There is no golden number. There are no certainties. Someone can rank two programs and still match, and someone can rank 14 and not match. All that can be said is, statistically, once you get over a certain number of interviews, it’s very unlikely you will not match. But nothing is 100%. Over 10% has a match rate over 90%, and I’m pretty sure over 12 interviews is an almost certainty. I don’t remember the exact statistics off hand. But statistics are population trends, and each Individual application is different.
Take two examples:
Example one: aoa student Who doesn’t take the USMLE. Comlex scores are in the 400s. Student has trouble setting up rotations at residency programs, because of their low board scores. Gets two rotations at noncompetitive sites, and does extremely well with on those rotstions, and nets two top-tier slows of those two programs. When the time comes for interviews, the student gets very few interviews because of the board scores getting filtered out. Gets 4 interviews total including the two places that loved the student during their rotation.
Example two: M.D. student with step scores in the 270s, secures numerous rotations are very competitive programs Thanks to their high board scores. Gets to middle third slows at the very competitive programs. When it comes time for interviews, still gets 12 interviews thanks to their scores. A third sloe is posted mid interview season, low 1/3 or DNR with some damning comment.
Student one only has four interviews compared to student two who has 12. Yet I would argue that student one has a far greater chance of matching, because student one was loved by two of the programs they rotated at who were going to rank them highly. Student two was going to be in the middle third of lists, which is typically fine, but their match stock would potentially fall greatly thanks to that last sloe.
My point is, there are no certainties. You can rank 1 Program and match, and you can rank 15 and not match. The statistical likelihood of either of those happening is unlikely, but they can happen.
All you can do is go on as many interviews as you can, within reason. Then roll the dice and see how they fall.