We study the scattering of solar wind protons off the lunar surface, using ion observations collected over 6 years by the ARTEMIS satellites at the Moon. We show the average scattered proton energy spectra, directional scattering distributions, and scattering efficiency, for different solar wind incidence angles and impact speeds. We find that the protons have a scattering distribution that is similar to existing empirical models for scattered hydrogen energetic neutral atoms, with a peak in the backward direction (toward the Sun). We provide a revised model for the scattered proton energy spectrum. We evaluate the positive to neutral charge state ratio by comparing the proton spectrum with existing models for scattered hydrogen. The positive to neutral ratio increases with increasing exit speed from the surface but decreases with increasing impact speed. Combined, these counteracting effects result in a scattering efficiency that decreases from ~0.5% at 300 km/s solar wind speed to ~0.3% at 600 km/s solar wind speed.