Parameter distributions of simulated systems for which Jupiter-like oblateness is detectable with Δχ² > 60, assuming an isotropic distribution of true obliquities. Results are shown separately for stellar masses 0.9 < M_⋆/M_⊙ < 1.6 (black) and 0.1 < M_⋆/M_⊙ < 0.9 (red). Above each histogram are the median and 16th/84th percentiles. The upper-right panel shows how the number of detections scales with the Δχ² threshold. Solid curves use the ETC noise model, dashed curves use the empirical noise model, and shaded bands indicate the 1σ range. The dotted line shows the reference scaling ﹩N\propto {({\rm{\Delta }}{\chi }_{{\rm{thr}}}^{2})}^{-3/2}﹩.