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Bateman's experimental study of Drosophila melanogaster produced conclusions that are now part of the bedrock premises of modern sexual selection. Today it is the most cited experimental study in sexual selection, and famous as the first experimental demonstration of sex differences in the relationship between number of mates and relative reproductive success. We repeated the experimental methodology of the original to evaluate its reliability. The results indicate that Bateman's methodology of visible mutations to assign parentage and reproductive success to subject adults is significantly biased. When combined in offspring, the mutations decrease offspring survival, so that counts of mate number and reproductive success are mismeasured. Bateman's method overestimates the number of subjects with no mates and underestimates the number with one or more mates for both sexes. Here we discuss why Bateman's paper is important and present additional analyses of data from our monogamy trials. Monogamy trials can inform inferences about the force of sexual selection in populations because in monogamy trials male-male competition and female choice are absent. Monogamy trials also would have provided Bateman with an a priori test of the fit of his data to Mendel's laws, an unstated, but vital assumption of his methodology for assigning parentage from which he inferred the number of mates per individual subject and their reproductive success. Even under enforced monogamous mating, offspring frequencies of double mutant, single mutant and no mutant offspring were significantly different from Mendelian expectations proving that Bateman's method was inappropriate for answering the questions he posed. Double mutant offspring (those with a mutation from each parent) suffered significant inviability as did single mutant offspring whenever they inherited their mother's marker but the wild-type allele at their father's marker locus. These inviability effects produced two important inaccuracies in Bateman's results and conclusions. (1) Some matings that actually occurred were invisible and (2) reproductive success of some mothers was under-estimated. Both observations show that Bateman's conclusions about sex differences in number of mates and reproductive success were unwarranted, based on biased observations. We speculate about why Bateman's classic study remained without replication for so long, and we discuss why repetition almost 60 years after the original is still timely, necessary and critical to the scientific enterprise. We highlight overlooked alternative hypotheses to urge that modern tests of Bateman's conclusions go beyond confirmatory studies to test alternative hypotheses to explain the relationship between mate number and reproductive success.