Realism dictates that while observation can often get you close-ish, nothing is certain until it's measured and verified.
I can go outside, look at a telephone pole, and guess how tall it is; but until-unless I climb up and measure it* all I'll have is a guess. Is it 17 feet tall? 20 feet? 22 feet? I can't tell from down here. I can look at a person across the street and think "that guy looks tough" by the way he dresses, walks, and so forth; but until-unless I see him fight (or fight him myself) I've no way of knowing whether my assessment is accurate or whether he's just a poser.
* - or look up "standard telephone pole lengths" on google, but our medieval-fantasy characters ain't got the interwebs and even if they did, (unlike their players sometimes!) they likely wouldn't be browsing in mid-combat.
It isn't that the character would know the numbers, it's that the character would have an intuitive sense of 'Can I climb that?', or 'Can I beat him in a fight?', or 'Can I run to that bus before it leaves?'. This is based on muscle memory and real experience but also a million different perceptual readings and brain processes.
In play we necessarily don't experience all those things and we rely instead on a very brief description from another party, with resolution then filtered through that person's (largely uncommunciated) sense of what's plausible. In such a game I have very little sense of what my character can achieve until I actually do it and see if I succeed.
I suggest that in real life the band of 'I dunno if I'll succeed at this' is pretty narrow. Mostly we know whether we can or can't do something. I have a pretty clear intuitive sense of my own abilities even if I couldn't articulate it in numerical terms.
The numbers in a game are an abstraction of that assessment and intuition that puts the player closer to the position of the character in terms of outcome prediction.