So I originally saw the problem in last year's IYPT. (#15 https://www.iypt.org/problems/problems-for-the-34th-iypt-2021/)
A spherical ball dropped onto a hard surface will never rebound to the release height, even if it has an initial spin. A capsule-shaped object (i.e. Tic Tac mint) on the other hand may exceed the initial height. Investigate this phenomenon.
My guess is that in case of ellipsoid, the normal force acting at the point of impact (off the center) converts rotational kinetic energy into vertical translational energy. In the case of a sphere, since the normal force does not act as torque, the rotational kinetic energy is converted only into the horizontal kinetic energy (by friction).
However, I have found that this energy conversion process is related to the elasticity of an object and is difficult to express quantitatively... Could anybody help me out?