Alkaline earth sub-nitrides were synthesised more than five decades ago, but their potential for high-performance electronics was only recently demonstrated [Lee et al., Nature, 2013]. Based on the formal valence of the elements, there is an intrinsic excess of electrons, which is unusual for a chemically stable compound. We report an electrostatic and electronic analysis of Ca2N, Sr2N and Ba2N, which reveals a highly anisotropic electronic band structure, with a subtle balance between localisation and delocalisation of excess electrons in between positively charged planes of [M2N]+. A deep potential well is found at empty crystallographic positions, which are occupied by anions in the structurally analogous ternary nitrides. A greater degree of delocalisation (conductivity) is predicted for heavier metals.