Average cluster matter profiles in the Magneticum simulation rescaled as in Eq. (12) to $\stackrel{\sim }{\mathrm{\Delta }\mathrm{\Sigma }}(R/R_{200\mathrm{c}})$. In the left plot, we average all the clusters (14.3 <  log(M_200c/M_⊙)< 15) for a given redshift and analyze the redshift trend. In the right plot, we average clusters over all redshift ranges (0.01 ≤ z ≤ 0.96) within a mass bin and analyze the mass trends. In both panels, the bottom plot shows the deviation of average profiles with respect to the mean of all the profiles. The rescaling dramatically reduces systematic trends in mass and redshift, highlighting the degree of self-similarity in the matter profiles even when baryonic components are included. The thickness of the lines in the upper panels represents the 68% credible region in the average matter profiles.