Strong applicants can be fine with 6 or 7. Moderate applicants should do 9 or 10. Red flag problems should do 20 - 30, but at some point, more will not add much to the odds. If you apply to 30 and get 10 interviews, you are going to 10 interviews. If you apply to 30 and get 30 interviews, you should go to 10 interviews.
Programs don’t interview applicants they are not willing to take. Please, please, don’t interview at places you know you would be unwilling to go to. If you do, do not put them on your list. Every match I get calls from people I interviewed that are looking for unexpected openings, but that matched in family medicine somewhere they don’t want to go. They always say something like “I don’t know why I put them in there, I’m begging to NRMP to let me out of my obligation.” This is serious business.
You will get the most data about how you are doing when you see what interview invites you get. Most people match near the top of their lists. If you don’t match in you top 5, you probably will not match in your top 30 either. There are exceptions, but it tends to go fairly black and white.
I would be poorly qualified to give advice on how to match in derm, but I do know psychiatry isn’t derm. Medical school advisors have a tendency to scare applicants into overkill because they don’t understand psychiatry. This causes problems on both sides. If all of the top applicants hold onto 20+ interviews and then run out of money and energy, they cancel late and space is lost for both sides. Our capacity to interview is finite, and as applicants keep ramping up the ratios, we have to begin to thin the interview experience, or risk not filling. Be good applicant citizens. If you are getting more than a dozen interviews and you know you are unlikely to want to go to a program, or if you know your time and budget will not get you somewhere, call and cancel. It makes room for others. Neither side likes wasting their time.
Bottom line, if you are getting invited to 90+% of where you apply, you are going to match. If you are getting only a handful of interviews, go to every single one of them. Apply broadly, but interview more narrowly if you are overwhelmed with opportunity. This can get expensive.