Impact-driven fluvial erosion is directly related to the energy delivered to the channel bed by moving bed load. Using a novel protocol, we have measured this energy in four mountain streams in Austria and Switzerland. Similar to bed load transport rates, the energy delivered to the bed displays large scatter over several orders of magnitude even for a constant discharge. We found that only a small fraction (<1%) of the total energy available to the stream is delivered to the bed and can be used for erosive work. Empirical predictive equations can be defined for specific sites, but there is large site-to-site variability. Prediction of energy delivered to the bed using the saltation-abrasion model of bedrock erosion only provides the observed trends when measured bed load transport rates are used as input. Using an empirical transport law calibrated to the conditions at one of the study streams leads to overprediction of delivered energies by more than 2 orders of magnitude. This overprediction decreases with increasing discharge, and thus, at high discharges, better predictive results are obtained. We find a correlation between the channels' bed slope or characteristic grain sizes of the channel bed and the fraction of energy delivered to the bed of the total energy available to the stream. This observation provides a tentative link between fundamental fluvial incision processes to the stream power model family that has widely been used to model fluvial bedrock incision in landscape evolution simulations.