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Distributed caching mechanism plays an important role to improve the performance of large-scale peer-to-peer video-on-demand (P2P-VoD) systems, especially in terms of server bandwidth costs. Nevertheless, existing research and analytical studies of P2P-VoD systems have not thoroughly investigated and understood distributed caching policies and their critical properties for helping to mitigate the bandwidth costs on streaming servers. In particular, there exists no prior analytical work that focuses on a new way of designing a distributed caching strategy, with the help of network coding. In this paper, we seek to show an analytical understanding of the potential fundamental benefits of using network coding in distributed passive caching. With our problem formulation, we present probability-based expressions for computing the steady-state average server bandwidth costs, with or without the use of network coding. Our analytical results are cross-validated by our extensive simulation studies in large-scale static and dynamic scenarios.