The relationships of optimal compositions of bulk metallic glasses (BMGs) have been analyzed with a set of thermodynamic quantities of mismatch entropy normalized with respect to Boltzmann's constant (Sσ!/kB) and mixing enthalpy (Hmix) and with assistance of classification result of BMGs. The analysis shows clear dependence of the location of Sσ!/kB and Hmix values for optimal compositions of ternary BMGs in Sσ!/kB-Hmix chart in each alloy system. The ternary BMGs are summarized into four types: (1) Cu-based, (2) La-, Zr- and Ca-based, (3) Pd-based and (4) Fe- and Mg-based BMGs according to their maximum value of Sσ!/kB ((Sσ!/kB)max) and the largest and negative value of Hmix ((Hmix)L.N.) or their half values which are obtained for each system. These types of BMGs are related with the local arrangements of BMGs, which are widely accepted as an icosahedral structure for Metal-Metal type, a transformed tetragonal dodecahedrons and triacontrahedrons structure for Pd-Metalloid type, and a network-like structure for Metal-Metalloid type.