  Understanding complex correlated oxides and their phase transitions has long
been a challenge. The difficulty largely arises from the intriguing interplay
between multiple degrees of freedoms. While degeneracy can play an important
role in determining material characteristics, there is no well-defined way to
quantify and to unveil its role in real materials having complicated band
structures. Here we suggest a way to quantify the `effective degeneracy'
relevant to metal-insulator transition by introducing entropy-like terms. This
new quantity well describes the electronic behaviors of transition-metal oxides
as a function of external and internal parameters. With $3d$ titanates, $4d$
ruthenates, and $5d$ iridates as our examples, we show that this new effective
quantity provides useful insights to understand these systems and their phase
transitions. For LaTiO$_3$/LaAlO$_3$ superlattice, we suggest a novel
`degeneracy control' metal-insulator transition.
