Top: binned mean of f_detected against number of simulated stars injected into Gaia data for simulated clusters in this study. See also Fig. A.2 for more examples of the logistic dependence of f_detected on n_∗. Bottom: 2D histogram of CST against number of injected stars for simulated clusters. The number of clusters at a given point is shown by the logarithmic colour-scale. The dashed grey line shows CST = 3, which is the threshold for a cluster to be detected and included in HR23. Only clusters with a CST below 38 are shown; values larger than 38 are calculated as infinity by our Python method due to floating point precision.