Different components forming part of a local configuration of n≥2 grains constitute a phase system in which the locally available masses define a working point in the corresponding phase diagram. Because the number of configurations can be larger than the number of possible phase diagrams, a basic issue of the single sample concept (SSC) may be addressed by a statistical analysis: is the large phase space of possible compounds efficiently explored by the SSC? In the present study, the compositional distribution functions p(XE) were calculated for some of the N components comprising a sample. Broad p(XE) distributions were obtained using reasonable assumptions for the distributions describing the grain size and the local coordination number of grains. p(XE) functions were calculated both analytically and using a fully numerical procedure. Application of the method to cuprate superconductors revealed that the observed stoichiometries conformed well with the corresponding p(XE) distributions. From the present analysis we conclude that the SSC can provide starting compositions for compounds expected to be present in phase systems for given reaction conditions T and p.