AbstractPrecipitation (P) and potential evaporation (Ep) are commonly studied drivers of changing freshwater availability, as aridity (Ep/P) explains ∼90% of the spatial differences in mean runoff across the globe. However, it is unclear if changes in aridity over time are also the most important cause for temporal changes in mean runoff and how this degree of importance varies regionally. We show that previous global assessments that address these questions do not properly account for changes due to precipitation, and thereby strongly underestimate the effects of precipitation on runoff. To resolve this shortcoming, we provide an improved Budyko‐based global assessment of the relative and absolute sensitivity of precipitation, potential evaporation, and other factors to changes in mean‐annual runoff. The absolute elasticity of runoff to potential evaporation changes is always lower than the elasticity to precipitation changes. The global pattern indicates that for 83% of the land grid cells runoff is most sensitive to precipitation changes, while other factors dominate for the remaining 17%. This dominant role of precipitation contradicts previous global assessments, which considered the impacts of aridity changes as a ratio. We highlight that dryland regions generally display high absolute sensitivities of runoff to changes in precipitation, however within dryland regions the relative sensitivity of runoff to changes in other factors (e.g., changing climatic variability, CO2‐vegetation feedbacks, and anthropogenic modifications to the landscape) is often far higher. Nonetheless, at the global scale, surface water resources are most sensitive to temporal changes in precipitation.