This paper analyses noise propagation in positron emission tomography (PET). It presents a method to compute the effective signal-to-noise ratio provided by the time-of-flight (TOF) measurement. The proposed method can be used to compare TOF-PET systems with different and possibly event-dependent TOF-kernels, as encountered when prompt photons, such as Cherenkov photons are present, or when the detector is composed of different scintillators.