We investigate the relationship between variation in reproductive potential among members of a family and genetic relatedness to determine which combinations favor natural selection for helping behavior. Conditions favoring helping are derived for the helper, the recipient, and the parents of these individuals. Our analysis reveals that a factor of general significance in the evolution of social organisms is variability in reproductive potential among offspring of a parent. To a limited extent this factor has already been appreciated because of its implicit role in "facultative altruism" and "parental manipulation", or suppression of offspring or sibs; however, the unifying role of variance per se and the ways by which it may act have not been widely appreciated. We show that suppression as a source of intra-brood variance is less powerful in the evolution of sociality than other, natural, sources of variance. The facts of natural history appear to be more consistent with a model utilizing natural variance than with a variance-enhancement model for most vertebrates. We present models for discrete and for overlapping generations. Fecundity of young potential helpers relative to adults is an important source of variance for the origin of helping.