Macroscopically, confined electron gases at polar oxide interfaces are rationalized within the simple "polar catastrophe" model. At the microscopic level, however, many other effects such as electric fields, structural distortions and quantum-mechanical interactions enter into play. Here we show how to bridge the gap between these two length scales, by combining the accuracy of first-principles methods with the conceptual simplicity of model Hamiltonian approaches. To demonstrate our strategy, we address the equilibrium distribution of the compensating free carriers at polar LaAlO3/SrTiO3 interfaces. Remarkably, a model including only calculated bulk properties of SrTiO3 and no adjustable parameters accurately reproduces our full first-principles results. Our strategy provides a unified description of charge compensation mechanisms in SrTiO3-based systems.