  The inspiral of binary black holes is governed by gravitational radiation
reaction at binary separations r < 1000 M, yet it is too computationally
expensive to begin numerical-relativity simulations with initial separations r
> 10 M. Fortunately, binary evolution between these separations is well
described by post-Newtonian equations of motion. We examine how this
post-Newtonian evolution affects the distribution of spin orientations at
separations r ~ 10 M where numerical-relativity simulations typically begin.
Although isotropic spin distributions at r ~ 1000 M remain isotropic at r ~ 10
M, distributions that are initially partially aligned with the orbital angular
momentum can be significantly distorted during the post-Newtonian inspiral.
Spin precession tends to align (anti-align) the binary black hole spins with
each other if the spin of the more massive black hole is initially partially
aligned (anti-aligned) with the orbital angular momentum, thus increasing
(decreasing) the average final spin. Spin precession is stronger for
comparable-mass binaries, and could produce significant spin alignment before
merger for both supermassive and stellar-mass black hole binaries. We also
point out that precession induces an intrinsic accuracy limitation (< 0.03 in
the dimensionless spin magnitude, < 20 degrees in the direction) in predicting
the final spin resulting from the merger of widely separated binaries.
