Network coding is a new technique to improve network capacity and reliability. COPE and DCAR are basic network coding schemes which have been proposed for opportunistic network coding in wireless networks. The performances of these coding mechanisms have been studied by simulations or experiments. There is an interest in modeling the performances of these coding schemes mathematically. In fact, analytical approach can provide quicker performance analysis and comparison between these network coding schemes. In this paper, we propose an analytical model for the DCAR coding gain. The analytical results are validated by simulations in NS-2.