  The observational follow-up campaign of the gravitational wave (GW)
multi-messenger event GW170817/GRB170817A has shown that the prompt
$\gamma$-rays are consistent with a relativistic structured jet observed from a
wide viewing angle $\gtrsim 20$\deg. We perform Bayesian inference using the
data from early and late EM observations to determine the jet profile of
GRB170817A assuming a structured jet model. We use the geometric dependence on
the burst luminosity to produce a short duration gamma-ray burst (sGRB)
efficiency function with redshift, which folded in with binary neutron star
detection rate, allows us to estimate the future joint GW/sGRB detection rates
for LIGO and Virgo detectors. We show that, if the jet structured profile of
GRB170817A is a relatively common feature of sGRBs, then there is a realistic
probability of another off-axis coincident detection during the third
aLIGO/Virgo observing run (O3). We also find that up to 4 yr$^{-1}$ joint
events may be observed during the advanced LIGO run at design sensitivity and
up to 10 yr$^{-1}$ by the upgraded advanced LIGO configuration A+. We show that
the detection efficiencies for wide-angled sGRB emissions will be limited by
GRB satellites as the GW detection range increases through proposed upgrades.
Therefore, although the number of coincident detections will increase with GW
detector sensitivity, the relative proportion of detected binary neutron stars
with $\gamma$-ray counterparts will decrease; 11\% for O3 down to 2\% during
A+.
