We perform a set of 38 fully-nonlinear numerical simulations of equal-mass black-hole binaries in a configuration where the two black-hole spins in the binary are equal in both magnitude and direction , to study precession effects .
We vary the initial direction of the total spin \vec { S } with respect to the orbital angular momentum \vec { 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 \mu = \cos \theta , and two configurations on the poles .
In all cases , we set the initial dimensionless black-hole spins to 0.8 .
We observe that during the late-inspiral stage , the total angular momentum of the system \vec { J } remains within 5 ^ { \circ } of its original direction , with the largest changes in direction occurring when the spins are nearly ( but not exactly ) counter-aligned with the orbital angular momentum .
We also observe that the angle between \vec { S } and \vec { 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 black holes 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-squared 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 a hundred 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 black-hole-spin distributions and gravitational radiation in cosmological scenarios involving several mergers .