Prompted by various analyses of long (type II) gamma-ray burst (GRB) rates and their relationship to the cosmic star formation history, metallicity and luminosity function evolution, we systematically analyse these effects with a Monte Carlo code. We test various cosmic star formation history models including analytical and empirical models as well as those derived from cosmological simulations. We also explore expressions for metallicity enhancement of the GRB rate with redshift, as presented in the literature, and discuss improvements to these analytic expressions from the point of view of galactic evolution. These are also compared to cosmological simulations on metal enrichment. Additionally, we explore possible evolutionary effects of the GRB rate and luminosity function with redshift. The simulated results are tested with the observed Swift sample including the L, z and peak flux (log N–log P) distributions. The observational data imply that an increase in the GRB rate is necessary to account for the observations at high redshift, although the form of this enhancement is unclear. A rate increase due to lower metallicity at higher redshift may not be the singular cause and is subject to a variety of uncertainties. Alternatively, evolution of the GRB luminosity function break with redshift shows promise as a possible alternative.