  Spectroscopic analysis of Ly$\alpha$ damping wings of bright sources at $z>6$
is a promising way to measure the reionization history of the universe.
However, the theoretical interpretation of the damping wings is challenging due
to the inhomogeneous nature of the reionization process and the proximity
effect of bright sources. In this Letter, we analyze the damping wings arising
from the neutral patches in the radiative transfer cosmological simulation
suite Cosmic Reionization on Computers (CROC). We find that the damping wing
profile remains a tight function of volume-weighted neutral fraction $\left<
x_{\rm HI} \right>_{\rm v}$, especially when $\left< x_{\rm HI} \right>_{\rm
v}>0.5$, despite the patchy nature of reionization and the proximity effect.
This small scatter indicates that with a well-measured damping wing profile, we
could constrain the volume-weighted neutral fraction as precise as $\Delta
\left< x_{\rm HI} \right>_{\rm v} \lesssim 0.1$ in the first half of
reionization.
