Abstract: The mechanical properties and plastic deformation mechanisms of crystalline solids are mainly determined by their structural defects, e.g., the motion of the versatile dislocations. However, how structures determine properties in non-crystalline solids remains as a major unsolved issue in both solid mechanics, materials sciences, as well as condensed matter physics. Structure determines property is the traditional paradigm of materials science. Following this rule, there are vast experimental characterizations, theoretical studies, and computer simulations appeared in the literature, trying to establish a one-to-one correspondence between a specific structural feature with a unique dynamic property in the general amorphous solids. However, up to date, people gain very little understanding of the structure-property relationships in amorphous solids, not to mention whether there exists any hidden rule behind the structure-property relationships. For this purpose, we focus on the unique features of deformations mechanisms in amorphous solids as well as their microstructure characteristics. Thorough proper samplings of the activation energies of the excitation of these structural parameters by an advanced molecular dynamics technique, we are trying to quantitatively assess the validity of simple short-range structures and medium- to long-range structures in determination of their properties. This is done by examination of the possible correlation between parameters of structures with their activation energies, which implies the level of difficulty in activation of the events. By this we find that the hidden governing rule of structure-property relationship in amorphous solids involves a critical role of spatial autocorrelation length of the specific structural parameter. Constraint is more relevant than geometry itself. If only one structural descriptor presents spatial autocorrelation length up to sub nanometer level, it might effectively predict the mechanical property of amorphous solids; otherwise, the short-range local structures lacking such correlation length fails to predict property. Furthermore, we present a general metric to assess the utilities of structures in determining functions of the amorphous solids, which can be served as a screening rule to seeking for effective structures in amorphous solids.