Large-scale, explosive volcanic eruptions are one of the Earth’s most hazardous natural phenomena. These super-eruptions expel tens to thousands of km3 of silicic magma and their global frequency is inversely proportional to the volume of magma released. We developed a numerical model to explore how large volumes of magma are periodically created and stored in the crust, as well as how the magma is then erupted from the crust. We found that the size, frequency, and composition of these large-scale eruptions are strongly controlled – or even dominated – by processes in long-lived, high crystallinity source reservoirs that control the episodic creation of large volumes of eruptible magma and its delivery to a subvolcanic chamber where it is stored prior to eruption. We identify an optimum reservoir size for the largest eruptions that is consistent with data from natural systems and explain why larger magnitude eruptions are not observed on Earth.