Injected vs. detected population distributions for BDs and its hosts in the optimistic (B1, solid), intermediate (B2, dashed), and pessimistic (A2, dotted) scenarios (cf. Table 1). The injected population distribution of the three scenarios is shown in grey for comparison. From top to bottom and left to right: BD semi-major axis, mass, inclination, K, BD period, DWD period (denoted as P_DWD rather than P_b), S/N of the DWD (denoted as S/N_DWD rather than S/N), system distance, chirp mass, total Gaia G magnitude of the two WDs.