edit:
@Karst
Earned or unearned doesn't really matter. If my opponent earns a hit on me and happens to deal more hit stun allowing for an easier link off a possibly difficult combo or something similar to that, it means that I've had my own odds of not having that combo completed and getting an escape dropped. I understand how you're trying to look at it, but ultimately it will lead to benefits vs banes.
That, unfortunately, still doesn't work in terms of fairness. If I'm playing against you in street fighter and you get any sort of random buff not based on an intentional decision within the game, then that gives you a legitimately unfair advantage. Unfair in the sense that there was no justified decision in the process.
Using tripping as an example again, while it's possible I could trip there's a chance that I won't and you will which benefits me. In that specific moment I might be thankful for tripping as it saved me. No matter how you cut it random effects are always negative to someone.
An example of random-negative benefiting someone: players randomly gain boosts during the match, and you are gaining them more than your opponent.
I'll compare two situations that are very similar to show the difference more clearly: Hsien-ko item toss (pretend the bomb doesn't exist) vs. Phoenix Wright item search.
Hsien-ko item toss is random-positive, because when you throw an item, your expected result is to just hit someone with a weak item. If you get a dizzy, that is a bonus. Your goal, the purpose of the move, is just to hit someone. Similarly, your opponent doesn't play any differently if he/she knows the item will dizzy. The goal for your opponent is the same: don't get hit.
Phoenix Wright's item search is random-negative, because when you go to gather an item, your expected result is to find a piece of evidence. If you get great evidence, it's a bonus, but if you get bad evidence, your time is wasted. You performed a move that is actually a burden on your character, because now you have to find a way to throw it away. You didn't do anything to deserve this, you didn't make a mistake. It's just inherent in the character that a lot of bad things will happen to you.
Yes, these effects are harmful/beneficial for your opponent. That's not what distinguishes them, though. What distinguishes them is whether you did something to deserve the state in the first place. Hsien-ko did something right: she hit the opponent with an item. Maybe she gets a little something extra, too, but she still earned the base state. Phoenix Wright did nothing wrong: he gathered an item. Yet he might be punished for doing nothing wrong.
Important differences:
Hsien-ko scenario: Hsien-ko did something right. Hsien-ko's opponent did something wrong. Bonus reward is okay. Random-positive.
Wright scenario: Wright did something right (found time to gather an item). Wright's opponent did nothing at all. Penalty is not okay even as a possibility. Random-negative.
I'm not sure the concept of "earned randomness" really helps.
Imagine if the amount of meter gain was randomized for every action. You "earned" your right to roll for that meter gain, but it would be competitively awful. Same thing with Halo when it replaced set power weapons with randomized "earned" ordnance drops.
(Maybe I'm not understanding what you mean by "positive" or "earned" randomness though.)
I don't think random-positive is
always good. It's usually not great as a fundamental part of the game's mechanics. It's okay for limited situations, however. I really don't like the randomized damage in ST, for example. Stupid design decision. But having a particular move with some random-positive elements isn't necessarily bad, and can add interesting moments to the game.
