Simulated distribution of spectral index and redshift. Left: distribution of the spectral indices of simulated BL Lac sources (red), along with simulated BL Lac that would have been detected with the HEGS observation (blue). For visibility purposes, both distribution are normalised to have a density of 1. Right: distribution of the redshift for all simulated BL Lac sources (red) and for the BL Lac expected to be detected (blue). In both graphics, the black line corresponds to the actual mean of the population of BL Lac objects.