It would be nice to have additional data. However, I think we can mine the case of Ramanujan for clues about difficulty of entry. What I find striking is that he only contacted three mathematicians. Had he contacted, say, twenty before being noticed, that would have suggested a higher barrier to entry. But it was apparently just three. My own experience is that the great scientific minds are very approachable, aside from a tiny handful of scientist celebrities who understandably have to learn to be less approachable.