Large-scale, explosive volcanic eruptions are one of the Earth's most hazardous natural phenomena. We demonstrate that their size, frequency, and composition can be explained by processes in long-lived, high-crystallinity source reservoirs that control the episodic creation of large volumes of eruptible silicic magma and its delivery to the subvolcanic chamber where it is stored before eruption. Melt percolates upward through the reservoir and accumulates a large volume of low-crystallinity silicic magma which remains trapped until buoyancy causes magma-driven fractures to propagate into the overlying crust, allowing rapid magma transfer from the reservoir into the chamber. Ongoing melt percolation in the reservoir accumulates a new magma layer and the process repeats. Our results suggest that buoyancy, rather than crystallinity, is the key control on magma delivery from the source reservoir. They identify an optimum reservoir size for the largest silicic eruptions that is consistent with data from natural systems and explain why larger magnitude eruptions are not observed on Earth.