log(Age_w/yr) of the BGGs as a function of the halo mass of groups (log(M₂₀₀/M_⊙)) in the observations (shaded KDE density maps), Magneticum (green contours), and H15 SAM (red contours) for S-I to S-V subsamples. Black points, green diamonds, and red squares present the median stellar age at given halo masses in the observations, Magneticum and H15, respectively. The bottom-right panel illustrates the stellar age of BGGe versus group mass for the combined sample of BGGs in S-II to S-V. All trends indicate no noticeable relationship between the stellar age of BGGs and the halo mass of their host groups.