  We present advances in modeling Type IIP supernovae using MESA for evolution
to shock breakout coupled with STELLA for generating light and radial velocity
curves. Explosion models and synthetic light curves can be used to translate
observable properties of supernovae (such as the luminosity at day 50 and the
duration of the plateau, as well as the observable quantity $ET$, defined as
the time-weighted integrated luminosity that would have been generated if there
was no ${\rm ^{56}Ni}$ in the ejecta) into families of explosions which produce
the same light curve and velocities on the plateau. These predicted families of
explosions provide a useful guide towards modeling observed SNe, and can
constrain explosion properties when coupled with other observational or
theoretical constraints. For an observed supernova with a measured ${\rm
^{56}Ni}$ mass, breaking the degeneracies within these families of explosions
(ejecta mass, explosion energy, and progenitor radius) requires independent
knowledge of one parameter. We expect the most common case to be a progenitor
radius measurement for a nearby supernova. We show that ejecta velocities
inferred from the Fe II$\lambda$ 5169 line measured during the majority of the
plateau phase provide little additional information about explosion
characteristics. Only during the initial shock cooling phase can photospheric
velocity measurements potentially aid in unraveling light curve degeneracies.
