The moisture budget is evaluated as a function of the probability distribution of precipitation for the end of the twentieth century and projected end of the twenty-first century in the Community Earth System Model Large Ensemble. For a given precipitation percentile, a conditional moisture budget equation relates precipitation minus evaporation (P - E) to vertical moisture transport, horizontal moisture advection, and moisture storage. At high percentiles, moisture advection and moisture storage cancel and evaporation is negligible, so that precipitation is approximately equal to vertical moisture transport, and likewise for projected changes. Therefore, projected changes to extreme precipitation are approximately equal to the sum of thermodynamic and dynamic tendencies, representing changes to the vertical profiles of moisture content and mass convergence, respectively. The thermodynamic tendency is uniform across percentiles and regions as an intensification of the hydrological cycle, but the dynamic tendency is more complex. For extreme events, per degree of warming, in the mid-to-high latitudes the dynamic tendency is small, so that precipitation approximately scales by the Clausius-Clapeyron 7% K-1 increase. In the subtropics, a drying tendency originating from dynamics offsets the thermodynamic wetting tendency, with the net effect on precipitation varying among regions. The effect of this dynamic drying decreases with increasing percentile. In the deep tropics, a positive dynamic tendency occurs with magnitude similar to or greater than the positive thermodynamic tendency, resulting in generally a 10%-15% K-1 precipitation increase, and with a > 25% K-1 increase over the tropical east Pacific. This reinforcing dynamical tendency increases rapidly for high percentiles.