Fraction of systems of interest as a function of |f_kick|:=f_kick under the assumption that the direction of the natal kick is isotropic. Bound systems (P_bound, num) are shown as purple circles. Bound binaries in which T_post/T_pre < 1 (or T_post/T_pre < 0.1) are shown as brown triangles (or teal diamonds). Analytic solutions are shown for bound systems (P_bound, purple solid line) and the fraction of those bound systems that lead to retrograde orbits (P_retro, gray dashed line).