Top: Redshift distribution of cluster counts for traditional forward model (with explicit scaling relations, orange histogram) and for the simulation-based model (with the LDL, blue histogram), here for a 50 deg² survey extending from z = 0.1 to z = 0.5. The shaded regions display the 3σ Poisson standard deviation for each model. Also shown is the observed distribution of C1 clusters in the XXL Survey (dashed black histogram), however one should keep in mind that the selection function is in this case more complex than a simple flux cut. We stress that this Figure is not a goodness of fit: both models are calibrated independently. Bottom: Cluster population in CR–HR space for simulation-based model, also for a 50 deg² survey extending from z = 0.1 to z = 0.5. The CR and HR in the simulation-based and scaling-relation-based models are computed differently; hence we did not compare their distributions.