I think I posted this last year, too... but if you wanna be "evidence-based" about how many interviews to go on, then based on this study using the
2003-2008 ophthalmology match data, you should aim to
go on about 11 interviews, and anything above that is diminishing returns.
"Figure 1A plots the number of programs ranked by an applicant and the likelihood of matching showing a linear relationship between increased programs ranked and likelihood of matching reaching a plateau after 11 programs." From the graph, it looks like the probability of matching is around 90-95% at that point. The student advisor at my med school always cited this study when she was advising us about how many interviews to aim to go on!
Loh AR1, Joseph D, Keenan JD, Lietman TM, Naseri A. Predictors of matching in an ophthalmology residency program. Ophthalmology. 2013 Apr;120(4):865-70.
Here's the PDF.
Obviously this highly depends on your individual situation, but the confidence intervals on that graph look pretty narrow, so its probably more-or-less applicable to most typical applicants who don't have extenuating circumstances.
So, if you have a lot of invites, consider canceling some random ones that you're not that excited about so they can trickle down to other applicants who might be really excited about getting those. Maybe if everybody collectively does this, then karma will come back around and you'll pick up a second-round invite to a program that you were really looking forward to after someone else cancels it!
Even when you cut down to 10-12, just remember to keep a spectrum of "top" "middle" and "bottom" tier programs, whatever that means to you. Theoretically, applicants could run into trouble with not matching if they only interview at "all the top places" and then for whatever reason end up getting ranked a smidge too low on each of those programs lists.
GOOD LUCK EVERYONE!
- Shemarty
(current PGY-1, I'm from last year's application cycle)