This paper develops a mathematical model for describing the within-plate variation as the RSD (relative standard deviation) of absorbance measurements in a wide concentration range in competitive ELISA and proposes a method for determining the limit of detection (LOD) and range of quantitation (ROQ). The ELISA for 17 alpha-hydroxyprogesterone is taken as an example. The theoretical RSD description involves analyte concentration as an independent variable and error sources as parameters which concern the pipetting and absorbance measurement. Our model can dispense with repeated experiments of real samples, but the error parameters should be determined experimentally. The theory is in good agreement with the experiments. The most influential error sources at low and high sample concentrations are shown to be the pipetting of a viscous solution of antiserum and the absorbance inherent to the wells of a plate, respectively. The LOD and ROQ are defined as the concentration with 30% RSD and the region with <10% RSD, respectively, and are found in the theoretical plot of the RSD of concentration estimates vs concentration.