Comparison between our MARs and previously published results. Upper panel: squares show MAR^3Ds from Fig. 8 as a function of and color coded by redshift, from dark blue to dark red as the redshift increases from bin to bin: z = 0.01, 0.21, 0.52, 0.82, and z = 1.04. The lines show MARs from merger trees by Fakhouri et al. (2010, dotted line) and by Diemer et al. (2017, solid line). Lower panel: squares again show the true MARs from TNG300-1 as a function of . Triangles show the MAR^3Ds from Pizzardo et al. (2022) as a function of in four redshift bins: z = 0.01, 0.19, 0.44, and z = 1.00. The stars show the MARs of ten observed stacked clusters from the HectoMAP survey (Pizzardo et al. 2022).