We investigate the origin of the shape of the globular cluster (GC) system scaling parameters as a function of galaxy mass, i.e. specific frequency (SN), specific luminosity (SL), specific mass (SM) and specific number () of GCs. In the low-mass galaxy regime (MV≳−16 mag), our analysis is based on Hubble Space Telescope/Advanced Camera for Surveys observations of GC populations of faint, mainly late-type dwarf galaxies in low-density environments. In order to sample the entire range in galaxy mass (MV=−11 to −23 mag =106– 1011 L⊙), environment and morphology we augment our sample with data of spiral and elliptical galaxies from the literature, in which old GCs are reliably detected. This large data set confirms (irrespective of the galaxy type) the increase in the specific frequencies of GCs above and below a galaxy magnitude of MV≃−20 mag. Over the full mass range, the SL value of early-type galaxies is, on average, twice that of late types. To investigate the observed trends, we derive theoretical predictions of GC system scaling parameters as a function of host galaxy mass based on the models of Dekel and Birnboim in which star formation processes are regulated by stellar and supernova feedback below a stellar mass of 3 × 1010 M⊙ and by virial shocks above it. We find that the analytical model describes remarkably well the shape of the GC system scaling parameter distributions with a universal specific GC formation efficiency, η, which relates the total mass in GCs to the total galaxy halo mass. Early-type and late-type galaxies show a similar mean value of η= 5.5 × 10−5, with an increasing scatter towards lower galaxy masses. This can be due to the enhanced stochastic nature of the star and star-cluster formation processes for such systems. Some massive galaxies have excess η values compared to what is expected from the mean model prediction for galaxies more luminous than MV≃−20 mag (LV≳ 1010 L⊙). This may be attributed to a very efficient early GC formation, less efficient production of field stars, accretion of predominantly low-mass/luminosity high-η galaxies or a mixture of all these effects.