  (Abridged): The total populations of globular cluster systems (GCSs) are
discussed in terms of their connection to the efficiency of globular cluster
formation---the mass fraction of star-forming gas that was able to form bound
stellar clusters rather than isolated stars or unbound associations---in galaxy
halos. Observed variations in GCS specific frequencies (S_N=N_gc/L_gal), both
as a function of galactocentric radius in individual systems and globally
between entire galaxies, are reviewed in this light. It is argued that trends
in S_N do not reflect any real variation in the underlying efficiency of
cluster formation; rather, they result from ignoring the hot gas in many large
ellipticals. This claim is checked and confirmed in each of M87, M49, and NGC
1399, for which existing data are combined to show that the volume density
profile of globular clusters, rho_cl, is directly proportional to the sum of
(rho_gas+rho_stars) at large radii. The constant of proportionality is the same
in each case: epsilon=0.0026 +/- 0.0005 in the mean. This is identified with
the globular cluster formation efficiency. The implication that epsilon might
have had a universal value is supported by data on the GCSs of 97 early-type
galaxies, on the GCS of the Milky Way, and on the ongoing formation of open
clusters. These results have specific implications for some issues in GCS and
galaxy formation, and they should serve as a strong constraint on more general
theories of star and cluster formation.
