Relationships between frequency and intensity of volcanic eruptions are actively sought by geophysicists for both monitoring and research purposes. By analyzing surveillance videos of persistent volcanic activity at Stromboli (Italy), we derived the frequency and jet height of >4000 explosions that occurred in 72 h-long time windows sampled yearly from 2005 to 2009. We found a positive relationship linking explosion frequency and jet height (linked to eruption intensity) when averaging the two parameters over time intervals from hours to days, with a stronger correlation for longer intervals. We interpret this behavior as the response of the magmatic system to variable influx of magma and gas at depth, increased flux at depth causing more frequent and stronger explosions at the surface. This relationship entails concurrent control of source processes over explosion frequency and intensity, directly impacting modeling of explosion sources at persistently active volcanoes in general and hazard assessment at Stromboli in particular.