Ploidy varies tremendously within and between species, yet the factors that influence when or why ploidy variants are adaptive remains poorly understood. Our previous work found that diploid individuals repeatedly arose within ten replicate haploid populations of Saccharomyces cerevisiae, and in each case we witnessed diploid takeover within ~1800 asexual generations of batch culture evolution in the lab. The character that allowed diploids to rise in frequency within haploid populations remains unknown. Here we present a number of experiments conducted with the goal to determine what this trait (or traits) might have been. Experiments were conducted both by sampling a small number of colonies from the stocks frozen every two weeks (~ 93 generations) during the original experiment, as well through sampling a larger number of colonies at the two time points where polymorphism for ploidy was most prevalent. Surprisingly, none of our fitness component measures (lag phase, growth rate, biomass production) indicated an advantage to diploidy. Similarly, competition assays against a common competitor and direct competition between haploid and diploid colonies isolated from the same time point failed to indicate a diploid advantage. Furthermore, we uncovered a tremendous amount of trait variation among colonies of the same ploidy level. Only late-appearing diploids showed a competitive advantage over haploids, indicating that the fitness advantage that allowed eventual takeover was not diploidy per se but an attribute of a subset of diploid lineages. Nevertheless, the initial rise in diploids to intermediate frequency cannot be explained by any of the fitness measures used; we suggest that the resolution to this mystery is negative frequency-dependent selection, which is ignored in the standard fitness measures used.