Heat assisted magnetic recording (HAMR) is often lauded as one of the key technologies poised to replace conventional granular magnetic recording (CGMR). Conventional recording is expected to eventually fail because as the information-bearing grains continue to shrink, they become thermally unstable and will spontaneously flip due to excitations from the ambient temperature. HAMR grains are smaller and have larger anisotropies making them thermally stable, but unwritable at room temperature. Heat from a laser is applied to assist during the writing. The grain flipping probability (GFP) model has been proposed to model and predict the densities achievable in conventional recording systems. In this work we modify the GFP to include a circular hot-spot of a laser as a 2 D Gaussian and predict the expected ensities that might be achieved on HAMR media with 4 nm grains. In this work we examine the effect of varying the hot-spot diameter, the hot-spot peak, and the alignment of the hot-spot to the magnetic footprint profile.