In this work, we investigate the statistical evolution from nano-conducting path generation to the switching-filament formation in ReRAM devices. We demonstrate the Gumbel statistics, a maxima-value distribution for switching-filament conductance as opposed to the minima-value Weibull model. In contrast to Poisson distribution for nano-path generation, we show the underlying spatial statistics is controlled by a binomial distribution as a result of filament-formation. The reorganization and conglomeration of interacting nano-paths or individual vacancies eventually leads to area-dependent single-filament formation, consistent with the Gumbel statistics. Our methodology provides the foundation for RRAM scaling as well as an essential tool for the development of RRAM technology.