Panel a: distribution of the differences between changes in eccentricity due to ZLK and due to repeated scatters (only looking at binaries that eventually merge). The black line corresponds to binaries initially 0.1 pc away from the SMBH and the red line to 0.3 pc. Panel b: scatter of these two terms. One point corresponds to one binary. The zero-lines are shown as dotted black lines, and the shaded areas correspond to the ±0.05 region around the zero-lines. The two diagonal lines show x + y = 0 (lower) and x + y = 1 (upper).