  It is widely believed that loops observed in the solar atmosphere trace out
magnetic field lines. However, the degree to which magnetic field
extrapolations yield field lines that actually do follow loops has yet to be
studied systematically. In this paper we apply three different extrapolation
techniques - a simple potential model, a NLFF model based on photospheric
vector data, and a NLFF model based on forward fitting magnetic sources with
vertical currents - to 15 active regions that span a wide range of magnetic
conditions. We use a distance metric to assess how well each of these models is
able to match field lines to the 12,202 loops traced in coronal images. These
distances are typically 1-2". We also compute the misalignment angle between
each traced loop and the local magnetic field vector, and find values of
5-12$^\circ$. We find that the NLFF models generally outperform the potential
extrapolation on these metrics, although the differences between the different
extrapolations are relatively small. The methodology that we employ for this
study suggests a number of ways that both the extrapolations and loop
identification can be improved.
