In video forensics, the study of the prediction residue across successive frames is key to verify the integrity of digital videos. Focusing on an MPEG-2 double compression scheme, we analyze how the variance of the prediction residue evolves during the second compression depending on the type of frame (either I or P) employed in the first encoding and exploring different compression strengths and deadzone widths for quantization. This analysis reveals that the width of the quantizer deadzones actually affects the performance of existing methods based on the Variation of Prediction Footprint (VPF) for double compression detection and Group Of Pictures (GOP) size estimation. The predicted behavior from the theoretical characterization of the prediction residue is confirmed through experimental results with real video sequences.