We provide the theoretical framework to understand the phenomenology and statistics of single molecule (SM) signals arising in surface enhanced Raman scattering (SERS) under the presence of so-called electromagnetic hot spots. We show that most characteristics of the SM-SERS phenomenon can be tracked down to the presence of a tail-like (power law) distribution of enhancements and we propose a specific model for it. We analyze, in the light of this, the phenomenology of SM-SERS and show how the different experimental manifestations of the effect reported in the literature can be analyzed and understood under a unified "universal" framework with a minimum set of parameters.