By simultaneously measuring individual and coincidence counts of two single photon detectors connected to a fiber-based entangled photon source and fitting the results with a theoretical model of the photon generation rates, we determine the average number of polarization-entangled photon pairs generated by four-wave mixing and the average number of noise photons generated by Raman scattering and self-phase modulation of the pump as a function of power. In contrast to previous efforts to characterize fiber-based entangled photon sources, this method does not require additional coherence-based measurements to distinguish SPM photons from FWM and Raman-scattered photons.