How does the Match algorithm actually work?

Dear Applicant,

The Match is decided by software. NRMP calls it the "matching algorithm," describes it as "a computerized mathematical algorithm," and says its job is "to place applicants into the most preferred residency and fellowship positions at programs that also prefer them." The mechanic that actually decides your outcome is one word: proposing.

Applicants rank programs. Program directors rank the applicants they interviewed. NRMP is explicit that nothing else counts: "It is the final preferences of applicants and program directors, as expressed on their rank order lists (ROLs), that determines the Match outcome."

NRMP defines its algorithm as "applicant proposing," meaning "the preferences expressed on the rank order lists submitted by applicants, not programs, initiate placement into training." Your list is the one the algorithm walks. A program's list is consulted only to answer whether a proposal holds.

NRMP's step-by-step page follows a single person it calls Applicant A. The algorithm "attempts to place an applicant (Applicant A) into the program indicated as most preferred on Applicant A's rank order list." If that fails "because the program doesn't also prefer Applicant A," it moves to the second choice, "and so on, until Applicant A obtains a tentative match, or all of Applicant A's choices have been exhausted."

A tentative match happens when "the program also ranks Applicant A on its rank order list" and one of two things is true. Either "the program has an unfilled position," or "the program is filled but Applicant A is more preferred by the program than another applicant (Applicant B) already tentatively matched." In the second case, "Applicant B is 'bumped' from the tentative match with the program to make room for Applicant A."

"The matching algorithm will return to Applicant B's rank order list and attempt to tentatively match Applicant B at the next most preferred position on Applicant B's list."

"When all applicants' rank order lists have been considered, the matching algorithm is complete and all tentative matches become final and binding for training."

Notice what a program's list does. At each step it answers one question: does this program rank this applicant, and if its positions are full, does it prefer this applicant to someone already tentatively matched there? It never changes which of your programs gets tried first. The order of attempts is yours.

That is why NRMP's ranking instruction is blunt: "The matching algorithm attempts to place you in the most preferred program possible, so be sure to rank programs in order of your true preference and not where you think you will match." Asked whether an applicant can rank multiple specialties, NRMP answers yes, and says the algorithm works "regardless of the specialty of the program."

Programs get the mirror instruction on their own page: "Rank applicants in order of your true preference, not how you think applicants will rank your program." NRMP adds that programs "are encouraged to submit rank order lists that are based on applicants' credentials and goodness of fit for the program rather than the likelihood of the applicant ranking the program."

One boundary the algorithm cannot cross: a match requires both lists. "Programs do not rank candidates they have not interviewed, and no match will occur."

Where a given program belongs on your list is a question for you and your advisor.

"Rank Order Lists cannot exceed 300 ranks total." The registration fee "includes the listing of up to 20 unique NRMP program codes on the primary rank order list (and in the Main Residency Match, up to 20 unique NRMP codes on all supplemental rank order lists combined)." Past that, "Additional ranks are $30 per rank for both individuals and couples." And "Rank fees are NOT REFUNDABLE if a shorter list is certified later."

Tracks count separately: "programs may offer multiple tracks and each track that you rank is included in your number of ranks." Lists of 100 or more ranks carry a Length of Rank Order List fee on top: $50 for 100 to 150 ranks, rising to $200 for 251 to 300.

Program lists have no such cap. "An unlimited number of applicants can be listed on the program ROL."

A couple, in NRMP's definition, is "Any two applicants who link their rank order lists in an NRMP Match." Partners "form pairs of choices on their primary rank order lists, which are considered in rank order when the matching algorithm is processed." "A couple matches to the most preferred pair of programs where each partner has been offered a position." Each partner can rank "up to 20 unique program codes, including the 'No Match' option," before extra rank fees apply.

The algorithm reads certified lists only, and certifying is the moment of commitment: "By certifying a ROL, applicants are entering a binding commitment to train at any program with which they match." You can edit after certifying, but "the new version must be re-certified to be used in the Match." Also: "The R3 system does not retain previous versions of a ROL, regardless of whether it was certified."

For the 2027 Main Residency Match, the applicant calendar lists Ranking Opens on February 1, 2027 at 12:00 PM EST and the Rank Order List Certification Deadline on March 3, 2027 at 9:00 PM EST. "Changes cannot be made after 9:00 p.m. Eastern Time on the day of the applicable Rank Order List Certification Deadline, and only certified lists will be used in the Match."

Between the deadline and Match Day, NRMP verifies credentials, withdraws ineligible applicants, moves the data to "the matching algorithm module," runs it, and prepares "50,000 individual Match Week reports" for applicants, programs, and schools. NRMP says those steps are "all completed in less than two weeks." Match status is released March 15, 2027 at 10:00 AM EDT. Match Day is March 19, 2027 at 12:00 PM EDT.

NRMP's About page says the algorithm is itself the subject of Nobel Prize winning research, and that with it NRMP "has built one of the most stable matching markets in the world." The page does not name the researchers, so neither will this one. It does state why the system holds: "Match outcomes are accurate and the process stable because participants control who and how their preferences for training are ranked." The software has no opinions. It runs your order.

Alex