How the Matching Algorithm Works

The NRMP uses a mathematical algorithm to place applicants into residency and fellowship positions.  The algorithm is “applicant-proposing”, meaning the preferences expressed on the rank order lists submitted by applicants, not programs, initiate placement into residency training. As a result, no applicant could obtain a better outcome than the one produced by the algorithm. Research on the algorithm was the basis for awarding the 2012 Nobel Prize in Economic Sciences.

To make the matching algorithm work best for you, create your rank order list in order of your true preferences, not how you think you will match.

The Matching Process

Matching Algorithm TutorialThe process begins with an attempt to match an applicant to the program most preferred on that applicant’s rank order list.  If the applicant cannot be matched to that first choice program, an attempt is made to place the applicant into the second choice program, and so on, until the applicant obtains a tentative match or all the applicant’s choices on the ROL have been exhausted.

A tentative match means a program on the applicant’s ROL also ranked that applicant and either:

  • the program has an unfilled position, in which case there is room in the program to make a tentative match between the applicant and program, or
  • the program does not have an unfilled position, but the applicant is more preferred by the program than another applicant who already is tentatively matched to the program.  In that case, the applicant who is less preferred by the program is removed to make room for a tentative match with the more preferred applicant.

Matches are “tentative” because an applicant who is matched to a program may be removed from that program to make room for an applicant more preferred by the program.  When an applicant is removed from a tentative match, an attempt is made to re-match that applicant, starting from the top of the applicant’s ROL.  This process is carried out for all applicants until each applicant has either been tentatively matched to the most preferred choice possible or all choices submitted by the applicant have been exhausted.

When the Match is complete, all tentative matches become final.  View an example of how the matching algorithm works


Can anyone else see my rank order list (ROL)?
Your rank order list is confidential.  Program rank order lists can be seen only by the program director and coordinator, the institutional official and administrator, and NRMP staff (unless you give your username and password to someone else, which is a violation of the Match agreement).
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