As EY mentioned, in Einstein's mind the apriori probability of this prediction being correct was very high, probably over 99%.
The reason is that GR was being tested in the "weak-field" static limit, the same one that was used to derive it from the Special Relativity and the Equivalence Principle in the first place. Nearly every theory compatible with these would produce the same predictions.
He probably would not have said anything remotely as flippant, were the experiment to look for, say, gravitational radiation, the effect he was not at all sure about at the time. On the other hand, his confidence that a rather small effect would be successfully measured was probably much lower than 99%. Hence the apparent "arrogance": he simply rejected the low-probability outcome.
It almost worked out that way.The experimental results were indeed barely passable from one expedition, poor from the other one, and did not unequivocally confirm the expected effect. In fact, were Eddington not convinced that Einstein was right to begin with, his publication on the matter may well have been much less sympathetic.
Today's post, Einstein's Arrogance was originally published on 25 September 2007. A summary (taken from the LW wiki):
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