Ratio of the baryonic fraction inside the virial radius with respect to the cosmic baryon fraction as a function of the virial mass for the three Magneticum adiabatic runs C1, C8, and C15 depicted in the three columns. Different rows correspond to the redshifts z ∈ {0.0, 1.0, 2.0}. The mean relation, as given by Eq. (14) as a function of redshift, is depicted as the horizontal black line while the red lines correspond to the measured mean and unbiased standard deviations in mass bins. The rightmost column shows the distribution of these ratios for the three simulations.