  We perform a set of 38 numerical simulations of equal-mass BH binaries in a
configuration where the BH spins in the binary are equal in both magnitude and
direction, to study precession effects. We vary the initial direction of the
total spin S with respect to the orbital angular momentum L, covering the 2
dimensional space of orientation angles with 38 configurations consisting of 36
configurations distributed in the azimuthal angle phi and polar angle theta,
and two configurations on the poles. In all cases, we set the initial
dimensionless BH spins to 0.8. We observe that during the late-inspiral stage,
the total angular momentum of the system J remains within 5 deg of its original
direction, with the largest changes in direction occurring when the spins are
nearly counter-aligned with the orbital angular momentum. We also observe that
the angle between S and L is nearly conserved during the inspiral phase. These
two dynamical properties allow us to propose a new phenomenological formula for
the final mass and spin of merged BHs in terms of the individual masses and
spins of the progenitor binary at far separations. We determine coefficients of
this formula (in the equal-mass limit) using a least-squares fit to the results
of this new set of 38 runs, an additional set of five new configurations with
spins aligned/counteraligned with the orbital angular momentum, and over 100
recent simulations. We find that our formulas reproduce the remnant mass and
spin of these simulations to within a relative error of 2.5%. We discuss the
region of validity of this dynamical picture for precessing unequal-mass
binaries. Finally, we perform a statistical study to see the consequence of
this new formula for distributions of spin-magnitudes and remnant masses with
applications to BH-spin distributions and gravitational radiation in
cosmological scenarios involving several mergers.
