Selection of oligonucleotide aptamers involves consecutive rounds of affinity isolation of target-binding oligonucleotides from a random-sequence oligonucleotide library. Every next round produces an aptamer-enriched library with progressively higher fitness for tight binding to the target. The progress of enrichment can only be accurately assessed with bulk affinity assays in which a library is mixed with the target and one of two quantitative parameters, the fraction of the unbound library (R) or the equilibrium dissociation constant (Kd), is determined. These quantitative parameters are used to help researchers make a key decision of either continuing or stopping the selection. Despite the importance of this decision, the suitability of R and Kd for bulk affinity assays has never been studied theoretically, and researchers rely on intuition when choosing between them. Different approaches used for bulk affinity assays expectedly hinder comparative analyses of selections. Our current work has two goals: to give bulk affinity assays a thorough theoretical consideration and to propose a scientifically justified and practical bulk-affinity-assay approach. We postulate a formal criterion of suitability: a quantitative parameter must satisfy the principle of superposition. R satisfies this principle, while Kd does not, suggesting R as a theoretically preferable parameter. Further, we propose a solution for two limitations of R: its dependence on target concentration and narrow dynamic range. Finally, we demonstrate the use of this algorithm in both computer-simulated and experimental aptamer selection. This study sets a cornerstone in the theory of bulk affinity assays, and it provides researchers with a scientifically sound and instructive approach for conducting bulk affinity assays.