This is a principled approach. And of course it does depend on the nature of the contractual relationship with your client. However, even if we charitably ass

This is a principled approach. And of course it does depend on the nature of the contractual relationship with your client. However, even if we charitably assume that the developers are accurately estimating the mean, that means that out of 100 projects, 50 of them will be delivered late. It is likely that you'd want to do better than that, and to do so in a principled manner, you're going to need to adjust the estimates that come out of the estimation process.