Probability density of the fractional (percentage) difference between the turnaround mass (here M₁₁) predicted from the scaling relation of Eq. (11) and its actual value, for the full MDPL2 simulated cluster sample at z = 0 (left panel), and for halo subsamples of different median M₂₀₀ (right panel). In each case, the solid line shows a Gaussian kernel estimator of the probability density function, and the vertical line marks the mode of the error distribution. The scaling relation tends to overpredict M₁₁ for lower M₂₀₀ and underpredict it for higher M_200.