An exemplary method includes a network DVR system identifying a total number of requests provided by a plurality of users to record a media program during a presentation of the media program, determining, based on the total number of requests and on a predicted playback rate associated with the media program, a maximum number of temporally overlapping playback sessions of the media program that will potentially be initiated by the plurality of users subsequent to the presentation of the media program, and storing, in response to the requests and based on the determining, a plurality of unique copies of the media program. Corresponding systems and methods are also described.