In recent years , detailed observations and accurate numerical simulations have provided support to the idea that mergers of compact binaries containing either two neutron stars ( NSs ) or an NS and a black hole ( BH ) may constitute the central engine of short gamma-ray bursts ( SGRBs ) . The merger of such compact binaries is expected to lead to the production of a spinning BH surrounded by an accreting torus . Several mechanisms can extract energy from this system and power the SGRBs . Here we connect observations and numerical simulations of compact binary mergers , and use the current sample of SGRBs with measured energies to constrain the mass of their powering tori . By comparing the masses of the tori with the results of fully general-relativistic simulations , we are able to infer the properties of the binary progenitors which yield SGRBs . By assuming a constant efficiency in converting torus mass into jet energy , \epsilon _ { jet } = 10 \% , we find that most of the tori have masses smaller than 0.01 M _ { \odot } , favoring “ high-mass ” binary NSs mergers , i.e. , binaries with total masses \gtrsim 1.5 the maximum mass of an isolated NS . This has important consequences for the gravitational-wave signals that may be detected in association with SGRBs , since “ high-mass ” systems do not form a long-lived hypermassive NS after the merger . While NS-BH systems can not be excluded to be the engine of at least some of the SGRBs , the BH would need to have an initial spin of \sim 0.9 , or higher .