Research summary: In this paper we adopt a core‐periphery approach to specify the direct and indirect effects of social capital on organizational performance. We suggest that social capital deriving from stable task relationships between organizational members has a direct positive effect on organizational performance. Said effect depends, in both strength and functional form, on whether actors involved in stable dyads are located at the core or at the periphery of the organization. We also argue that core and peripheral social capital affect performance indirectly by moderating the organization's ability to leverage its human capital to improve performance. Results from a 48‐year study of the National Basketball Association support our arguments and bear important implications for strategic human resource practices and organizational performance in competitive settings. Managerial summary: Stable work relationships among employees generate trust, more efficient work routines, common understanding and thus higher organizational performance. These benefits depend on the location of such stable relationships in the organization. Relational stability among core organizational members has an immediate, strong impact on performance, an effect that plateaus as stability grows. Stable relationships between core and peripheral members have instead a weaker, yet linear effect on performance. The location of stable relationships is also critical to leverage the talent of core employees, whose contribution to performance is stronger when relational stability is high in the organizational core, yet hindered by stable relations between core and periphery. Such findings provide relevant implications for strategic human resource management, in particular for choices regarding team composition and managing stars. Copyright © 2015 John Wiley & Sons, Ltd.