Law of Averages

Do consistency and the law of averages go hand in hand?
I do not know how else to put this thing? I mean, how long can one continue to perform at his optimum to achieve desired results, till something results that is not commensurate with his effort? At some stage, the person realizes that the things are not what he thought would be. I assume a fair amount of luck is involved in anything you accomplish. You can call it whatever you feel like- providence, destiny, whatever. Is the law of averages some sort of a nomenclature for “what goes round, comes round” - “advocated” by a person obsessed with the “laws”?
I think that’s right. You can try and equate it with the Karmic cycles. The realization of the happenings around you will be the same. Well, the psychological implication of the law of averages on a person is quite overwhelming in many cases. But the secret of being consistent lies in being able to stretch the winning streak as much as possible before the wheel turns.