Recently, a simple approximate framework has been developed to evaluate signal-to-interference ratio (SIR) distribution in downlink cellular networks. This framework approximates the SIR distribution in a network model based on a non-Poisson point process (PP) by scaling that in the corresponding model based on a Poisson PP, where the scaling factor, called an SIR gain, is determined from the two models. While this framework has much potential, a problem may lie in that the SIR gain is generally estimated through Monte Carlo simulation. In this letter, we propose to derive the SIR gain also approximately. The proposed approximate SIR gain can be obtained whenever the second moment of contact distance is available for a given PP. Numerical experiments show when our approximate SIR gain works well and when it does not.