Congrats LD! I, too, am more of a fan of the car.
Reno, to answer your question about my math:
For the interview stage, an applicant has an approximate random chance of 10% (1/10) to get an interview. There are about five regions (west, south, midwest, northeast, southeast) and so for schools that favor regional applicants, especially if you are from a coast, you have to adjust the probability with another 1/5 to 2/5 (we'll go with 2/5 since I give the benefit of the doubt that a regional will draw from a similar region...coast form a coast and midwest would prefer from midwest or adjacent region) so we are at 1/10x2/5 so far. Then there is the adjustment for internal candidates. There is no real accurate way to adjust for this but I would say that a school prefers a good known person much more over the unknown that shows up as a CV on their desk but a reasonable estimate is a factor of 4 (they know your work ethic and your personality...2x2) so you have another 1/4 against you. So we're at 1/10x2/5x1/4 = 1/100 to just get an interview. then you go through the whole elimination process again so you have another 1/10x2/5x1/4...except that schools talk to their preferred applicants at the time of ranking...if done right this is also within the rules of the NRMP as long as they do not solicit. You have to account for this and I think that it is another factor of 4 (likely an underestimate) because it makes it that much harder to proceed down the rank list beyond the preferred candidates. So for the interview/ranking phase it is 1/10x2/5x1/4x1/4 which works out to 1/400. Since the interview phase is in series with the ranking phase you have to multiply the probabilities together so you have 1/100x1/400 which gives you 1/40,000. I think the subjective factors are very important and connections are so important in derm. And I believe that this number is an overestimated probability in favor of the applicant. But, it's only for certain schools where you have the odds stacked against you and it's not an average across the board. That's why I say that your chance of matching will be close to zero in certain situations. Still, for some, the right choice is still to apply everywhere.
Don't hold on to my 1/40,000 as fact...both of our numbers are our estimates.
I only make this estimate for certain programs. It's is NOT meant to be a generalization and it also depends on the applicant since one applicant can have a 1/40,000 shot but another applicant applying to the same program may have a 1/5 shot because all of the subjective odds (ie. connections, internal well liked candidate, etc.) are in your favor.
Well, now that you've given me some numbers, I can tell you why you're wrong.
1. First, the idea that there exists a significant population of applicant that have a 1/40,000 chance of matching at a given program (even with a regional bias) is just ridiculous on face. I guarantee if you look at every single derm program (even those with a strong regional bias), they will have in their history someone who wasn't in their region that had no connection. They simply had something on their application that attracted someone's attention and cause them to match. And no derm program has ever had anywhere near 40,000 residents, so it is very unlikely that the chance is 1/40,000.
Furthermore, I can tell you that in my experience as faculty at a program which had a very strong regional bias (despite my efforts to neutralize it), that the chance of an any applicant matching (even an FMG) is far greater than 1/40,000. You can choose to believe that or not.
But even if you don't believe the above, your calculation is still obviously wrong for the following reasons:
2. You're double counting and triple counting some things. First you say that the average applicant has a 10% chance to get an interview, which I think is fine. Then you say that you have to adjust for region, which I guess is fine (there's a small problem with this, but let's forget that for now). And then you go on to say that you have to adjust for internal candidates. Now you're double counting. The reason for the regional bias of many programs is because many of their spots are filled with their own med students and people from nearby schools who rotate there. So you're basically counting the same thing twice.
3. You further double count by then taking your 1/10*2/5*1/4 and multiply it by itself again. There's no reason for this. Once you've already got past the interview stage, you don't have to go through this same filtering process again. You also add some other factor of 4 which I can't understand after reading your explanation multiple times.
What you are suggesting is patently ridiculous.
What you're saying is that for this hypothetical regional candidate is the following:
Once this person has secured an interview, the chance of them matching is 1/400.
Ask any academic faculty member you want. We would never invite someone for an interview if the chance of their actually matching is 0.25%. That would be an absurd waste of everyone's time. With the possible exception of the courtesy interview to a med student or rotator, we only invite people who we think would have a decent shot of matching. And 0.25% is way too low.
You can also look at the absurdity another way. If we assume that we interview 10 candidates per slot (which is pretty close to average in my experience), then the average match rate of an interviewee is 10%. You are suggesting that the average interviewee is about 40 times more likely to match (once they have been invited for an interview) than this hypothetical non-regional candidate. That too is absurd.
With the exception of perhaps a rotator or med student who is given a courtesy interview (and clearly that's not what would be going on here for this hypothetical unconnected applicant), there is no way that anyone is invited to interview if they are 40 times less likely than the average candidate to match.
Generally speaking, and I can say this after having discussed this issue with many colleagues, once you secure an interview you are on roughly equal footing. Sure, the better applicants on paper will have a little bit of a leg up, but it's nowhere near 40x, which is the conclusion your assumptions would lead us to.
Hopefully, this will help you understand why you are wrong. I sincerely hope no one takes your advice seriously.