Mass-richness diagram displayed three ways. The left and center panels are respectively log-log and linear plots of converted to mass versus richness, while the right panel is a linear plot of unconverted versus richness. On left and in the center, the best-fit scaling relation is shown as computed when including (blue) and excluding (yellow-orange) the weight parameter of Eq. (17) corresponding to noise-like data points. For each band, the solid line corresponds to the best-fit scaling, while the bands correspond to the 68% credible interval. The lighter blue band denotes the confidence interval σ_lnM|λ due to the intrinsic scatter around the mean scaling relation obtained when considering the mixed model of Eq. (17). The dot-dashed line denotes the scaling reported by Gonzalez et al. (2019a), with the solid section marking the range of richness employed to derive the relation. The green points correspond to the masses or values without any correction for the steepness of the halo mass function (Hilton et al. 2021). These are color coded according to their weight w (color bar in the bottom right corner of the right panel). In red are the masses or values computed per richness bin. For comparison, we include, as a yellow diamond, the average mass estimate computed by Madhavacheril et al. (2020) from CMB lensing, shown at the mean value of λ₁₅ used in that work. We note that the left and center plots do not show the negative points, but those points are included in all fits shown.