Previous studies have identified a projected increase in precipitation variability in a future warming climate. This may be manifested as an increasing tendency for extremely wet years and extremely dry years to occur interchangeably. However, the well known projected increase in wet extremes alone can cause an increase in variability (i.e., without any increase in dry extremes). We investigate the projected increase in precipitation variability in terms of both wet and dry extremes in the Multi-Model Large Ensemble Archive (MMLEA). For each large ensemble we aggregate 20 members in the late-20th and late-21st Centuries separately. The aggregation of members in a large ensemble generates a sufficiently long quasi-stationary climate, facilitating the identification of wet-year and dry-year frequency globally. Moreover, we compute the atmospheric moisture budget conditioned on wet and dry years to identify the physical drivers of this increased interannual variability. Increased wet years are driven by increasing evaporative fluxes, moisture convergence, and moisture advection. Meanwhile, increased dry years are primarily driven by decreased moisture convergence. Because of the importance of the moisture-convergence term for both wet and dry years, we break it down into "themodynamic" and "dynamic" terms, representing the impacts of enhanced moisture and the changing global circulation, respectively. While the thermodynamic term is uniform between wet and dry years, the dynamic term effects wet and dry years differently. In particular, the dynamic term alone enhances both wet and dry extremes in certain regions. These are generally regions of known ENSO teleconnections, illustrating how the projected increase in ENSO variability simultaneously enhances the frequency of both extremely wet and extremely dry years in affected regions. On a global scale, the identification of increased frequency of both extremely wet and dry years is important for planning for mitigation against both flooding and disruption to water resources.