In the present work the concept of a binding polynomial is revisited for the most widely used case of self-assembly of identical molecular units and results in the re-construction of a link to the grand partition function of such a system. It is found that if the self-assembly process is not pronounced (i.e., the product of the equilibrium constant and the monomer concentration is close to zero), the binding polynomial has the meaning of a molecular partition function that is given by the summation over energy levels of any molecule in the system. In other cases the concept of a binding polynomial may be misleading.