The yield strength of many materials is much higher for minute specimens than for bulk samples. The region around the point of highest shear stress in a solid undergoing deformation by a small spherical indenter can be regarded as such a minute specimen which may be ``protected'' by the size effect against plastic yielding if it is small enough. Formulating the effective yield strength and the elastic stress under the indenter in terms of a common parameter provides a basis for assessing the influence of size scale on the plastic yield threshold. Four size categories are identified, including a critical case for which a small change of loading may cause a discontinuous transition from the elastic to the plastic regime throughout the region of contact, and another, more frequently encountered, in which the supportable pre‐yield elastic stress is materially enhanced. The latter effect may exert an important influence on the rate of rubbing wear since it can make available a wider range of loading for which a low wear rate prevails. Reported wear tests on steel riders and on sapphire phonograph styli confirm these predictions qualitatively.