Video popularity is an essential reference for optimizing resource allocation and video recommendation in online video services. However, there is still no convincing model that can accurately depict a video's popularity evolution. In this paper, we propose a dynamic popularity model by modeling the video information diffusion process driven by various forms of recommendation. Through fitting the model with real traces collected from a practical system, we can quantify the strengths of the recommendation forces. Such quantification can lead to characterizing video popularity patterns, user behaviors and recommendation strategies, which is illustrated by a case study of TV episodes.