Linking tectonic setting to eruptive activity in volcanic arcs provides a framework to understand processes that control the production, accumulation and eruption of magma on Earth. We use the Holocene eruptive records of 162 volcanoes, which are selected based on an assessment of recording biases, to calculate the probability of recording large eruptions (between Magnitudes 4 and 7). We quantify regional variability in the sizes of volcanic eruptions and compare it with subduction parameters influencing the generation, transport and storage of magma. Given the tectonic setting of a subduction zone is multidimensional (e.g., age, speed, obliquity of the subducting plate) we use a graphical model to explore the strength of probabilistic relationships between tectonic and volcanic variables. The variable that exhibits the strongest probabilistic relationship with eruption size is convergence obliquity, with larger eruptions favored in settings where convergence is normal. Normal convergence favors the storage and accumulation of larger volumes of magma, whereas oblique convergence favors the transport and eruption of smaller volumes of magma. In low-obliquity arcs where magma storage is promoted, the subduction of older slabs results in higher mantle productivity, which thermally favors the accumulation of eruptible magma and larger eruptions on average. However, the highest mantle productivity also results in more frequent magma injection and pressurization of crustal reservoirs. Consequently, arcs with moderate slab ages and low obliquity produce the highest proportion of larger eruptions. In high-obliquity arcs mantle productivity does not dominantly control eruption sizes. Instead, thinner crust facilitates frequent transport of magma to the surface, resulting in smaller eruptions. For the largest eruptions on Earth (e.g., Magnitude 8), however, accumulation of eruptible magma will be dominantly controlled by thermomechanical modification of the crust and not the frequency of magma intrusion. Despite the importance of convergence obliquity, our results show that variability in the sizes of volcanic eruptions is controlled by complex relationships with other parameters including slab age and crustal thickness. By using a graphical model, we have been able to explore complex volcano-tectonic relationships. We suggest a similar approach could be extremely valuable for exploring other complex multidimensional datasets within the Earth Sciences.