A mole of water contains 2N lone pairs and 2N hydrogens. In theory these could all pair up (probably in reality that never quite happens) to give 2N hydrogen bonds, an average of 4 per molecule (4 rather than 2 because each bond is shared between two molecules).
A mole of ammonia contains N lone pairs and 3N hydrogens. You can't get more than N hydrogen bonds out of that, an average of two per molecule. An individual molecule might have four, but that means others must have less.