Chemical mixing enthalpy (ΔH^chem) and mismatch entropy normalized by Boltzmann constant (S_σ⁄k_B) corresponding to the three empirical rules for the achievement of high amorphous-forming ability (AFA) were calculated with thermodynamical functions for the gross number of 6450 alloys in 351 ternary amorphous systems. The ternary amorphous alloys have ΔH^chem of −86 to 25 kJ/mol and S_σ⁄k_B of 1.0×10⁻³ to 5.7. The average values of ΔH^chem and S_σ⁄k_B are calculated to be −33 kJ/mol and 0.33, respectively. The 30 alloys in 9 ternary amorphous systems including 10 alloys in Ag–Cu–Fe system have positive values of ΔH^chem. Most of the ternary amorphous alloys have the values of ΔH^chem and S_σ⁄k_B inside a trapezoid region in ΔH^chem−log(S_σ⁄k_B) chart except mainly for the H- and the C-containing alloys, Si–W–Zr system and the 32 alloys having positive values of ΔH^chem. The analysis of AFA was carried out for typical five ternary amorphous systems. The following four results are derived. 1) Al–La–Ni and B–Fe–Zr alloys have high AFA in accordance with the concept of the three empirical rules. 2) The further multiplication of alloy components causes an increase in the AFA of Al–B–Fe alloys. 3) Thermodynamical factors represented by melting temperature and viscosity at the melting temperature are required for evaluation of AFA for Mg- and Pd-based amorphous alloys. 4) A tendency for log(S_σ⁄k_B) to increase with decreasing ΔH^chem is recognized in each alloys system, implying the stabilization of an amorphous phase against solid solution and intermediate phase.