The significance of estimating video watch time has been highlighted by the rising importance of (short) video recommendation, which has become a core product of mainstream social media platforms. Modeling video watch time, however, has been challenged by the complexity of user-video interaction, such as different user behavior modes in watching the recommended videos and varying watching probability over the video progress bar. Despite the importance and challenges, existing literature on modeling video watch time mostly focuses on relatively black-box mechanical enhancement of the classical regression/classification losses, without factoring in user behavior in a principled manner. In this paper, we for the first time take on a user-centric perspective to model video watch time, from which we propose a white-box statistical framework that directly translates various user behavior assumptions in watching (short) videos into statistical watch time models. These behavior assumptions are portrayed by our domain knowledge on users' behavior modes in video watching. We further employ bucketization to cope with user's non-stationary watching probability over the video progress bar, which additionally helps to respect the constraint of video length and facilitate the practical compatibility between the continuous regression event of watch time and other binary classification events. We test our models extensively on two public datasets, a large-scale offline industrial dataset, and an online A/B test on a short video platform with hundreds of millions of daily-active users. On all experiments, our models perform competitively against strong relevant baselines, demonstrating the efficacy of our user-centric perspective and proposed framework.