Collapsed mass inside an ionized region as a function of its volume. The gray colormap represents the distribution of halos the HIRRAH-21 simulation and its numerical mean and dispersion are shown as black lines in the corresponding panels. The inferred relations using the logarithmic Softplus parameterization from Sect. 3.1.2 considering the dispersion with percolation (purple line) and without percolation (orange line) are shown. The fit is done at x_H II ∼ 10% (top) and x_H II ∼ 22% (bottom).