The ability of fish to migrate past velocity barriers results from both attempt rate and swimming capacity. Here, I formalize this relationship, providing equations for estimating the proportion of a population successfully passing a barrier over a range of distances and times. These equations take into account the cumulative effect of multiple attempts, the time required to stage those attempts, and both the distance traversed on each attempt and its variability. I apply these equations to models of white sucker (Catostomus commersoni) and walleye (Stizostedion vitreum) ascending a 23-m-long flume against flows ranging from 1.5 to 4.5 m??s-1. Attempt rate varied between species, attempts, and over time and was influenced by hydraulic variables (velocity of flow and discharge). Distance of ascent was primarily influenced by flow velocity. Although swimming capacity was similar, white sucker had greater attempt rates, and consequently better passage success, than walleye. Over short distances, models for both species predict greater passage success against higher velocities owing to the associated increased attempt rate. These results highlight the importance of attraction to fish passage and the need for further investigation into the hydraulic and other environmental conditions required to simultaneously optimize both attempt rate and passage success.