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tokens: and our purity of is calculated for real clusters with . However, our completeness decreases (80%) in this mass range (), as shown in Licitra et al. ( 2016a ). When fixing the slope at unity, we obtain () and a scatter of ( dex) for the complete (published) catalogs. In this case, the difference in a for the two samples is negligible, . The small shift in normalization (∼0.2 dex) compared to the diagonal is expected, because lensing mass estimates are generally higher than X-ray masses (Zhang et al. 2008 ; Rasia et al. 2012 ; Simet et al. 2017a ). When leaving the slope as a free parameter, we find and , with a scatter of ( and , with a scatter of ) for the complete (published) catalogs. The incompleteness when using the published catalogs appears to bias our fit slope, which becomes much shallower than the diagonal. In Figure 10 , we show the mass–luminosity and mass–temperature relations. We apply a logarithmic linear fit, in the form: where , for the , for the , , and . For the mass–luminosity relation, we find and , with a scatter ( and , with a scatter ) for the complete ( published ) catalogs. For the mass–temperature relation, we find and , with a scatter ( and , with a scatter ), for the complete ( published catalogs). The relations obtained with the published catalogs show again shallower slopes. Our results are consistent with the expected deviations from self-similarity (Böhringer et al. 2011 ). We summarize our results in Table 4 . Table 4 Results of the Fit of the Weak Lensing Mass vs. X-Ray Mass and Mass Proxy Relations: Note. “CC” refers to the complete catalogs and “PC” to the published catalogs (see text for the catalog definitions and values of the pivot mass, luminosity, and temperature used in the fit of the scaling relations). 6. Discussion 6.1. Comparison to Previously Derived Mass–Richness Relations In this section, we discuss our results in the context of similar current studies. As stated before and shown in Licitra et al. ( 2016a , 2016b ), our richness estimator λ is defined in a similar way as the richness from redMaPPer (Rykoff et al. 2014 ). The redMaPPer richness is defined as , where is the probability that each galaxy in the vicinity of the cluster is a red-sequence member and are weights that depend on luminosity and radius. In this calculation, only galaxies brighter than and within a scale radius are considered. The radius is richness-dependent and scales as . The RedGOLD richness is a simplified version of . We constrained the radial distribution of the red-sequence galaxies with an NFW profile and applied the same luminosity cut and radius scaling as in Rykoff et al. ( 2014 ), but did not apply a luminosity filter. Unlike the redMaPPer definition, our richness is not a sum of probabilities. Those choices were made to minimize the scatter in the mass–richness relation. For redshifts , the difference is only of 5–15%, while it increases to 40–60% at , where the redMaPPer richness is systematically higher