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tokens: We are grateful to Peter Behroozi, for updating the Bolshoi halo catalogue upon our request, to Hao-Yi Wu for sharing data from the Rhapsody simulation project, and to the anonymous referee for an insightful report that greatly helped to improve the presentation. We also thank the organizers of the programme ‘First Galaxies and Faint Dwarfs: Clues to the Small Scale Structure of Cold Dark Matter’ held at the Kavli Institute for Theoretical Physics (KITP) in Santa Barbara, for creating a stimulating, interactive environment that started the research presented in this paper, and the KITP staff for all their help and hospitality. This research was supported in part by the National Science Foundation under Grant No. PHY11-25915.