It should be noted that it is arguable whether supersymmetry was introduced in order to solve the hierarchy problem. Many people, including myself, think supersymmetry is sufficiently well-motivated even ignoring the fact that it can solve the hierarchy problem. Hence, as HMHW points out, it depends who you listen to…
String theory, incidentally, naturally predicts supersymmetry that doesn’t solve the hierarchy problem.
But before these experiments, wasn’t a similar analogy also true - that as most (all?) of the other particles predicted by the SM were found, then it was almost certain that when they went looking for it they would find the Higg’s? What were people estimating the chances of not finding it beforehand?
In what sense? I’m no string theorist, but the way I heard the story, you postulate (worldsheet) SUSY in order to be able to describe fermionic excitations, so how does this prediction come about? (Of course, string theory has extra dimensions, so you don’t need SUSY for the hierarchy problem…)
OK, it depends on how you define “predict.” String theory doesn’t work without supersymmetry, and string theory was the motivating context in which supersymmetry was first invented. Since string theory requires supersymmetry, it could be said to predict supersymmetry. And in string theory landscape, naturalness is of course not a problem; the phase space of supersymmetry models in the context of the landscape tends to suggest SUSY being broken at a higher scale. A good introduction might be the first paper on Split SUSY, here. Split SUSY is an example of supersymmetry “predicted” (ie favored) by string theory which does not solve the hierarchy problem.