Predictive adaptive media streaming

A method and corresponding apparatus for controlling streaming of media content from a server to a client. A computing device predicts the hit rate of an upcoming portion of the media content for each of a plurality of variable bit-rate versions of the media content, and uses the predicted bit rates, as well as a measure of network bandwidth, as a basis to select one of the variable bit-rate versions to be streamed to the client. By repeating this prediction and selection function on a sliding window basis over the course of the media content, the selection of variable bit-rate version can dynamically change, to help accommodate variations in bit rate throughout the media content as well as variations in network bandwidth.