Distribution of the maximum ratio between a evaluated at subsequent apocentres for EMRIs for selected values of M_• and a₀. The black dotted vertical line shows (a_α/a_β)_max^EMRI = 2, which roughly delimits cliffhanger EMRIs to its right. In the left panel, the orange dashed and green dash-dotted vertical lines show a₀/a_f^lc from Eq. (38), which is a rough prediction of the highest possible (a_α/a_β)_max^EMRI ratio. Each histogram is normalised to 1. We note the different x-axis scales and binning strategies in the two panels.