Dimension Reduction for Hybrid Paired Comparison Models

Rating -- and subsequently ranking -- college football teams requires making sense of sometimes conflicting pair-wise comparisons. Classical statistical techniques fall into one of two classes: win/loss models, which focus on binary outcomes, and point-scoring models, which consider the distribution of component scores. Annis and Craig (2005) illustrate deficiencies of both, and propose a hybrid method that considers both sources of data. Their method, while providing satisfactory results in many circumstances, can be difficult to implement numerically. This paper presents a refinement of their hybrid rating algorithm which preserves their original intent but simplifies greatly its implementation. Like its predecessor, the new model enjoys robustness to model misspecification, while offering substantial simplification.