Contact resistance is a main parameter to characterize the connector's fretting performance, this paper uses the improved sigmoid function to establish a mathematical model of the fretting contact resistance of the contact pairs; then applies the mathematical model to validate the fretting contact resistance datasets of 17 contact pairs with the reliability ranging from 0.78–0.99; then analyses the effect of three factors, namely, the plating metal, the contact pressure and the environment, on the parameters in the mathematical model; finally evaluates and grades the micro-motion contact performance of the contact pairs according to the mathematical model, The conclusions are as follows: When C>8000 it is a “good” grade, with precious metals (flash Au+PdNi) predominating, and a “flash Au+PdNi” coating can be used instead of thick Au. At 4000