  Gravitational wave backgrounds generate correlated noises to separated
detectors. This correlation can induce statistical losses to actual detector
networks, compared with idealized noise-independent networks. Assuming that the
backgrounds are isotropic, we examine the statistical losses specifically for
the angular averaged sensitivity curves, and derive simple expressions that
depend on the overlap reduction functions and the strength of the background
noises relative to the instrumental noises. For future triangular
interferometers such as ET and LISA, we also discuss preferred network
geometries to suppress the potential statistical losses.
