  We make a quantitative prediction for the detection rate of orphan GRB
afterglows as a function of flux sensitivity in X-ray, optical, and radio
wavebands, based on a recent model of collimated GRB afterglows. We find that
the orphan afterglow rate strongly depends on the opening angle of the jet
(roughly \propto \theta_jet^{-2}), as expected from simple geometrical
consideration, if the total jet energy is kept constant as suggested by recent
studies. The relative beaming factor b_rel, i.e., the ratio of all afterglow
rate including orphans to those associated with observable prompt GRBs, could
be as high as b_rel >~ 100 for searches deeper than R ~ 24, depending on
afterglow parameters. To make the most plausible predictions, we average the
model emission for ten sets of afterglow parameters obtained through fits to
ten well-observed, collimated GRB jets, weighted by the sky coverage of each
jet. Our model expectations are consistent with the results (or constraints)
obtained by all past searches. We estimate the number of orphan afterglows in
the first 1500deg^2 field of the SDSS to be about 0.2. The relative beaming
factor b_rel is rapidly increasing with the search sensitivity: b_rel ~ 3 for
the SDSS sensitivity to transient objects in the northern sky (R ~ 19), ~14 for
the past high-z supernova searches (R ~ 23), and ~50 for the sensitivity of the
Subaru Suprime-Cam (R ~ 26). Predictions are made for the current facilities
and future projects in X-ray, optical, and radio bands. Among them, the
southern-sky observation of the SDSS (sensitive to transients down to R ~ 23)
could detect ~40 orphan afterglows during the five-year operation. Allen
Telescope Array would find about 200 afterglows in a radio band at ~0.1-1mJy
with b_rel ~ 15.
