Each computing device in a peer-to-peer network stores particular digital content. A computing device in the peer-to-peer network includes a peer prediction system that obtains an indication of digital content that has not been downloaded to the computing device but is predicted to be downloaded by the computing device in the future (e.g., in response to a user request for the digital content). The peer prediction system obtains a list of peer computing devices in the peer-to-peer network that have at least part of the digital content, and communicates with those peer computing devices to determine connectivity information for each of those peer computing devices. The computing device maintains a record of this connectivity information, and in response to a subsequent user request to download the digital content, uses the maintained record to determine which peer computing devices to access to obtain the digital content.