The contribution of extra-pair paternity (EPP) to sexual selection has received considerable attention, particularly in socially monogamous species. However, the importance of EPP remains difficult to assess quantitatively, especially when many extra-pair young have unknown sires. Here, we combine measurements of the opportunity for selection (I), the opportunity for sexual selection (IS), and the strength of selection on mating success (Bateman gradient, βSS) with a novel simulation of random mating tailored to the specific mating system of the blue tit (Cyanistes caeruleus). In a population where social polygyny and EPP are common, the opportunity for sexual selection was significantly stronger and Bateman gradients significantly steeper for resident males than for females. In general, success with the social mate(s) contributed most to variation in male reproductive success. Effects of EPP were small, but significantly higher than expected under random mating. We used sibship analysis to estimate the number of unknown sires in our population. Under the assumption that the unknown sires are nonbreeding males, EPP reduced the variance in and the strength of selection on mating success, a possibility that hitherto has not been considered.