In security systems the risk assessment in the sense of common criteria testing is a very relevant topic; this requires quantifying the attack potential in terms of the expertise of the attacker, his knowledge about the target and access to equipment. Contrary to those attacks, the recently revealed morphing attacks against Face Recognition Systems (FRSs) can not be assessed by any of the above criteria. But not all morphing techniques pose the same risk for an operational face recognition system. This paper introduces with the Morphing Attack Potential (MAP) a consistent methodology, that can quantify the risk, which a certain morphing attack creates.