Rescaling using weak-lensing masses. From top to the bottom: (i) entropy profiles of the sub-sample of 16 clusters with weak-lensing masses available, scaled using $M_{500}^{\mathrm{WL}}$, where shaded grey lines show the impact of accounting for statistical errors on $M_{500}^{\mathrm{WL}}$ in the rescaling, as described in the text; (ii) median entropy profiles, obtained using M₅₀₀^Y_X (red dotted line) and $M_{500}^{\mathrm{WL}}$ (blue dotted line) in the rescaling; continuous lines are the measurements after including statistical errors on mass measurements; (iii) same as centre, but for the intrinsic dispersion; here, simple scalings without including errors on mass measurements are shown as shaded areas.