When will we observe binary black holes precessing?

After eleven gravitational-wave detections from compact-binary mergers, we are yet to observe the striking general-relativistic phenomenon of orbital precession. Measurements of precession would provide valuable insights into the distribution of black-hole spins, and therefore into astrophysical binary formation mechanisms. Using our recent two-harmonic approximation of precessing-binary signals [S. Fairhurst et al., Phys. Rev. D 102, 024055 (2020)], we introduce the ``precession signal-to-noise ratio'', ${\ensuremath{\rho}}_{p}$. We demonstrate that this can be used to clearly identify whether precession was measured in an observation (by comparison with both current detections and simulated signals), and can immediately quantify the measurability of precession in a given signal, which currently requires computationally expensive parameter-estimation studies. ${\ensuremath{\rho}}_{p}$ has numerous potential applications to signal searches, source-property measurements, and population studies. We give one example: assuming one possible astrophysical spin distribution, we predict that precession has a one in $\ensuremath{\sim}25$ chance of being observed in any detection.