  We study abelian dominance for confinement in terms of the local gluon
properties in the maximally abelian (MA) gauge, where the diagonal component of
the gluon is maximized by the gauge transformation. We find microscopic abelian
dominance on the link-variable for the whole region of $\beta$ in the lattice
QCD in the MA gauge. The off-diagonal angle variable, which is not constrained
by the MA-gauge fixing condition, tends to be random besides the residual gauge
degrees of freedom. Within the random-variable approximation for the
off-diagonal angle variable, we analytically prove that off-diagonal gluon
contribution $W^{\rm off}$ to the Wilson loop obeys the perimeter law in the MA
gauge. The perimeter-law behavior of $W^{\rm off}$ is also confirmed using the
lattice QCD simulation. This indicates macroscopic abelian dominance for the
string tension.
