Parameter distributions of simulated systems for which Jupiter-like oblateness is detectable with Δχ² > 60, shown for three true obliquity distributions: isotropic (black), Rayleigh peaking at 10^∘ (red), and Rayleigh peaking at 3^∘ (blue). Above each histogram are median values and 16th/84th percentiles. The upper-right panel shows how the number of detections scales with the Δχ² threshold for the ETC noise model; shaded bands indicate the 1σ range, and the dotted line shows the reference scaling ﹩N\propto {({\rm{\Delta }}{\chi }_{{\rm{thr}}}^{2})}^{-3/2}﹩.