Linear Inference for Paired Comparisons

In this paper, we propose a team rating system that accounts for differences in strength of schedule by computing an additive correction factor which adjusts team winning percentage. This approach permits teams to be ranked appropriately despite disparate schedules. Our method is easy to compute as it only requires a simple matrix inversion, and we prove that the needed inverse exists for all reasonable classes of schedules. We also prove some mathematical properties of the ratings system and apply our method to data from the 2007 Major League Baseball season.