From my perspective, it's not actually correct. Although yes, the dice roll does not in itself describe the quality of the result (it's binary, you either succeed or fail, there is no notion of the quality of the result obtained), the problem with your interpretation is that it assumes that the outcome was precisely described at the start of the action, which is actually not necessarily the case.
The "outcome was precisely described at the start of the action" by whom? The player? The player should be indicating some idea of the goal the PC is trying to accomplish. But it's the DM who decides what actual outcomes are possible when the dice fall, though. I'm clarifying as, while I am not sure we disagree here, I am having trouble understanding what you mean or are implying here.
Since the actual results of success of failure are (usually) not pre-determined with any precision, It is therefore totally supported by the rules to say that the actual outcome of the ability check and its description are in any case totally determined by the DM, who is therefore absolutely free to take into account the result of the dice roll to indicate the quality of the result.
Ok, I see now. This answers what I was getting at above. A DM can take into account the result of the dice to describe quality. I've argued previously that this way leads to the possibility of low rolls being described as the PC engaged in some kind of slapstick routine (not a style I want to play - but hey, if that's fun for a table, go for it) and high rolls being described as... well... "You unlocked the crap out of that door!" or similar. Those are optional flourishes, in other words.
In our game, I typically will clearly lay out the stakes of ability checks so the players know what is on the line. They then know the success/fail states and the DC, and so can make an informed decision, as a capable adventurer, to continue with the action or not. I typically do not overlay the success or failure with flourishes for exceptionally high or low ability check rolls, though. If I ever do, it usually is to give the player an opportunity to contribute some narrative as to what something (like an acrobatic move) done really well (or really poorly) looked like.
It's easy to see from the description of success and failure at an ability chech:
- Success: "If the total equals or exceeds the DC, the ability check is a success — the creature overcomes the challenge at hand." But as nothing here indicates how the challenge is overcome and by how much, the DM is absolutely supported to describe that success any way he chooses, including with a quality of result if he so chooses.
I wouldn't choose the words "absolutely supported" in conjunction with a lack of rules. But I catch your meaning.
- Failure: "Otherwise, it's a failure, which means the character or monster makes no progress toward the objective or makes progress combined with a setback determined by the DM." Here it's even more obvious, you can even have a success through (partial) progress, but the DM can set any setback or consequence he chooses, including one based on the quality of the result.
"Quality of the result" strikes me as potentially arbitrary in the moment depending on how one runs the game. I see many DMs asking for rolls without providing stakes or DCs and we're left to wonder what any given result will mean after the dice have settled. I personally prefer a style where the DC is announced so the players know if they've succeed or failed in the moment. The anticipation is in how the dice fall rather than in how the DM "reads" them.
Another angle: if you want to reflect "quality of the result" in play, set multiple DCs ahead of time. I've seen this done in some published adventures where failure by 5 or more has a greater penalty, for example.
So while the rules indicate a binary result, because that result can be described in any term the DM chooses, he is supported in doing exactly that. The rules do not set a degree, but again the game is incredibly open and actually tell that the DM chooses the degree himself according to any criterion he chooses.
I can agree with this as a rulings not rules type of approach. Again, if outcome flourishes described by the dice are fun for the DM and table, use 'em.
