While fully opportunistic network coding is one of the pioneer works to successfully implement network coding in wireless networks, the analytical model of its performance is still not well understood. In particular, the end-to-end average bit error rate of the scheme is still unclear due to the complexity of the scheme. In this paper we provide a generalized model to analyze the performance of regenerative multi-hop wireless ad hoc networks where opportunistic network coding is applied. By using the model, a closed-form expression of the exact average end-to-end bit error rate of the system over Rayleigh fading channels can be derived. The results obtained in our work allow us to have a more complete understanding of the factors that affect performance, especially the error propagation when packets traverse the network.