Ratio of the cumulative halo abundance in the hydro simulation to the halo abundance of virial halos in the dmo simulation. The results are shown for the simulated virial mass and the prediction of our model based on the individual baryon fractions, a predictive baryon fraction relation, and a stochastic baryon fraction relation. Error bars are displayed for the first case, assuming uncorrelated Poisson errors. Different panels correspond to redshifts z ∈ {0.0, 0.5, 1.0, 2.0} using Magneticum Box 2b, except for z = 0.0, where Box 2 is used. The grey regions correspond to 2.5 and 5 percent.