It is widely suspected that a small percentage of males have exceptional reproductive output (ERO) but progeny numbers of males are rarely measurable, even in humans. If we define the variance ratio of reproductive-output in males and females as alpha ' = V-M/V-F, the ERO hypothesis would predict alpha ' >> 1. Since autosomal, X, and, Y chromosomes are found in males 1/2, 1/3, and 100% of the time, their DNA diversities can inform about alpha '. For example, autosomal and Y-linked diversities are governed, respectively, by (V-M + V-F)/2 and V-M. When comparing the chromosomal diversities, alpha ' appears to be near 20 for chimpanzees and orangutans, and 1-10 for gorillas. The exception is bonobos with alpha ' < 1. In humans, extensive genomic data are coupled to a theory, developed herein, that can filter out selection influences on Y-linked diversities. Hence, the estimation of alpha ' is rigorous, yielding values near or above 20, depending on the population. When alpha ' > 10, the presence of ERO males is very likely. These analyses can be applied more generally to species with XY sex determination.