Caching at edge servers can smooth the temporal traffic variability and reduce the service load of base stations in wireless streaming. However, the assignment of the cached content for possibly multiple versions of different video sequences is still a challenging question in the context of adaptive streaming. In this paper, we propose a wireless video caching placement optimization problem for dynamic adaptive video streaming that properly takes into account the different rate-distortion (R-D) characteristics of the video sequences. Our objective is to minimize the expected video distortion by the optimal caching of compressed video sequences, such that the clients can effectively access video content storage and bandwidth constraints. We prove that our optimization problem is a submodular maximization problem subject to a knapsack constraint. A cost benefit greedy algorithm is developed to obtain an approximate solution with polynomial time complexity and theoretical approximation guarantees. Simulation results demonstrate significant video distortion reduction relative to different baseline caching placement schemes.