The Curvature Engine
The difference between the club path and the face angle at impact determines the spin axis tilt. If the face is open to the path, the ball fades/slices. If closed, it draws/hooks.
The 3:1 Rule
With a driver, every 1 degree of face-to-path difference creates approximately 3 degrees of spin axis tilt. With shorter irons, this ratio drops closer to 2:1 due to higher spin loft overriding the axis tilt.