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NRMP Match Algorithm
How the Matching Algorithm Works

Source: 1999 NRMP


The NRMP matching algorithm uses the preferences expressed in the Rank Order Lists submitted by applicants and programs to place individuals into positions. The process starts off with an attempt to place an applicant into the program indicated as most preferred on that applicant's list. If the applicant cannot be matched to this first choice program, an attempt is then 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 have been exhausted.

An applicant can be tentatively matched to a program in this process if the program also ranks the applicant on its Rank Order List, and either:

  • the program has an unfilled position. In this case, there is room in the program to make a tentative match between the applicant and program.
  • the program does not have an unfilled position, but the applicant is more attractive to the program than another applicant who is already tentatively matched to the program. In this case, the applicant who is the least preferred current match in the program is removed from the program, to make room for a tentative match with the more preferred applicant.

Matches are "tentative" because an applicant who is matched to a program at one point in the matching process may be removed from the program at some later point, to make room for an applicant more preferred by the program, as described in the second case above. When an applicant is removed from a previously made tentative match, an attempt is made to re-match this applicant, starting from the top of his/her list. 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 all applicants have been considered, the match is complete and all tentative matches become final.

Applicants' Rank Order Lists
Eight applicants are applying to four programs. After considering the relative desirability of each program, the applicants submit the following rank order lists to the NRMP.

Anderson Brown Chen Davis Eastman Ford Garcia Hassan
1. City 1. City 1. City 1. Mercy 1. City 1. City 1. City 1. State
  2. Mercy 2. Mercy 2. City 2. Mercy 2. General 2. Mercy 2. City
      3. General 3. State 3. Mercy 3. State 3. Mercy
      4. State 4. General 4. State 4. General 4. General

Applicant Anderson makes only a single choice, City, because he believes, based on remarks he heard from the program director that he would be ranked very highly at City, and he in turn assured the director that he would rank City number one. It is okay for programs to express a high level of interest in applicants to recruit them into their program, and for applicants to say that they prefer one program over others. Such expressions, however, should not be considered as commitments.

Applicant Brown ranks only the two programs that were on every applicant's list -- Mercy and City. A member of Alpha Omega Alpha chosen in his junior year, he believes that he is a most particularly desirable applicant. However, he has not been assured of a match with either of these programs. Applicants should consider ranking all programs that they are willing to attend, to reduce the likelihood of not matching at all.

Applicant Chen ranks City, which she prefers, and Mercy. Standing first in her class in her junior year, she knows that she is a desirable applicant, and she has been assured by the program director at Mercy that she will be ranked first. She is certain that Mercy will in fact rank her first, and so she reasons that there is no risk of her being left unmatched, even if she does not rank additional programs. If applicants are certain that they will be able to match to a program, and will not be left unmatched, they need not include the less preferred programs on their list.

Applicant Ford would be very pleased to end up at State, where she had a very good clerkship, and feels that they will rank her high on their list. However, she does not think she has much of a chance, she in fact prefers City, General, or Mercy, so she ranks them higher and ranks State fourth. This applicant is using NRMP to maximum advantage.

Applicant Hassan is equally sure he will be able to obtain a position at State, but he too, would prefer the other programs. He ranks State first because he is afraid that State might fill its positions with others if he does not place it first on his list. Applicants should rank programs in actual order of preference. Their choices should not be influenced by speculations about whether a program will rank them high, low, or not at all. The position of a program on an applicant's rank order list will not affect that applicant's position on the program's rank order list, and therefore will not affect the program's preference for matching with that applicant as compared with any other applicants to the program. During the matching process, an applicant is placed in the most preferred program that ranks the applicant and does not fill all its positions with more preferred applicants. Therefore, rank number one should be the applicant's most preferred choice.

Applicants Davis, Eastman, and Garcia have interviewed at the same programs. Like the other applicants, they desire a position at City or Mercy and rank these programs either first or second, depending on preference. However, since they are not assured of a match to either of these desirable programs, these applicants also list State and General lower on their Rank Order Lists. They are using NRMP well.


Programs' Rank Order Lists

Two positions are available at each program. The four programs, having determined their preferences for the eight applicants, also submit rank order lists to the NRMP.

