Reward functions are at the heart of every reinforcement learning (RL) algorithm. In robotic grasping, rewards are often complex and manually engineered functions that do not rely on well-justified physical models from grasp analysis. This work demonstrates that analytic grasp stability metrics constitute powerful optimization objectives for RL algorithms that refine grasps on a three-fingered hand using only tactile and joint position information. We outperform a binary-reward baseline by 42.9% and find that a combination of geometric and force-agnostic grasp stability metrics yields the highest average success rates of 95.4% for cuboids, 93.1% for cylinders, and 62.3% for spheres across wrist position errors between 0 and 7 centimeters and rotational errors between 0 and 14 degrees. In a second experiment, we show that grasp refinement algorithms trained with contact feedback (contact positions, normals, and forces) perform up to 6.6% better than a baseline that receives no tactile information.