Top panel: the vertical axis measures the rarity of fluctuations ("number of σ's") needed to produce a baryonic clump of mass M_b (horizontal axis) at a given redshift (different solid lines); δ_c = 1.686 is the critical over-density for collapse and S_b is the variance of δ_b (Equation (6)). Results are for a stream velocity v_bc = 1σ_vbc and θ = 0. Bottom panel: corresponding results for a different measure of fluctuation rarity, .