Smoothed distribution of log(SFR/M_⊙ yr⁻¹) for all BGGs within subsamples of S-I to S-V (solid black curve); Additionally, we illustrate the smoothed distributions for BGG subsamples categorized by their proximity to the X-ray center: those with offset ≤0.2 are represented by the dashed black curve, while those with offset > 0.2 are shown with a dotted black curve. To have a comprehensive comparison with the prediction of SAM and hydrodynamical simulations, the smoothed SFR distribution of BGGs predicted by H15 and Magneticum are shown with red and green lines, respectively. The bottom-right panel displays density maps of log(SFR/M_⊙ yr⁻¹) over cosmic time for all BGGs in both observations and models. The cumulative distribution of the SFR of galaxies in both observations and models is displayed within each panel of the figure as a subplot.