The system of 'oxidation numbers' and 'reduction potentials', the oxidation-reduction system, is a shorthand method to account for the tendency of polar bonds to be stronger.
In the context of covalent bonding, the reduction potential of an element depends primarily on its electronegativity. The more electronegative an atom, the greater the internal energy decrease involved in bond formation as it pulls electrons towards itself. Electronegative elements love to gain electron control and form strong bonds.
A discussion of bond dissociation energies and standard chemical thermodynamics, like we are having here, is actually more conceptually transparent than the redox system, which is more convenient, though, from an accounting perspective, having oxidation numbers and the Nernst equation and useful stoichiometric congruence with electrical current in applied electrochemistry.
Somewhere along in the history of science education, though, these two systems of meaning seem to have detached from each other, and not too many students learn the underlying basis of the oxidation-reduction system. In biology, for example, there is constant reference to 'high energy electrons' when the understanding would benefit greatly from refering to these as 'electrons shared in weak bonds' that are on their way to strong bonds, such as the oxygen-hydrogen bonds of water at the end of oxidative metabolism.