Large-scale magnetic field configurations are important for the transport of solar wind strahl electrons, which are suprathermal and directed along the field outward from the Sun. Strahl electrons are routinely used to infer not only the field configurations between the Sun and Earth but also local field structures, i.e., field inversions, where the magnetic field is locally folded back or inverted. Using solar wind data from ACE observations and a 2-D data-driven solar wind model with nonzero azimuthal magnetic field at the solar wind source surface, magnetic field lines are mapped between the Sun and Earth and beyond, in the solar equatorial plane. Standard verification metrics are used to assess, for five solar rotations at different phases of solar cycle 23, the performance of the mapping predictions for observed inversions, which are inferred from solar wind suprathermal electrons and magnetic fields measured by ACE. The probability of detection is consistently ≈0.70 across the different phases. The success ratio, the Hanssen-Kuipers skill score, and the Heidke skill score are ≈0.55–0.70 for the four rotations in the rising, solar maximum, and declining phases, but ≈0.35–0.60 for the rotation near solar minimum, during which almost half of the samples have undetermined field configurations. Our analyses confirm the persistence of inversions throughout solar cycle 23, suggest for most observed inversions a solar/coronal origin at the wind's source surface or below, and predict that inversions should be less common for larger heliocentric distance r ∼> 3 AU than for smaller r.