Top: distributions of orbital inclination of the encounters with respect to the black hole binary, at first passage (green) as well as before and after the energetic interaction (blue and orange lines, respectively). Middle: cumulatively summed maximum energy changes in prograde (blue) and retrograde (orange) orbits as a function of specific energy change. Bottom: two-dimensional histogram of the initial (x-axis) and final inclination (y-axis). The green points correspond to the 27 most energetic encounters (with ΔE/m_* > 7.9 × 10⁷ [km²s⁻²]). The size of points is correlated with the total energy extracted.