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 α′ = V M /V F , the ERO hypothesis would predict α′ >>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 α′. For example, autosomal and Y-linked diversities are governed, respectively, by (V M +V F )/2 and V M . When comparing the chromosomal diversities, α′ appears to be near 20 for chimpanzees and orangutans, and 1-10 for gorillas. The exception is bonobos with α′ < 1. In humans, the extensive genomic data are coupled to a theory, developed herein, that can filter out selection influences on Y-linked diversities. Hence, the estimation of α′ is rigorous, yielding values near or above 20, depending on the population. When α′ >10, the presence of ERO males is very likely. These analyses can be applied more generally to species with XY sex determination.