Ok. So what is it that the character does differently to allow them to jump further than they can do with certainty?
Nothing. They don't have to.
In the real world it is certain that I can maintain a running pace of about 12 kph for about an hour. I know this because from time-to-time I do it. It is also possible, in the real world, that I might maintain that pace for an hour-and-a-half, but it's not certain. (I know this also, because between 10 and 20 km is my comfortable distance for a run - after that I get tired and old joint injuries start to play up.)
What do I do differently to have a chance of maintaining my pace for that extra half-hour? Nothing, other than think hard about my hips and thighs, concentrate on my breathing, and try not to get distacted (which disrupts those other things and causes me to slow my pace). Sometimes that works; sometimes it doesn't. That's the nature of uncertain things.
I don't jump as much as I run, and mostly it's high-jumping (eg to scale fences and gates if keys have been locked in the house). Sometimes I can jump higher than others, depending on what seems to me like luck (given that I don't have a coach or the training on my own part to monitor and correct my technique) but is presumably a function of anything from placement of feet at launch, to whether I'm breathing in or out at a crucial moment, to what sort of movement I make with my ams, and probably all sort of other stuff that (for the reason just given) I can't identify or even think to speculate about.
So it's certain that with a single jump I can grab the top of, and reasonably quickly scale, a 6' fence, but a 7' fence (approximate figures only, but they'll do) is possible but not certain.
Given that, in the real world, physical performance sometimes exceeds what can be done with certainty, but doesn't always (that's what makes it an
exceeding of the
certain), I don't see why the gameworld should be any different.
People in this world can make double-digit foot long jumps with 100% certainty. Realism has never entered the equation.
There are two elements to the realism issue - (i) the distances, and (ii) the possibility of sometimes doing better than one can do with certainty.
Are the distances that can be jumped with certainty realistic? Frankly I think they're not too bad - really strong PCs (ie STR 18+) can jump with certainty distances that are, in historical terms and especially allowing for load and less than optimatl conditions, Olympic level. Ordinary people (ie STR 10 or thereabouts) can jump with certainty distances that I think are within cooee of the sorts of distances I and my non-athlete friends can jump with certainty.
Is it realistic that a person, by trying, can jump
this distance with certainy, but with equal certainty can jump
no further. That doesn't seem that realistic to me, and once we factor in the heroic nature of the genre it seems even less fitting for the game.
EDIT: I just saw this, which puts the issue front-and-centre in a pithy way:
To try just jumping like normal, when you're aware your best long jump wouldn't clear the distance?
You are taking p 64 to state a character's
best jump, which s/he can also make
with certainty. To me that doesn't fit with either experience or genre. The distance a character can clear with certainty may be a
typical jump but is not his/her
best. Whether, on any given jump, a person can jump his/her best is uncertain. (Even for professional athletes in the real world.) Hence the use of a STR (Athletics) check to get an answer.
FURTHER EDIT: I also saw this, which Charlaquin XPed and so presumably agrees with:
If you give a DC every time they say "Hey, I just want to roll athletics to go farther," they will do so every single time they hit a jump that is longer than their base distance. That means that going farther isn't going to be unusual, it's going to be the norm. There's no reason not to try to jump further at every single distance that's longer than automatic.
What's the objection to a player having his/her PC trying to jump further than normal every time s/he wants to? Does that seem unrealistic? No. Does it break the game, or even put it under strain? Almost certainly not. Does it mean (as you assert) that those longer jumps are not going to be unusual? Well, how often they are attempted will depend on how often those larger distances become salient in the ficiton, so in advance of actual play who can tell? But even if the attempts are quite frequent, who knows - in advance of setting a DC and making some rolls - what the frequency of success will be?