Though theoretical and computational studies typically agree on the low energy, equilibrium structure of metallic nanoparticles, experimental studies report on samples with a distribution of shapes; including high-index, non-equilibrium morphologies. This apparent inconsistency is not due to inaccuracy on either side, nor the result of unquantifiable competition between thermodynamic and kinetic influences, but rather a lack of clarity about what is being inferred. The thermodynamic stability, statistical probability, and the observed population of a given structure are all straightforward to determine, provided an ensemble of possible configurations is included at the outset. To clarify this relationship, a combination of electronic structure simulations and mathematical models will be used to predict the relative stabilities, probability and population of various shapes of Ag, Au, Pd and Pt nanoparticles, and provide some explanation for the observation of high-index, non-equilibrium morphologies. As we will see, a nanoparticle can be in the ground-state, and therefore most thermodynamically stable, but can still be in the minority.