We use a parent sample of 118 gamma-ray burst (GRB) afterglows, with known redshift and host galaxy extinction, to separate afterglows with and without signatures of dominant reverse-shock emission and to determine which physical conditions lead to a
prominent reverse-shock emission. We identify 10 GRBs with reverse shock signatures - GRBs 990123, 021004, 021211, 060908, 061126, 080319B, 081007, 090102, 090424 and 130427A. By modeling their optical afterglows with reverse and forward shock analytic light curves and using Monte Carlo simulations, we estimate the parameter space of the physical quantities describing the ejecta and circumburst medium. We find that physical properties cover a wide parameter space and do not seem to cluster around any preferential values. Comparing the rest-frame optical, X-ray and high-energy properties of the larger sample of non-RS-dominated GRBs, we show that the early-time ($<$ 1ks) optical spectral luminosity, X-ray afterglow luminosity and $gamma$-ray energy output of our reverse-shock dominated sample do not differ significantly from the general population at early times. However, the GRBs with dominant reverse shock emission have fainter than average optical forward-shock emission at late time ($>$ 10 ks). We find that GRBs with an identifiable reverse shock component show high magnetization parameter $R_{mathrm{B}} = varepsilon_{rm B,r}/varepsilon_{rm B,f} sim 2 - 10^4$. Our results are in agreement with the mildly magnetized baryonic jet model of GRBs.
