Distribution of the logarithmic χ² improvement, $\left({\chi }_{\text{single }}^2/{\chi }_{\text{binary }}^2\right)$, showing the statistical evidence favoring binary over single-star spectral models. Left panel: distributions for Gaia DR3 NSS sources: systems with orbital solutions (blue), single-lined spectroscopic binaries (SB1/SB1C; orange), and double-lined spectroscopic binaries (SB2; green). Right panel: distributions for specialized populations with likely dark companions: neutron star binaries (El-Badry et al. 2024) (red) and WDMS (Li et al. 2025) (blue). The Gaia DR3 NSS SB2 sample (green dotted line) is shown for reference. Common elements in each panel: the distribution for all stars within 1 kpc (black dashed line) acts as a control representing the general population. A vertical dashed line marks 0.2 for reference. Higher values of the χ² improvement indicate stronger evidence for binarity; known binaries typically show significant positive values.