We examined the packing structure of polystyrene-coated gold nanoparticles (Au@PS) as a function of grafting density. A series of Au@PS nanoparticles with grafting densities in the range of 0.51-1.94 chains nm(-2) were prepared by a ligand exchange process using thiol-terminated PS and then self assembled at a liquid-air interface. We observed a transition from disordered to body-centered cubic (bcc) to face-centered cubic (fcc) arrangements with increasing grafting density, even though the ligand length-to-core radius ratio (lambda) was as high as 3.0, a condition that typically favors nonclose-packed bcc symmetry in the self-assembly of hard nanoparticles. To explain this phenomenon, we define lambda(eff) to include the concentrated polymer brush regime as part of the "hard core", which predicts that the softness of Au@PS nanoparticles is reduced from 1.53 to 0.14 in a theta solvent as the grafting density increases from 0.51 to 1.94 chains nm(-2). This new definition of lambda can also predict the effective radii of nanoparticles using the established optimal packing model. The experimental findings are supported by a combination of coarse-grained molecular dynamics simulation and adaptive common neighbor analysis, which show that changes in grafting density can drive the observed transitions in nanoparticle packing. These studies provide new insights for controlling the self-assembled symmetries of polymer-coated nanocrystals using a simple ligand exchange process to tune particle softness.