BBH merger rate density in FIREbox estimated from the results of our cluster sampling algorithms (model ‘Gamma’, ‘EB18’, and ‘SFRpeak’ presented from left to right respectively) combined with predictions of the 3D grid of massive clusters integrated with CMC. A re-weighting factor corresponding to the halo mass of the host galaxy (see Sect. 2.1) is applied to each BBH obtained. Different colours indicate the contribution of galaxies grouped in different bins of stellar mass. The black solid line shows the mean total merger rate density obtained from 20 different random realisations, and the grey shaded area is the 90% credible interval. The blue shape shows the evolution of the BBH merger rate density with redshift as reported by the LVK Collaboration in Abbott et al. (2023a).