Ratio of the stellar BH birth rate measured in BBH mergers and in GRBs, as a function of α the index of the power law distribution of the coalescence times of BBH mergers. The solid and dashed lines show the fraction calculated for the median value of the local rate of BBH mergers measured by Advanced LIGO (Abbott et al. 2017), while the shaded areas indicate the full range of allowed values considering the errors on the local rate of BBHs mergers. The four panels correspond to different values (given in the inset) of the parameters appearing in Eq. (5).