Two independent, explicit expressions are derived which relate optimum concentration of binding protein or labeled analyte to concentration of analyte to be measured. Optimum reactant concentrations are determined on the basis of two distinct criteria. One criterion is that the response variable and analyte concentration be related, as closely as possible, in a hyperbolic, rather than sigmoid, manner. The other criterion is that a proper hyperbolic response curve be found which provides most precise measurement of a particular concentration of analyte. Sources of error taken into consideration, which lead to measurement imprecision, include variation in misclassifying bound and free fractions, counting error, errors in pipetting of binding protein, labeled and unlabeled analyte. © 1979, American Chemical Society. All rights reserved.