Tsunamigenic earthquakes pose a large hazard in subduction zones, but it is currently unclear in which - if any - tectonic setting they preferentially occur. We compile the Subduction Nature & Interconnected Tsunamigenic earthquake Characteristics (SNITCH) database with parameters on the geodynamics, megathrust seismicity, and tsunami characteristics for tsunamis caused by earthquakes in all subduction zones. We use a bivariate regression analysis to detect possible relationships between the tsunamigenic earthquake characteristics of a subduction zone and its interplate seismicity, as well as its geometric, structural, and kinematic parameters. We focus our analysis on the normalised number of tsunamigenic earthquakes Nt. The bivariate analysis does not reveal any significant correlations between Nt and the seismogenic zone geometry of the megathrust. However, we do find correlations between Nt and the megathrust seismicity and tectonic parameters characterising a subduction zone. We employ a multivariate Fisher analysis on the tectonic parameters to see which combinations best distinguish the subduction zone segments in which relatively many and few tsunamis occurred. We find that the type of margin (i.e., erosional or accretionary), the trench-normal component of the subduction and convergence velocity, the amount of sediments at the trench and the roughness of the incoming plate are the most important parameters to achieve this. Therefore, tsunamigenic earthquakes may be more prone to occur in tectonic settings where plates subduct relatively fast beneath a sediment-starved, erosional margin. A complex, shallow subduction interface, characterised by multiple faults and fractures that arise at a margin with little trench sediments to smooth subducting plate topography, could account for the larger number of tsunamigenic earthquakes. These results could have implications for hazard assessment.