In this paper, we present a theoretical analysis of the distortion in multilayer coding structures. Specifically, we analyze the prediction structure used to achieve temporal, spatial, and quality scalability of scalable video coding (SVC) and show that the average peak signal-to-noise ratio (PSNR) of SVC is a weighted combination of the bit rates assigned to all the streams. Our analysis utilizes the end user's preference for certain resolutions. We also propose a rate-distortion (R-D) optimization algorithm and compare its performance with that of a state-of-the-art scalable bit allocation algorithm. The reported experiment results demonstrate that the R-D algorithm significantly outperforms the compared approach in terms of the average PSNR.