Background: In honey bees, observations are usually made on colonies. The phenotype of a colony is affected by the average breeding value for the worker effect of the thousands of workers in the colony (the worker group) and by the breeding value for the queen effect of the queen of the colony. Because the worker group consists of multiple individuals, interpretation of the variance components and heritabilities of phenotypes observed on the colony and of the accuracy of selection is not straightforward. The additive genetic variance among worker groups depends on the additive genetic relationship between the drone-producing queens (DPQ) that produce the drones that mate with the queen. Results: Here, we clarify how the relatedness between DPQ affects phenotypic variance, heritability and accuracy of the estimated breeding values of replacement queens. Second, we use simulation to investigate the effect of assumptions about the relatedness between DPQ in the base population on estimates of genetic parameters. Relatedness between DPQ in the base generation may differ considerably between populations because of their history. Conclusions: Our results show that estimates of (co)variance components and derived genetic parameters were seriously biased (25% too high or too low) when assumptions on the relationship between DPQ in the statistical analysis did not agree with reality.