Photon time-of-flight information increases the effective sensitivity of time-of-flight (TOF) positron emission tomography (PET). We have previously quantified the relation between the size and shape of the TOF-kernel and the signal-to-noise ratio (SNR) of the TOF-PET data for a very simple detection task. In addition, it was shown analytically that for the center of a uniform cylinder, the variance of the reconstructed pixel values is inversely proportional to the squared SNR for this detection task. With this analytic result, one can compare TOF-PET systems with TOF-PET kernels of different size and shape, and rank them according to the variance in their reconstructed images for the same number of measured coincidences. This approach only considers the efficacy of TOF for noise suppression in the reconstruction of the activity image, when the attenuation is known. Here, we apply a similar approach to predict the performance of TOF-PET for joint reconstruction of the attenuation and activity images. A simple and elegant expression is obtained, which is found to agree well with the variance observed in MLAA reconstructions in a simple 2D TOF-PET simulation experiment.