Molecular orientation anisotropy of the emitter molecules used in organic light emitting diodes (OLEDs) can give rise to an enhanced light-outcoupling efficiency, when their transition dipole moments are oriented preferentially parallel to the substrate, and to a modified internal quantum efficiency, when their static dipole moments give rise to a locally modified internal electric field. Here, the orientation anisotropy of state-of-the-art phosphorescent dye molecules is investigated using a simulation approach which mimics the physical vapor deposition process of amorphous thin films. The simulations reveal for all studied systems significant orientation anisotropy. Various types are found, including a preference of the static dipole moments to a certain direction or axis. However, only few systems show an improved outcoupling efficiency. The outcoupling efficiency predicted by the simulations agrees with experimentally reported values. The simulations reveal in some cases a significant effect of the host molecules, and suggest that the driving force of molecular orientation lies in the molecule-specific van der Waals interactions of the dye molecule within the thin film surface. The electrostatic dipole-dipole interaction slightly reduces the anisotropy. These findings can be used for the future design of improved dye molecules.