A proposed general rating system for which the Colley Matrix Rating System is a special case

The Colley Matrix Rating System (CMRS) has been a component of the Bowl Championship Series (BCS) rankings. As such it is important that the assumptions that lead to and differentiate it from other rating systems be well understood. This work investigates an approach to justifying the CMRS based on an approach taken by Massey. This approach leads to both the CMRS and a version of a Massey Matrix Rating System. When approached in the manner proposed here these rating systems can be presented as special cases of one more general rating system.