  Gamma-ray burst (GRB) afterglows have been observed across the
electromagnetic spectrum, and physical parameters of GRB jets and their
surroundings have been derived using broadband modeling. While well-sampled
lightcurves across the broadband spectrum are necessary to constrain all the
physical parameters, some can be strongly constrained by the right combination
of just a few observables, almost independently of the other unknowns. We
present a method involving the peaks of radio lightcurves to constrain the
fraction of shock energy that resides in electrons, $\epsilon_e$. This
parameter is an important ingredient for understanding the microphysics of
relativistic shocks; Based on a sample of 36 radio afterglows, we find
$\epsilon_e$ has a narrow distribution centered around $0.13-0.15$. Our method
is suggested as a diagnostic tool for determining $\epsilon_e$, and to help
constrain the broadband modeling of GRB afterglows. Some earlier measurements
of the spreads in parameter values for $\epsilon_e$, the kinetic energy of the
shock, and the density of the circumburst medium, based on broadband modeling
across the entire spectrum, are at odds with our analysis of radio peaks. This
could be due to different modeling methods and assumptions, and possibly
missing ingredients in past and current modeling efforts. Furthermore, we show
that observations at $\gtrsim10$~GHz performed $0.3-30$ days after the GRB
trigger, are best suited for pinpointing the synchrotron peak frequency, and
consequently $\epsilon_e$. At the same time, observations at lower radio
frequencies can pin down the synchrotron self-absorption frequency and help
constrain the other physical parameters of GRB afterglows.
