Ratio of the BBH − BBH interaction rate and the binary-single interaction rate as a function of the cluster’s number of BHs at the time the interactions took place. The blue dots correspond to the median values obtained from the CMC models (contour is the 64% region). In green, the analytical prediction of Eq. (6), which considers the interaction of three-body BBHs ; yellow is the naïve prediction of Eq. (7), which only considers the interactions of primordial binaries.