The optimal solution of the NRMP match algorithm is deceptively simple, but its implication for the lives of applicants is anything but simple.
Three years ago, my then-girlfriend and I sat down and parsed through what would become the most important determinant of our lives moving forward.
Because we attended different medical schools, we carried on a long distance relationship for five years. The NRMP match was more than just a residency choice. It was also a solution that could finally close our distance and take the relationship forward again.
The ranked list seemed like the most difficult decision we had to make. There were so many variables, each with differing levels of importance.
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It is a variant to the “stable marriage problem” and a full solution can be coded in half a page in its entirety. And Couples matching (which makes for a very progressive scenario in the context of the original stable marriage problem but much more relevant in NRMP) only slightly complicates the calculations.
Someone out there calculated that it takes approximately 17 seconds for a modern computer to solve the NRMP match problem.
Assuming that 34,000 students submitted a ranked list (just making math easier, as the real number is probably closer to 40,000), that’s barely 1/2 millisecond for your personal match, in which you are assigned one of your future lives as you ranked from 1 to N.
So what does the algorithm take into consideration in that 1/2 millisecond?
The Considerations
Residency programs evaluate their applicants in constructing a ranked list that takes into account of some combination of the application, the scores, and the interview.
In college I have often received advice to “build your CV.” Spend some time with patients as a volunteer. See if you like it, and it’s good for your CV. Why are you not doing research? It’s good for your CV. Read a books by this dude or that gal, so you can sound intelligent at the interviews.
There was USMLE that was partly aimed to select for the low-end outliers and partly as a metric to determine the competitiveness of the highest achieving applicants.
For the applicants, the process can be a lot more nuanced.
You determined some internal scale (or an external scale for some), gauging each program based on some objective data, some anecdotes, some “ask good questions at interviews and remember to send thank-you cards,” and a whole lot of gut feeling. All of these components come together as a weighed sum. Implicitly or explicitly, we then ranked each program based on this complex evaluation of each program.
The Retrospective
Now, three years after going through the match and looking back, there were a lot of things I considered that ended up didn’t matter. For instance, I wanted to continue doing research in genomic science, and I cared about and that interest has so far taken a backseat. Several other things ended up mattering. For example, I…
- Couples-matched to the same city with my then-girlfriend and then got married.
- Am working with incredible classmates
- Am advised by outstanding mentors.
But here is the thing:
- My wife and I could have matched to a variety of cities.
- I couldn’t have predicted who my classmates were going to be.
- The mentors I work most closely with were not even faculty members when I matched.
In short, life happens and priorities change. Sometimes what you planned going in worked exactly as expected (couples match to the same city). Sometimes the things you thought mattered didn’t (genomic science opportunities). And sometimes serendipitously you ended up loving things that
In this sense, perhaps the output of this 1/2 millisecond algorithm is not really your future ranked 1 through N.
It is more like an unranked new beginning, one of many possibilities. The things you will grow to like (and dislike) about it is yet to come.
This year, the NRMP match will be released on Friday, so good luck if you or your loved one is matching this week.
