the differential of player ability

Consider competitors pitted in a game which is commonly accepted as a game of skill.  Let us accept the inclusion of a random element to create a test of ability but not allow that risk to define the outcome of any single game.  As the competitor’s abilities approach equilibrium our game of pure skill now approaches a game of pure chance.  

So to begin the discussion lets consider eliminating the baselines of skill and chance, let’s reconsider basic completive mathematics using the differential of player ability.