Comparison between some interesting global values X (hydrostatic mass, spectroscopic-like temperature, bolometric luminosity, and gas mass fraction) estimated from the i(cm)z model and the predicted revised scaling laws (see Eqs. (6)). For each quantity X, we plot the value normalized at (M₅₀₀, z) = (5 × 10¹⁴ M_⊙, 0.05) and estimated at Δ = 500 estimated for the grids of M₅₀₀/10¹⁴ M_⊙ = [0.15, 0.5, 1, 2, 5, 8] and redshift [0.05, 0.2, 0.6, 1, 1.5]. Filled dots indicate the estimates at the extreme of the redshift distribution, with the smallest dots corresponding to the highest z. The crosses show the predicted values from the revised scaling laws (orange, f_g; purple, T_sl; and green, L_bol).