The resilience to averaging over an initial energy distribution of reducibi
lity and thermal scaling observed in nuclear multifragmentation is studied.
Poissonian reducibility and the associated thermal scaling of the mean are
shown to be robust. Binomial reducibility and thermal scaling of the eleme
ntary probability are robust under a broad range of conditions. The experim
ental data do not show any indication of deviation due to averaging. [S0556
-2813(99)04608-7].