Conflicting views about the degree of long-run mobility across multiple generations persist because direct empirical evidence is scarce. Predictions are instead routinely derived by iteration of intergenerational measures, a procedure which implies high long-run mobility even when intergenerational mobility is low. However, the assumption that regression implies perpetual regression is a statistical fallacy. I examine this fallacy, its historical background, and its prevalence. I then present various simple models of intergenerational transmission to consider how the relation between intergenerational and multigenerational mobility is affected by elements of the transmission process. I discuss the role of market luck and indirect transmission; the multiplicity of skills; the role of grandparents; and the causal effect of parental income. The direction of bias depends on modeling assumptions, but elementary properties of the transmission process imply that long-run mobility will likely be lower, possibly much lower, than predictions from intergenerational evidence suggest.