[MENTION=6787503]Hriston[/MENTION], I'd thought about "mentioning" you into this thread, so I'm glad that you found it on your own!
I don't think I would personally use a formula, but just the standard DCs - jumping an extra foot for that 15 STR PC is probably easy (DC 10, so better than 50% chance of succes), while jumping an extra 4' for that 12 STR PC seems Medium or even Hard (so DC 15 or 20, ie quite a bit less than 50% chance of success without solid Athletics proficiency).
Another consideration (harking back to the Thief-Acrobat jumping abilities in Unearthed Arcana) is whether the character lands standing, or prone and hence needing to recover.
To comment on the "rulings/rules" aspect of the thread: I don't see any intention in 5e that certain rules are not to be followed -like the rule that uncertainy is resolved via checks, and that checks consist in rolling a d20 and adding mods from a fairly standard list. A GM could - for some sense of "could" - call for a Burning Wheel "die of fate" check to find out what happens when a PC jumps, or use the Moldvay Basic approach of setting a percentage chance of success and calling for a d% roll - but I don't see the least suggestion in the Basic PDF that this is what the game expects.
[MENTION=71699]clearstream[/MENTION] has mentioned the idea of (certain) rules being constitutive of a game - for D&D it's tempting to see d20 rolls to hit, doing polyhedral dice hit points of damage on a success; d20 rolls to save; and, in 5e, d20 checks to resolve action declarations with uncertain outcomes, as constitutive in that sense. A few departures from this are neither here nor there, but systematic departure would make it unclear in what sense the game is a 5e D&D one. (And that's before we get to the rather specific and intricate PC build rules, which play a constitutive role in themselves, and which don't contribute meaningfully to play if the constitutive action resolution rules aren't generally used.)
I don't set DCs based on the abilities of the character. If a situation includes a gap to be jumped, for example, that's unusually far for some characters such that they need to make a STR (Athletics) check to clear the span, the DC would be the same for each person making the attempt.
I see the designations, easy, medium, hard, etc., to refer to the difficulty for the average person, not the difficulty for the individual making the check.
My intuition is closer to [MENTION=6919838]5ekyu[/MENTION] and [MENTION=6802765]Xetheral[/MENTION] - the DC is objective in the sense of relfective of the pre-established ingame difficulty (which constrasts with some other sytems, including some aspects of 4e) but the character's STR is part of that pre-estabished ingame difficulty. That is, if a character can certainly jump 15' (STR 15) then it seems that s/he can probably jump 16' about as easily as someone who can certainly jump 12' (STR 12) can jump 13' or 14'. But a DC = distance approach will tend to exaggerate things in favour of the weaker character.DCs appear to be intended to be objective, not subjective. That seemed to mean focus on the jump distance, not the jumper. When I do that, it feels easy to reach a consistent ruling.
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players have all kinds of resources to bear on this, that can make a high DC doable, or circumvent it all together (cast Fly?) That makes scaling subjectively for me a questionable pursuit, but if I did scale, I'd scale percentually.
I don't think I would personally use a formula, but just the standard DCs - jumping an extra foot for that 15 STR PC is probably easy (DC 10, so better than 50% chance of succes), while jumping an extra 4' for that 12 STR PC seems Medium or even Hard (so DC 15 or 20, ie quite a bit less than 50% chance of success without solid Athletics proficiency).
Another consideration (harking back to the Thief-Acrobat jumping abilities in Unearthed Arcana) is whether the character lands standing, or prone and hence needing to recover.
To comment on the "rulings/rules" aspect of the thread: I don't see any intention in 5e that certain rules are not to be followed -like the rule that uncertainy is resolved via checks, and that checks consist in rolling a d20 and adding mods from a fairly standard list. A GM could - for some sense of "could" - call for a Burning Wheel "die of fate" check to find out what happens when a PC jumps, or use the Moldvay Basic approach of setting a percentage chance of success and calling for a d% roll - but I don't see the least suggestion in the Basic PDF that this is what the game expects.
[MENTION=71699]clearstream[/MENTION] has mentioned the idea of (certain) rules being constitutive of a game - for D&D it's tempting to see d20 rolls to hit, doing polyhedral dice hit points of damage on a success; d20 rolls to save; and, in 5e, d20 checks to resolve action declarations with uncertain outcomes, as constitutive in that sense. A few departures from this are neither here nor there, but systematic departure would make it unclear in what sense the game is a 5e D&D one. (And that's before we get to the rather specific and intricate PC build rules, which play a constitutive role in themselves, and which don't contribute meaningfully to play if the constitutive action resolution rules aren't generally used.)