Assemblies of coupled plasmonic nanoparticles are used as sensors and rulers for the measurement of nanoscale distances and dynamic distance changes in biological and macromolecular systems. Since such rulers are employed at the single-device level, variations from one construct to another can greatly influence their reliability as sensors. In this work, we performed an experimental and simulation-based analysis of the structural and functional heterogeneity in model assemblies consisting of a Au nanosphere (NS) attached to a highly polarizable Au nanoplate (NP). Spectral characteristics, including the number, nature, and energy position of plasmon modes, varied significantly from one construct to another. The coupling-induced localized surface plasmon resonance (LSPR) shift, which can be the optical readout for sensing applications, ranged over an order of magnitude across the set of constructs measured. By correlating scattering spectra with construct morphologies obtained from scanning electron microscopic (SEM) images for a large set of individual constructs, we determined that, of all possible structural factors, the NS size was the largest contributor to heterogeneity in the optical response. Small NSs resulted in spectra with a single LSPR mode, whereas large NSs resulted in complex spectra with multiple polarization-dependent LSPR modes. From the heterogeneous population of constructs, we were able to formulate, with the help of electrodynamic simulations, a systematic structure-property relationship, according to which the magnitude of the coupling-induced shift increases with increasing NS size, approaching saturation in the limit of large NS diameter. We discuss the theoretical basis and practical utility of this structure sensitivity in the construction of sensitive plasmon rulers, in the determination of fidelity of individual ruler constructs, and in the development of new sensors for measuring optical polarizabilities of emitters.