We obtain the joint distribution function of the gravitino mass and the cosmological constant in KKLT and Large Volume Scenario models with an anti-D3 brane at the bottom of a warped throat as the uplift sector. Moduli stabilisation is incorporated so that we sample only over points corresponding to vacua. The effects of the anti-D3 brane are computed using the nilpotent goldstino formalism. The distribution function for the hierarchies of warped throats serves as a key input. In the limit of zero cosmological constant, we find that the distribution functions are tilted favourably towards lower scales of supersymmetry breaking.