We present an analytical model and measurements of the pump to signal relative intensity noise (RIN) transfer characteristics of copumped and counterpumped Raman amplifiers. We give a quantitative analysis of noise averaging from chromatic dispersion in copumped systems and from different propagation directions in counterpumped systems. It is shown that nondispersion-shifted fibers and other fibers with high dispersion between the signal and pump wavelengths give a greater potential for use in copumped Raman amplified systems.