CMIP5 models exhibit a mean dry bias and a large inter-model spread in simulating South Asian monsoon precipitation but the origins of the bias and spread are not well understood. Using moisture and energy budget analysis that exploits the weak temperature gradients in the tropics, we derived a non-linear relationship between the normalized precipitation and normalized precipitable water that is similar to the non-linear relationship between precipitation and precipitable water found in previous observational studies. About half of the 21 models analyzed fall in the steep gradient of the non-linear relationship where small differences in the normalized precipitable water in the equatorial Indian Ocean (EIO) manifest in large differences in normalized precipitation in the region. Models with larger normalized precipitable water in the EIO during spring contribute disproportionately to the large inter-model spread and multi-model mean dry bias in monsoon precipitation through perturbations of the large-scale winds. Thus the intermodel spread in precipitable water over EIO leads to the dry bias in the multi-model mean South Asian monsoon precipitation. The models with high normalized precipitable water over EIO also project larger response to warming and dominate the inter-model spread in the multi-model projections of monsoon rainfall. Conversely, models on the flat side of the relationship between normalized precipitation and precipitable water are in better agreement with each other and with observations. On average these models project a smaller increase in the projected monsoon precipitation than that from multi-model mean. This study identified the normalized precipitable water over EIO, which is determined by the relationship between the profiles of convergence and moisture and therefore is an essential outcome of the treatment of convection, as a key metric for understanding model biases and differentiating model skill in simulating South Asian monsoon precipitation.