High energy lithium-ion batteries have improved performance in a wide variety of mobile electronic devices. A new goal in portable power is the achievement of safe and durable high-power batteries for applications such as power tools and electric vehicles. Towards this end, olivine-based positive electrodes are amongst the most important and technologically enabling materials. While certain lithium metal phosphate olivines have been shown to be promising, not all olivines demonstrate beneficial properties. The mechanisms allowing high power in these compounds have been extensively debated. Here we show that certain high rate capability olivines are distinguished by having extended lithium nonstoichiometry (up to ca. 20 %), with which is correlated a reduced lattice misfit as the material undergoes an electrochemically driven, reversible, first-order phase transformation. The rate capability in several other intercalation oxides can also be correlated with lattice strain, and suggests that nanomechanics plays an important and previously unrecognized role in determining battery performance.