According to an outstanding article at advancedfootballanalytics.com, the historical probability of success is 26%. However, with most onside kicks, the other team is expecting it, which lowers the probability of success. For surprise onside kicks, the probability of success is 60%! The thrust of the article is that smart strategy would be to do surprise onside kicks more often. I agree; it was a brilliant move by the Saints.
This question was raised and discussed in the forum of my companion site Wizard of Vegas.