We show the peak magnitude for orphan afterglows from the jets of gravitational wave (GW) detected black-hole/neutron star -neutron star (BH/NS-NS) mergers highly depends on the jet half-opening angle θ j . Short γ-ray bursts (GRB) with a homogeneous jet structure and θ j > 10• , the orphan afterglow viewed at the typical inclination for a GW detected event, 38• , is brighter at optical frequencies than the comparable macronova emission. Structured jets, where the energetics and Lorentz factor Γ vary with angle from the central axis, may have low-Γ components where the prompt emission is suppressed; GW electromagnetic (EM) counterparts may reveal a population of failed-GRB orphan afterglows. Using a Monte Carlo method assuming a NS-NS detection limit we show the fraction of GW-EM counterparts from homogeneous, two-component, power-law structured, and Gaussian jets where the variable structure models include a wide low energy and Γ component: for homogeneous jets, with a θ j = 6• and typical short GRB parameters, we find r-band magnitude m r ≤ 21 counterparts for ∼ 13.6% of GW detected mergers; where jet structure extends to a half-opening angle of 25• , two-component jets produce m r ≤ 21 counterparts in ∼ 30% of GW detected mergers; power-law structured jets result in ∼ 37%; and Gaussian jets with our parameters ∼ 13%. We show the features in the lightcurves from orphan afterglows can be used to indicate the presence of extended structure.