Random linear network coding is a promising coding scheme to increase the robustness and reliability of network systems. However, one of its major drawbacks is the high computational complexity. Sparse Network Coding (SNC) was proposed to reduce the computational complexity at the expense of larger communication overhead. However, the performance evaluation of SNC is still a major research topic due to an inaccurate expression for the behavior of sparse matrices. In this letter, we present two approximation models to analyze the probability distribution of the rank of sparse matrices. We use our models to derive the average number of required transmissions in the SNC scheme. Our results show that the proposed models predict the rank of sparse matrices and the average number of transmissions with a maximum deviation of 4% and 6%, respectively.