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MgAgAs-type "half-Heusler" compounds are known to realize two out of three possible atomic arrangements of this structure type. The number of transition metal components typically determines which of the alternatives is favored. On the basis of DFT calculations for all three variants of 20 eight- and eighteen-valence-electron compounds, the experimentally observed structural variant was found to be determined by basically two different bonding patterns. They are quantified by employing two complementary position-space bonding measures. The Madelung energy E((M)(QTAIM)) calculated with the QTAIM effective charges reflects contributions of the ionic interactions to the total energy. The sum of nearest-neighbor delocalization indices ςnn characterizes the covalent interactions through electron sharing. With the aid of these quantities, the energetic sequence of the three atomic arrangements for each compound is rationalized. The resulting systematic is used to predict a scenario in which an untypical atomic arrangement becomes most favorable.