If you insist on looking at exceptional people who are actually the peers of the adventuring heroes in D&D, that's fine. But in order to have that discussion, you need to pull up some running long jumps performed by adult Olympic athletes. Those would be the high-end jumps with proficiency and high strength scores and good rolls. NOT these jumps made by not-fully-grown children at local track meets.
I chose children because it was the closest thing i could think of to average adult humans with strength scores well below 16. No one really keeps records of average people performing averagely in track and field.
the problem is, Joe, the "kids" are already +3σ from norm, typically, to make the level where they are being tracked. (The pun wasn't intended, but I find it amusing, so it stays.)
And what I've seen of normal adults is not close to +3σ of kids; it's more like the ±1σ level - typically about one's own height, running.
I've seen people trying to make running leaps not in track and field in two circumstances: SCA events doing "Quests" (essentially a Larp-style quest during an SCA event), and combat fishing on the Kenai River. The latter, some dufus or another tries to leap in his reboks out to a sandbar some 6-8 feet from shore, and I've NEVER seen someone successfully make that leap (having been to the kenai and seen 2-3 people try every time, about 30 times) without pole vaulting it. The most spectacular fail was the guy who, failing the leap, wound up face down across the sandbar, in mud up to his ears. One guy used a walking stick, and misjudged his own strength... he wound up 3 feet past the sandbar, in ice cold (33°F) crotch-deep water.
At SCA questing activities... one year, there was a 10' "Pit" (marked off with rope). Nobody made it across without using a walking stick to vault it. Not even the Track letterman.... (She was a hurdler, not a running jumper. But she put up a 10' long when doing it at a track meet)... but she was in armor, so lightly encumbered. When it was done again a couple years later, it was reduced to 6' across, and about 2/3 made it without vaulting, and the rest would have had a chance to grab the side. Not a statistically significant sample, but interesting, because some of the people trying it were physically fit. (The rest tended to "Plus Sizes" or bigger...)
Now, I've seen a LOT of attempts at standing jumps... Spring in Alaska results in a LOT of puddles... it gets comical at times. Most of the time, it fails to clear past about half the height of the person - a long step, really. But, that's got a serious observer bias, as you only really notice when someone misses and ends up cold and wet, or worse, on their arse in the water.
Now, I
routinely see teens hop up 1/2 their height standing. (Orchestra and theater kids hopping up to stages or risers).
But thats why I think the idea that even middle school track records are above normal adult performance levels... because in the real world, I've never seen people succeed at it.
Then again, we get used to seeing people on TV do improbable things, so...
I think it shouldn't be automatic past one's own height; an acrobatics roll to get past it.