The last 4 years have seen the rapid emergence of a new solar cell technology based on organic-inorganic lead halide perovskites, primarily CH3NH3PbI3 and related halides involving Cl and Br. Debate continues on the role of excitons and free carriers in these materials. Recent studies report values of exciton binding energy for the iodide ranging from 0.7 meV to 200 meV, with vastly different implications for device operation and design. In the present work, previously neglected polarons are shown likely to have a major impact in determining excitonic properties. Polaronic exciton binding energies calculated using effective longitudinal optical phonon energies, deduced from permittivity measurements, are shown consistent with experimental energies for good quality samples of CH3NH3PbI3 and CH3NH3PbBr3 , as determined over a large temperature range from optical absorption data. Bandgaps determined simultaneously show a discontinuity at the orthorhombic to tetragonal phase transition for the iodide, but not for the bromide.