  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.
