  The need for improved functionalities is driving the search for more
complicated multi-component materials. Despite the factorially increasing
composition space, ordered compounds with 4 or more species are rare. Here, we
unveil the competition between the gain in enthalpy and entropy with increasing
number of species by statistical analysis of the AFLOW data repositories. A
threshold in the number of species is found where entropy gain exceeds enthalpy
gain. Beyond that, enthalpy can be neglected, and disorder - complete or
partial - is unavoidable.
