HTTP-based video streaming techniques have now been widely deployed to deliver video streams over communication networks. With HTTP-based adaptive streaming protocols, a video player can dynamically select a video stream from a set of pre-encoded representations of the video source based on its available bandwidth and viewport size. The bitrates of the encoded representations thus determine the video quality presented to viewers. We propose to minimize the average delivered bitrate on a per-chunk basis by modeling the probability that a player observes a particular representation. We evaluate the method through both extensive numerical simulation and real-world experiments. The proposed method with the investigated experiment settings demonstrates an overall bandwidth savings of 9.6% comparing with state of the art without loss of average delivered video quality.