If the fitnesses of n haploid alleles in a finite population are assigned at random and if the alleles can mutate to one another, and if the population is initially fixed for the kth most fit allele, then the mean number of substitutions that will occur before the most fit allele is fixed is shown to be (formula; see text) when selection is strong and mutation is weak. This result is independent of the parameters that went into the model. The result is used to provide a partial explanation for the large variance observed in the rates of molecular evolution.