The Variation of Prediction Footprint (VPF), formerly used in video forensics for double compression detection and GOP size estimation, is comprehensively investigated to improve its acquisition capabilities and extend its use to video sequences that contain bi-directional frames (B-frames). By relying on a universal rate-distortion analysis applied to a generic double compression scheme, we first explain the rationale behind the presence of the VPF in double compressed videos and then justify the need of exploiting a new source of information such as the motion vectors, to enhance the VPF acquisition process. Finally, we describe the shifted VPF induced by the presence of B-frames and detail how to compensate the shift to avoid misguided GOP size estimations. The experimental results show that the proposed Generalized VPF (G-VPF) technique outperforms the state of the art, not only in terms of double compression detection and GOP size estimation, but also in reducing computational time.