NRMP Match Algorithm Explained (US Residency Application Process)

The National Resident Matching Program uses formulas and computer algorithms to match applicants with residency and fellowship programs.

Before the advent of such a system, candidates entered residency programs, much as students now enter medical schools.
The earlier a future resident applied for admission to a particular program, the better his or her chances. It resulted in applicants leaving their applications 2 years (!) before the residency was to begin. In response to this issue, medical schools in the US only provide letters of recommendation to students in their final year of study. Residency programs also require that future residents accept an offer to enroll within 24 to 48 hours of receiving it. Yet that is not all.
Graduating students applied to several hospitals, and hospitals at the same time competed for talented candidates. A future resident could choose a program, apply for it, and then cancel their application if they found a more promising program. Several residency programs have begun accepting applications early so as not to miss out on promising candidates. In general, the situation was chaotic and confusing.

As a result, a certain algorithm was required to assist future residents and residency programs in working together.

That is how the NRMP, National Resident Matching Program, came about. This program uses a computer algorithm that was first described in the 1960s. This algorithm won Lloyd Stowell Shapley and Alvin Roth the 2012 Nobel Prize in Economics.

Lloyd Stowell Shapley
Alvin Roth

Final year students apply to residency programs using ERAS – The Electronic Residency Application Service – every September. Applicants receive interview invitations from various residency programs between October and January.

In February, applicants and residency programs publish their ROLs. On this list, prospective residents rank their preferred residency programs in descending order, or the residency program places a list of candidates they would like to have on their list.

Let’s see how it works in practice

Suppose we have 5 applicants and 3 residency programs, and each has completed the Rank order list. Rather than focusing on the preferences of residency programs, the algorithm focuses more on the preferences of candidates.

The algorithm will first select John, who chose CITY as 1st. He was selected for the CITY program as well (2nd place). Therefore, John is more likely to be admitted to the program. Next, the algorithm moves on to Charlene, who also ranked CITY first. Charlene is 3rd on the CITY list, and there are only 2 vacancies in the program, so she has a chance to get into the program.

Zach is next in the algorithm. City was also first on his list, but since Zak is ranked 5th and 2 places are already occupied, Zack will not be able to join the City program. Country is Zack’s second place, and County has Zack on the list, so Zack can get there.

As for Linda – she selected Private, but she does not appear on the list. Next, CITY is selected in her list, but City has already chosen 2 candidates that have a higher priority than Linda. The algorithm then moves to the third position – County. County has Linda on the list, hence she will be included in this program.

As of now, Mark is at the top of the algorithm. Both he and CITY chose each other. Thus, Mark 100% gets into this program.

Charlene has been screened out of the City program. Her second choice is the Private program, but she is not listed on the Private list. The residency application for Charlene is rejected.

This resulted in John and Mark getting into the City program, Zach and Linda getting into the County program, Charlene not getting into the residency, and the Private program without a resident.

Match days take place in the second half of March. Yet it is not all lost for those who have not been selected for the program. At the same time, SOAP – supplemental offer and acceptance program – begins, so that candidates who didn’t receive a place in their desired residency program and programs that did not receive residents can interact. Candidates will be able to complete a one-year “preliminary” residency program before applying again for MATCH in the coming year.

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