During the last century, descriptions of sediment transport on the surface of Earth have been mostly deterministic and strongly influenced by concepts from continuum mechanics. The assumption that particle motions on hillslopes and in rivers satisfy the continuum hypothesis has provided an important foundation for this topic. Recent studies, however, have recognized that bed load and hillslope sediment transport conditions often are rarefied and do not satisfy continuum assumptions, therein pointing to the need for new ways of describing particle motions and transport. The problem of rarefied sediment transport is probabilistic in nature, and emerging methods for describing particle motions hark back to the pioneering work of Einstein (1938), who conceptualized bed load transport as a probabilistic problem. Here we provide a data set of particle travel distances and supplemental high-speed videos of particle-surface collisions collected during laboratory experiments to assess a theoretical formulation of the probabilistic physics of rarefied particle motions and deposition on rough hillslope surfaces. The formulation is based on a description of the kinetic energy balance of a cohort of particles treated as a rarefied granular gas, and a description of particle deposition that depends on the energy state of the particles. Both laboratory and field-based measurements are consistent with a generalized Pareto distribution of travel distances and predicted variations in behavior associated with the balance between gravitational heating and frictional cooling by particle-surface collisions. These behaviors vary from a truncated distribution associated with rapid thermal collapse to an exponential distribution representing approximately isothermal conditions to a heavy-tailed distribution associated with net heating of particles. The transition to a heavy-tailed distribution likely involves an increasing conversion of translational to rotational kinetic energy leading to larger travel distances with decreasing effectiveness of collisional friction. The analysis points to the need for further clarity concerning how particle size and shape in concert with surface roughness influence the extraction of particle energy and the likelihood of deposition.