Both the initial spin and this precession have kinetic energy associated with them. Also there is potential energy associated with the ball's center of gravity being elevated due to the long axis not being horizontal. When the ball's angular velocity about the long axis is large, the lowest energy configuration is with the long axis vertical and no precession. As the spin velocity decreases due to friction losses, the lowest energy configuration shifts to include some precession, some spin and somewhat less potential energy of elevation. As the ball continues to slow, the potential energy seeks its minimum value, the spin if manifest as rolling and the precession degenerates into rotation about a short axis. Ultimately the ball comes to rest with its center of gravity as low as possible and no spin or precession.
The observed behavior of the football then is nothing more than Mother Nature's tendency to be a lazy dame, always driving systems to their lowest available energy configuration. The mathematical determination of the minimum energy combination of spin, precession and elevation of center of gravity, as a function of spin velocity is pretty much a mess.