  We perform a statistical analysis of the binary black hole problem in the
post-Newtonian approximation by systematically sampling and evolving the
parameter space of initial configurations for quasi-circular inspirals. Through
a principal component analysis of spin and orbital angular momentum variables
we systematically look for uncorrelated quantities and find three of them which
are highly conserved in a statistical sense, both as functions of time and with
respect to variations in initial spin orientations. We also look for and find
the variables that account for the largest variations in the problem. We
present binary black hole simulations of the full Einstein equations analyzing
to what extent these results might carry over to the full theory in the
inspiral and merger regimes. Among other applications these results should be
useful both in semi-analytical and numerical building of templates of
gravitational waves for gravitational wave detectors.
