It is important to quantitatively and graphically characterize the four core effects, the most fundamental yet disputable issues of high-entropy alloys. Yet, the traditional and commonly believed special quasirandom structure (SQS) based on the prefect random mixing structure hypothesis is insufficient as the SQS model ignores the difference of the types of different constituent atoms, the difference of the types of different crystal lattice structure, such as FCC, BCC and HCP, and the difference of the different heat treatment temperatures. In this contribution, based on crystal structure, we propose an alloy thermodynamics model based on the crystallographic structure and then establish the thermodynamic database of the end-member involved by combining computational thermodynamics and first-principle calculations. Thus, the four core effects of high-entropy alloys with various phase structures were quantitatively and graphically characterized, including the site occupying fractions (SOFs), and then the atomic distribution model construction based on SOFs, short-range ordering (SRO) cluster, diverse mechanical property, interstitial atom diffusion, and catalytic characteristic of selected high-entropy alloys. Meanwhile, such behaviors of the commonly believed SQS based on the prefect random mixing structure were also simulated and compared with those of the SOF structures. We conclude that it is quite necessary and also feasible to consider the inherent and inevitable sublattice preference of constituent atoms to simulate the structure and diverse properties of HEAs theoretically, which extends beyond the commonly believed but baseless SQS based on the random mixing hypothesis.