Metal-to-insulator transitions1 driven by strong electronic correlations occur frequently in condensed matter systems, and are associated with remarkable collective phenomena in solids, including superconductivity and magnetism. Tuning and control of the transition holds the promise of low-power, ultrafast electronics2, but the relative roles of doping, chemistry, elastic strain and other applied fields have made systematic understanding of such transitions difficult. Here we show that existing data3,4,5 on the tuning of metal-to-insulator transitions in perovskite transition-metal oxides through ionic size effects provides evidence of large systematic effects on the phase transition owing to dynamical fluctuations of the elastic strain, which have usually been neglected6. We illustrate this using a simple yet quantitative statistical mechanical calculation in a model that incorporates cooperative lattice distortions coupled to the electronic degrees of freedom. We reproduce the observed dependence of the transition temperature on the cation radius in the well studied manganite7 and nickelate8 materials. Because elastic couplings are generally strong, we anticipate that these conclusions will generalize to all metal-to-insulator transitions that couple to a change in lattice symmetry.