  During the first few days after explosion, Type II supernovae (SNe) are
dominated by relatively simple physics. Theoretical predictions regarding
early-time SN light curves in the ultraviolet (UV) and optical bands are thus
quite robust. We present, for the first time, a sample of $57$ $R$-band Type II
SN light curves that are well monitored during their rise, having $>5$
detections during the first 10 days after discovery, and a well-constrained
time of explosion to within $1-3$ days. We show that the energy per unit mass
($E/M$) can be deduced to roughly a factor of five by comparing early-time
optical data to the model of Rabinak & Waxman (2011), while the progenitor
radius cannot be determined based on $R$-band data alone. We find that Type II
SN explosion energies span a range of $E/M=(0.2-20)\times 10^{51} \;
\rm{erg/(10 M}_\odot$), and have a mean energy per unit mass of $\left\langle
E/M \right\rangle = 0.85\times 10^{51} \; \rm{erg/(10 M}_\odot$), corrected for
Malmquist bias. Assuming a small spread in progenitor masses, this indicates a
large intrinsic diversity in explosion energy. Moreover, $E/M$ is positively
correlated with the amount of $^{56}\rm{Ni}$ produced in the explosion, as
predicted by some recent models of core-collapse SNe. We further present
several empirical correlations. The peak magnitude is correlated with the
decline rate ($\Delta m_{15}$), the decline rate is weakly correlated with the
rise time, and the rise time is not significantly correlated with the peak
magnitude. Faster declining SNe are more luminous and have longer rise times.
This limits the possible power sources for such events.

High Energy Astrophysical Phenomena;Cosmology and Nongalactic Astrophysics