Group mass vs luminosity density of selected BGGs (grey points) in the EAGLE simulation. The thick green dashed line shows the median of a Gaussian fit to the group mass of the data points at different density values, while the thinner green dash-dotted lines show 1σ standard deviations from the median. The relation between the logarithms of group mass and luminosity densities shows a clear correlation that can be approximated by a linear fit, shown with the red line and the corresponding formula in the top of the figure.