In our earlier work we have proposed a watermarking algorithm for JPEG/MPEG streams that is based on selectively discarding high frequency DCT coefficients. Like any watermarking algorithm, the performance of our method must be evaluated by the robustness of the watermark, the size of the watermark, and the visual degradation the watermark introduces. These performance factors are controlled by three parameters, namely the maximal coarseness of the quantizer used in re-encoding, the number of DCT blocks used to embed a single watermark bit, and the lowest DCT coefficient that we permit to be discarded. It is possible to determine these parameters experimentally. In this paper, however, we follow a more rigorous approach and develop a statistical model for the watermarking algorithm. Using this model we derive the probability that a label bit cannot be embedded. The resulting model can be used, for instance, for maximizing the robustness against re-encoding and for developing adequate error correcting codes for the label bit string.