  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~\cite{Fairhurst:2019_2harm}, we introduce the
``precession signal-to-noise ratio'', $\rho_p$. 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.
$\rho_p$ 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 $\sim 25$ chance of being observed in any detection.
