[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.)
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.
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.)
