Peer-to-peer (P2P) video streaming is a scalable and cost-effective technology to stream video content to a large population of users and has attracted a lot of research for over a decade now. Recently, network coding has been introduced to improve the efficiency of these systems and to simplify the protocol design. There are already some successful commercial applications that utilize network coding. However, previous analytical studies of network-coding-based P2P streaming systems mainly focused on fundamental properties of the system and ignored the influence of the protocol details. In this study, a unique stochastic model is developed to reveal how segments of the video stream evolve over their lifetime in the buffer before they go into playback. Different strategies for segment selection have been studied with the model, and their performance has been compared. A new approximation of the probability of linear independence of coded blocks has been proposed to study the redundancy of network coding. Finally, extensive numerical results and simulations have been provided to validate our model. From these results, in-depth insights into how system parameters and segment selection strategies affect the performance of the system have been obtained.