We estimate the activity of the oxygen reduction reaction on platinum nanoparticles of sizes of practical importance. The proposed model explicitly accounts for surface irregularities and their effect on the activity of neighboring sites. The model reproduces the experimentally observed trends in both the specific and mass activities for particle sizes in the range between 2 and 30 nm. The mass activity is calculated to be maximized for particles of a diameter between 2 and 4 nm. Our study demonstrates how an atomic-scale description of the surface microstructure is a key component in understanding particle size effects on the activity of catalytic nanoparticles.