Probability that the most luminous satellite galaxy is brighter than the central galaxy in a halo, as a function of halo mass (equation 23). Result is shown for three slopes in the satellite CLF (equation 9): s = 1 (dotted curve), the fiducial s = 2 (solid curve) and s = 3 (dashed curve). For comparison, the f_BNC(M_halo) result from Fig. 7 (solid triangle points) is also shown. The predictions from the morgana semi-analytic model (open triangles) and Croton et al. (2006) semi-analytic model (open squares) are also shown, with Poisson errors.