  We consider the defocusing nonlinear wave equation of power-type on
$\mathbb{R}^3$. We establish an almost sure global existence result with
respect to a suitable randomization of the initial data. In particular, this
provides examples of initial data of super-critical regularity which lead to
global solutions. The proof is based upon Bourgain's high-low frequency
decomposition and improved averaging effects for the free evolution of the
randomized initial data.
