The performance of supported catalysts is largely decided by metal-support interactions, which is of great significance for the rational design of catalysts. However, how to quantify the structure-activity relationship of supported catalysts remains a great challenge. In this work, taking MoS2 and WS2 supported single atom catalysts (SACs) as prototypes, a simple descriptor, namely, effective d electron number (labeled as Φ), is constructed to quantitatively describe the effect of metal-support interaction on the nitrogen reduction reaction (NRR) activity. This descriptor merely consists of intrinsic properties of the catalyst (including the number of d electrons, electronegativity of the metal atoms and generalized electronegativity of the substrate atoms) and can accurately predict the limiting potential (UL) for the NRR, with no need for any density functional theory calculations. Moreover, this descriptor possesses superb expansibility that can be applied to other materials, including other metal dichalcogenide (MoSe2, MoTe2, WSe2, WTe2 and NbS2) and even MXene (V2CO2, Ti2CO2 and Nb2CO2)-supported SACs. On this basis, a fast screening of excellent NRR catalysts among these systems is performed and three promising NRR catalysts (i.e. Mo@WTe2, Mo@V2CO2 and Re@NbS2) are successfully selected with UL as low as -0.32, -0.24 and -0.31 V, respectively. This work offers new opportunities for advancing the rapid discovery of high-efficiency NRR catalysts, and the design principle is expected to be widely applicable to other catalytic systems and beyond.