People prove their ability with a system that is known to work. Because the system works, there's a known result, based on how much effort you put into your training. For example, you know you can dodge or parry a punch because you do it a lot of times against someone who is really trying to hit you. It's not theoretical any more, I think you are confusing Theoretical vs Probability.
Definition of Theoreetical - concerned with or involving the theory of a subject or area of study
rather than its practical application.
If you train to parry punches against someone who is trying to hit you then you have moved into the practical application of things. From this point it's no longer a theory. Now the question becomes. "
What is the probability that you can do the same thing in a street fight."
The probability of an untrained person beating a trained fighter in a street fight, 1 vs 1 without weapons, is very low. There's nothing theoretical about that. I'm not sure what you train. But the way that I train and the system that I train, the chances that an untrained fighter will beat me is very low. It's not an ego thing, it's just that my training gives me a set of additional skills that I can use, while an untrained fighter will only have what he is born with.
Here's the difference between trained and untrained. None of this is theoretical