Fraction of simulated GCs that are above the detection threshold as a function of distance, for each galaxy in the HECATE-based sample. The two-dimensional density represented with red shaded bins summarizes the theoretical GC detectability fraction of all galaxies in 100 Monte-Carlo realisations (i.e., 100 × 26 711 galaxies). The solid line is the analytic predicted fraction for I_E ≤ 26.2 and the dashed line is for I_E ≤ 25. Panel a: Only systems with N_GC > 50. Panel b: Only GC systems with N_GC ≤ 50 to illustrate the stochasticity introduced by small galaxies and their small total number of GCs.