  In recent years, there has been a significant effort to extract the
temperature-dependent shear ($\eta/s$) and bulk ($\zeta/s$) viscosity over
entropy ratios of the quark-gluon plasma from a global comparison of heavy-ion
data with results of hydrodynamic simulations. However, anisotropic flow, which
is arguably the most sensitive probe of viscosity, is only sensitive to an {\it
effective\/} viscosity over entropy ratio, which is obtained by taking a
weighted average over the temperature, and summing the contributions of shear
and bulk. We estimate this effective viscosity using existing first-principles
calculations, which give $0.17<(\eta/s)_{\rm eff}<0.21$, and $(\zeta/s)_{\rm
eff}<0.08$, implying that the damping of anisotropic flow at the LHC is mostly
due to shear viscosity. The values extracted from global data analyses are
compatible with these theory predictions.
