The general reasoning for why the variation is so big isn't that hard.
Set asks you to look for cards that sit at the edges of the bell curve. Most combinations will be "mostly similar" or "mostly different" but not entirely one way or the other.
When you start with a 12-card no-set combination, that means that your first 12 cards were already of a low "quality" and sit in the middle of the curve; the 3 cards added can't push the distribution to an extreme by themselves.
Edit: to think of it another way, inverse the problem; Of the usable 12-card combinations, any number of cards could be added and they'd still have at least one set. Hence you're filtering most good 15-card sets when you do the opposite.
Set asks you to look for cards that sit at the edges of the bell curve. Most combinations will be "mostly similar" or "mostly different" but not entirely one way or the other.
When you start with a 12-card no-set combination, that means that your first 12 cards were already of a low "quality" and sit in the middle of the curve; the 3 cards added can't push the distribution to an extreme by themselves.
Edit: to think of it another way, inverse the problem; Of the usable 12-card combinations, any number of cards could be added and they'd still have at least one set. Hence you're filtering most good 15-card sets when you do the opposite.