The number of planet detections predicted by our semianalytic model as a function of the detection threshold, N_σ, defined as the astrometric signal amplitude (Equation (1)) divided by σ_fov, the per-point measurement uncertainty (Equation (7)). The number of detections scales approximately as ﹩{N}_{\sigma }^{-2}﹩. The more statistically rigorous criterion Δχ² > 50 corresponds to N_σ ≳ 1.5 for DR4 and N_σ ≳ 1 for DR5. To measure planet masses with 20% precision for 90% of systems requires N_σ ≳ 4 for DR4 and N_σ ≳ 2.5 for DR5 (see Section 3.2).