In structure-based screens for new ligands, a molecular docking algorithm must rapidly score many molecules in multiple configurations, accounting for both the ligand's interactions with receptor and its competing interactions with solvent. Here we explore a context-dependent ligand desolvation scoring term for molecular docking. We relate the Generalized-Born effective Born radii for every ligand atom to a fractional desolvation and then use this fraction to scale an atom-by-atom decomposition of the full transfer free energy. The fractional desolvation is precomputed on a scoring grid by numerically integrating over the volume of receptor proximal to a ligand atom, weighted by distance. To test this method's performance, we dock ligands versus property-matched decoys over 40 DUD targets. Context-dependent desolvation better enriches ligands compared to both the raw full transfer free energy penalty and compared to ignoring desolvation altogether, though the improvement is modest. More compellingly, the new method improves docking performance across receptor types. Thus, whereas entirely ignoring desolvation works best for charged sites and overpenalizing with full desolvation works well for neutral sites, the physically more correct context-dependent ligand desolvation is competitive across both types of targets. The method also reliably discriminates ligands from highly charged molecules, where ignoring desolvation performs poorly. Since this context-dependent ligand desolvation may be precalculated, it improves docking reliability with minimal cost to calculation time and may be readily incorporated into any physics-based docking program.