The ratio of the effective population size to adult (or census) population size (N_e/N) is an indicator of the extent of genetic variation expected in a population. It has been suggested that this ratio may be quite low for highly fecund species in which there is a sweepstakes-like chance of reproductive success, known as the Hedgecock effect. Here I show theoretically how the ratio may be quite small when there are only a few successful breeders (N_b) and that in this case, the N_e/N ratio is approximately N_b/N. In other words, high variance in reproductive success within a generation can result in a very low effective population size in an organism with large numbers of adults and consequently a very low N_e/N ratio. This finding appears robust when there is a large proportion of families with exactly two progeny or when there is random variation in progeny numbers among these families.