Terry ; generalized linear model ; football
Abstract:

"We're Number One! We're Number One!" By what criterion? Most wins? Strength of schedule? Is, as Vince Lombardi said, winning everything? The Bowl Championship Series (BCS) has spurred much debate over the proper way to account for and weight factors such as the number of wins, strength of schedule, and point differential. We look at the 2002-2003 NCAA Division I college football season, and rank the teams according to two criteria: (1) winning is everything, and (2) integrated point differential. The winning-is-everything criterion, with its binary win/lose outcome, is well known and has many incarnations, the most common of which is the Bradley-Terry model, in existence for over 40 years. The integrated point differential model uses a latent Poisson process to model the propensity to score and be scored upon. Each model has appealing properties; however, each also suffers in certain scenarios based on information that is "ignored." We present each model, illustrate these limitations, and discuss a mixture of these models to help overcome them.

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