We discuss a mechanism for the apparently universal scaling in the high-multiplicity tail of charged particle distributions for high-energy nuclear collisions. We argue that this scaling behavior originates from rare fluctuations of the nucleon density. We discuss a pair of simple models of proton shape fluctuations. A "fat" proton with a size of 3 fm occurs with observable frequency. In light of this result, collective flow behavior in the ensuing nuclear interaction seems feasible. We discuss the influence of these models on the large-x structure of the proton and the likely influences on the distribution of initial-state spatial eccentricities εn. © 2014 American Physical Society.