Upper panel:f_{ICL + BCG} versus formation redshift z_form, for the galaxy clusters from the Magneticum (blue), TNG100 (purple), Horizon-AGN (gold), and Hydrangea simulations (orange). The gray box displays the Pearson correlation coefficient for each simulation between f_{ICL + BCG} and z_form. The closer the absolute value is to unity, the tighter the correlation. We further include best fit lines for each simulation determined via the least squares method (colored lines). Middle panel: Center shift between the 3D gas barycenter and the location of the BCG (normalized by R_200c), plotted as a function of the formation redshift, with the colors the same as the upper panel. Lower panel: Fraction of the total halo mass mass which is in all subhalos f_sub (so excluding the central and diffuse halo) versus formation redshift, with colors as in the upper two panels.