A few examples I can think of off the top of my head, to give a feel for the reference class I'm looking for:
- The existence and position of Neptune were predicted from observations of Uranus's orbit, before anyone had ever observed Neptune directly
- Black holes were predicted from the equations of General Relativity before we'd ever observed them or their effects on stars' motion
- Not as quantitative, but Darwin's theory of Evolution predicted that we'd find some method by which natural selection actually occurs, before we ever knew about DNA.
Are there other cool examples like these?