  Since the initial discovery of gravitational waves in 2015, significant
developments have been made towards waveform interpretation and estimation of
compact binary source parameters. We present herein an implementation of the
generalized precession parameter $\langle \chi_p \rangle$, which averages over
all angular variations on the precession timescale, within the RIFT parameter
estimation framework. Relative to the originally-proposed precession parameter
$\chi_p$, which characterizes the single largest dynamical spin in a binary,
this new parameter $\langle \chi_p \rangle$ has a unique domain $1 < \langle
\chi_p \rangle < 2$, which is exclusive to binaries with two precessing spins.
After reviewing the physical differences between these two parameters, we
describe how $\langle \chi_p \rangle$ was implemented in RIFT and apply it to
all 36 events from the second half of the Advanced LIGO and Advanced Virgo
third operating run (O3b). In O3b, ten events show significant amounts of
precession $\langle \chi_p \rangle > 0.5$. Of particular interest is
GW191109_010717; we show it has a $\sim28\%$ probability that the originating
system necessarily contains two misaligned spins.
