Temperature in kK (top row), magnetic field strength in kG (second row), line-of-sight velocity in km/s (third row), and the Wilson effect (as compared to the quiet Sun τ = 1 height) in km (last row) at optical depth τ_5nm = 1 for the MHD simulation (left column), the first run of the MHS inversion (S^r1, middle column), and the second run of the MHS inversion (S^r2, right column). All the panels per row share the same color scaling, shown at the right. Sub-panels in panels b-c, e-f, h-i, and k-l show in black the histogram of the difference between the MHD and the MHS inversion of S^r1 (S^r2) in panels b, e, h, and k (in panels c, f, i, and l). For the sake of comparison, panels c, f, i, and l show the same histograms presented in b, e, h, and k in gray. The values in the top part of each histogram are the median value together with percentile 16 as sub-index and percentile 84 as super-index. Vertical gray lines appear every 0.05 kK, 0.05 kG, 0.4 km/s, and 50 km for the temperature, magnetic field strength, line-of-sight velocity, and Wilson effect, respectively, and are centered at 0 (shown with a dark dashed line). The blue contour in panel a represents the normalized continuum intensity threshold of 0.65, highlighting the position of the pores.