  We analyze the size of quantum gravity effects near black hole horizons. By
considering black holes in asymptotically AdS spacetime, we can make use of the
"quantum deviation" to estimate the size of quantum gravity corrections to the
semiclassical analysis. We find that, in a typical pure state, corrections to
correlation functions are typically of order exp(-S/2). Both the magnitude and
time dependence of the correlator differ from previous results related to the
spectral form factor, which estimated the correlator in a thermal state. Our
results severely constrain proposals, such as non-violent unitarization and
some versions of fuzzballs, that predict significant corrections to the
semiclassical computation of correlation functions near black holes. We point
out one possible loophole: our results rely on the standard result that bulk
reconstruction is state independent for small perturbations outside the black
hole.
