The efficacy of drug treatments depends on how tightly small molecules bind to their target proteins. The rapid and accurate quantification of the strength of these interactions (as measured by binding affinity) is a grand challenge of computational chemistry, surmounting which could revolutionize drug design and provide the platform for patient-specific medicine. Recent evidence suggests that molecular dynamics (MD) can achieve useful predictive accuracy (< 1 kcal/mol). For this predictive accuracy to impact clinical decision making, binding free energy computational campaigns must provide results rapidly and without loss of accuracy. This demands advances in algorithms, scalable software systems, and efficient utilization of supercomputing resources. We introduce a framework called HTBAC, designed to support accurate and scalable drug binding affinity calculations, while marshaling large simulation campaigns. We show that HTBAC supports the specification and execution of free-energy protocols at scale. This paper makes three main contributions: (1) shows the importance of adaptive execution for ensemble-based free energy protocols to improve binding affinity accuracy; (2) presents and characterizes HTBAC -- a software system that enables the scalable and adaptive execution of binding affinity protocols at scale; and (3) for a widely used free-energy protocol (TIES), shows improvements in the accuracy of simulations for a fixed amount of resource, or reduced resource consumption for a fixed accuracy as a consequence of adaptive execution.