The unique catalytic activity of small nanoparticles can be attributed to their distinctive electronic structure and/or their ability to expose sites with a unique geometry. Quantifying and distinguishing the contributions of these effects to catalytic performance presents a challenge, given the complexity arising from multiple influencing factors and the lack of a quantitative structure-activity relationship. Here, we show that the intrinsic activity of platinum atoms at the perimeter corner sites is three orders of magnitude higher as a result of an electronic structure effect, with a threshold occurring at an average nanoparticle size of 1-1.5 nm. The contributions to the activity of atomically dispersed platinum, large nanoparticles and sodium-induced support modification are minor. This comprehensive and quantitative structure-activity correlation was demonstrated and verified on real-world Pt/CeO2 catalysts for the water-gas shift reaction by utilizing operando X-ray photoelectron spectroscopy, in situ scanning transmission electron microscopy, electron energy-loss spectroscopy, theoretical calculations, and kinetic models.