We study the statistical distributions of the spins of generic black-hole binaries during the inspiral and merger , as well as the distributions of the remnant mass , spin , and recoil velocity . For the inspiral regime , we start with a random uniform distribution of spin directions \vec { S } _ { 1 } and \vec { S } _ { 2 } over the sphere and magnitudes | \vec { S } _ { 1 } / m _ { 1 } ^ { 2 } | = | \vec { S } _ { 2 } / m _ { 2 } ^ { 2 } | = 0.97 for different mass ratios , where \vec { S } _ { i } and m _ { i } are the spin-angular momentum and mass of the i th black hole . Starting from a fiducial initial separation of r _ { i } = 50 M , we perform 3.5-post-Newtonian-order evolutions down to a separation of r _ { f } = 5 M , where M = m _ { 1 } + m _ { 2 } , the total mass of the system . At this final fiducial separation , we compute the angular distribution of the spins with respect to the final orbital angular momentum , \vec { L } . We perform 16 ^ { 4 } = 65536 simulations for six mass ratios between q = 1 and q = 1 / 16 and compute the distribution of the angles \hat { \vec { L } } \cdot \hat { \vec { \Delta } } and \hat { \vec { L } } \cdot \hat { \vec { S } } , directly related to recoil velocities and total angular momentum . We find a small but statistically significant bias of the distribution towards counter-alignment of both scalar products . A post-Newtonian analysis shows that radiation-reaction-driven dissipative effects on the orbital angular momentum lead to this bias . To study the merger of black-hole binaries , we turn to full numerical techniques . In order to make use of the numerous simulations now available in the literature , we introduce empirical formulae to describe the final remnant black hole mass , spin , and recoil velocity for merging black-hole binaries with arbitrary mass ratios and spins . Our formulae are based on the post-Newtonian scaling , to model the plunge phase , with amplitude parameters chosen by a least-squares fit of recently available fully nonlinear numerical simulations , supplemented by inspiral losses from infinity to the ISCO . We then evaluate those formulae for randomly chosen directions of the individual spins and magnitudes as well as the binary ’ s mass ratio . The number of evaluations has been chosen such that there are 10 configurations per each dimension of this parameter space , i.e . 10 ^ { 7 } . We found that the magnitude of the recoil velocity distribution decays exponentially as P ( v ) \sim \exp ( - v / 2500 km s ^ { -1 } ) with mean velocity < v > = 630 { km s } ^ { -1 } and standard deviation \sqrt { < v ^ { 2 } > - < v > ^ { 2 } } = 534 { km s } ^ { -1 } , leading to a 23 \% probability of recoils larger than 1000 km s ^ { -1 } , and a highly peaked angular distribution along the final orbital axis . The studies of the distribution of the final black-hole spin magnitude show a universal distribution highly peaked at S _ { f } / m _ { f } ^ { 2 } = 0.73 and a 25 ^ { \circ } misalignment with respect to the final orbital angular momentum , just prior to full merger of the holes . We also compute the statistical dependence of the magnitude of the recoil velocity with respect to the ejection angle . The spin and recoil velocity distributions are also displayed as a function of the mass ratio . We finally also compute the effects of the observer orientation with respect to the recoil velocity vector to take into account the probabilities to measure a given redshifted ( or blueshifted ) radial velocity of accretion disks with respect to host galaxies .