Using x-ray magnetic circular dichroism, we have detected the very interfacial spins that are responsible for the horizontal loop shift in three different exchange bias sandwiches, chosen because of their potential for device applications. The "pinned" uncompensated interfacial spins constitute only a fraction of a monolayer and do not rotate in an external magnetic field since they are tightly locked to the antiferromagnetic lattice. A simple extension of the Meiklejohn and Bean model is proposed to account quantitatively for the exchange bias fields in the three studied systems from the experimentally determined number of pinned moments and their sizes.