Observed optical richness $\widehat{\lambda }$ of SPT clusters as a function of the cluster halo mass (top) and redshift (bottom). The clusters are shown with filled circles, where the error bars also capture the error in the observable-mass relations and the estimated cluster halo mass. The top and bottom plots shows the richness $\widehat{\lambda }$ normalized at the pivot redshift z_piv = 0.6 and the pivot mass M_piv = 3 × 10¹⁴h⁻¹ Mpc, respectively. The intrinsic model (Eq. (27)) is shown in blue. The light and dark-shaded regions in both the panels represent 68% and 95% credible intervals of the mean model respectively.