A critical component of any video transmission system is an objective metric for evaluating the quality of the video signal as it is seen by the end-user. In packet-based communication systems, such as a wireless channel or the Internet, the quality of the received signal is affected by both signal compression and packet losses. Due to the probabilistic nature of the channel, the distortion in the reconstructed signal is a random variable. In addition, the quality of the reconstructed signal depends on the error concealment strategy. A common approach is to use the expected mean squared error of the end-to-end distortion as the performance metric. It can be shown that this approach leads to unpredictable perceptual artifacts. A better approach is to account for both the mean and the variance of the end-to-end distortion. We explore the perceptual benefits of this approach. By accounting for the variance of the distortion, the difference between the transmitted and the reconstructed signal can be decreased without a significant increase in the expected value of the distortion. Our experimental results indicate that for low to moderate probability of loss, the proposed approach offers significant advantages over strictly minimizing the expected distortion. We demonstrate that controlling the variance of the distortion limits perceptually annoying artifacts such as persistent errors.