  We investigate the thermoelectric properties of CaAl$_2$Si$_2$-type Zintl
phase compounds $AB_2X_2$ ($A$ = Mg, Ca, Sr, Ba, $B$ = Mg, Zn, Cd, and $X$ = P,
As, Sb) using first principles band calculations within the Boltzmann transport
theory assuming the constant relaxation time approximation. We introduce the
effective degree of valley degeneracy $n_{TE}$ to focus on the relationship
between the thermoelectric properties and the multivalley character of the
electronic band structure around the Fermi level. We also introduce a quantity
$\gamma_{TE}$, which takes into account $n_{TE}$ and anisotropy of the valley
structure, and it is found that $\gamma_{TE}$ enables us to well understand the
overall trend of the material dependence of the power factor. We finally
suggest promising thermoelectric materials, e.g. BaMg$_2$P$_2$ for PF $\sim
20\mu$W/cmK$^2$ and $ZT > 0.2$ at 300K and SrZn$_2$As$_2$ for PF $\sim
35\mu$W/cmK$^2$ and $ZT > 0.35$ at 300K assuming a relaxation time of 10 fs and
a lattice thermal conductivity value of 2 W/mK.
