Previous work highlights the need for data collection to identify appropriate models for temporal evolution of tracer dispersal in rivers. Results of 64 gravel-bed field tracer experiments covering a wide range of flow and sediment supply regimes are compiled here to determine the probabilistic character of gravel transport. We focus on whether particle travel distances and waits are thin- or heavy-tailed. While heavy-tailed travel distance distributions are observed between successive monitoring events in different hydrological and sediment supply regimes, heavy-tailedness does not persist through total travel distance over multiple monitoring events, suggesting that individual monitoring events occur before particle travel distance exceeds the characteristic correlation length for the channel (such that particles that start in fast paths remain in fast paths and particles in slow paths remain in slow paths). After a large number of transport events, super-diffusive spreading was not observed at any of the gravel bed streams. Continuous-time tracking of x, y, z coordinates of tracers in natural streams is necessary to capture exact step and waiting time distributions.