Mercy City General State
1. Chen 1. Garcia 1. Brown 1. Brown
2. Garcia 2. Hassan 2. Eastman 2. Eastman
  3. Eastman 3. Hassan 3. Anderson
  4. Anderson 4. Anderson 4. Chen
  5. Brown 5. Chen 5. Hassan
  6. Chen 6. Davis 6. Ford
  7. Davis 7. Garcia 7. Davis
  8. Ford   8. Garcia

The program director at Mercy Hospital ranks only two applicants, Chen and Garcia, for his two positions, although several more are acceptable. He has insisted that all applicants tell him exactly how they will rank his program and both of these applicants have assured him that they will rank his program very highly. He delights in telling his peers at national meetings that he never has to go far down his Rank Order List to fill his positions. The advantage of a matching program is that decisions about preferences can be made in private and without pressure. Both applicants and programs may try to influence decisions in their favor, but neither can force the other to make a binding commitment before the Match. The final preferences of program directors and applicants as reflected on the submitted Rank Order Lists will determine the placement of applicants.

The program director at State feels that his program is not the most desirable to most of the applicants, but that he has a good chance of matching Ford and Hassan. Instead of ranking these two applicants at the top of his list, however, he ranks more desired applicants higher. He also ranks all of the acceptable applicants to his program. He is using the NRMP well.

The program directors at City and General have participated in the matching process before. They include all acceptable applicants on their Rank Order Lists with the most preferred ranked high. These program directors are not concerned about filling their available positions within the first two ranks. They prefer to try to match with the strongest, most desirable candidates. They are using the NRMP to maximum advantage.

Here's another example of the Matching Algorithm process at work, in tabular form.




(Shaded boxes indicate the final matches when the process is completed.)

ANDERSON 1. City City has 2 unfilled positions. Tentatively match Anderson with City.
BROWN 1. City City has 1 unfilled position. Tentatively match Brown with City.
CHEN 1. City City is filled with more preferred applicants.  
2. Mercy Mercy has 2 unfilled positions. Tentatively match Chen with Mercy.
DAVIS 1. Mercy Mercy did not rank Davis.   
 2. City City is filled with more preferred applicants.  
 3. General General has 2 unfilled positions. Tentatively match Davis with General.
EASTMAN 1. City Although filled, City prefers Eastman to its least preferred current match (Brown). Brown is removed from City to make room for Eastman. Tentatively match Eastman with City.
Since Brown has just been removed from a previous tentative match, an attempt must now be made to re-match Brown.
BROWN 1. City City is filled with more preferred applicants.  
 2. Mercy Mercy did not rank Brown. Brown remains unmatched.
FORD 1. City City is filled with more preferred applicants.   
 2. General General did not rank Ford.  
 3. Mercy Mercy did not rank Ford.  
 4. State State has 2 unfilled positions. Tentatively match Ford with State.
GARCIA 1. City Although filled, City prefers Garcia to its least preferred current match (Anderson). Anderson is removed from City, to make room for Garcia. Tentatively match Garcia with City.
 Since Anderson has just been removed from a previous tentative match, an attempt must now be made to re-match Anderson.
ANDERSON 1. City City is filled with more preferred applicants. Anderson remains unmatched.
HASSAN 1. State State has 1 unfilled position. Tentatively match Hassan with State.

The process is now complete: as each applicant has either been tentatively matched to the most preferred choice possible, or all choices submitted by the applicant have been exhausted. Current tentative matches are now finalized.

Note that the applicants Anderson and Brown went unmatched, because they listed too few choices. Applicant Hassan could have matched at City, had Hassan ranked choices in order of preference.

Also note that Mercy, which ranked only two applicants, and General, which ranked seven out of eight, had unfilled positions. General could have matched with Ford, who ranked it #2, had Ford been on its Rank Order List.

Summary of Guidelines for the Preparation of Applicant Rank Order Lists

  1. Applicants are advised to include on their Rank Order List only those programs that represent their true preferences.
  2. Programs should be ranked in sequence, according to the applicant's true preferences.
  3. Factors to consider in determining the number of programs to rank include the competitiveness of the specialty, the competition for the specific programs being ranked, and the applicant's qualifications. In most instances, the issue is not the actual number of programs on the Rank Order List, but the dilemma of whether to add one or more additional programs to the list in order to reduce the likelihood of being unmatched.
  4. Applicants are advised to rank all of the programs deemed acceptable to the applicant, i.e., a program where they would be happy to undertake residency training. Conversely, if an applicant finds certain programs unacceptable and is not interested in accepting offers from these programs, said program(s) should not be included on the applicant's Rank Order List.
  5. It is highly unlikely that either applicants or programs will be able to influence the outcome of the match in their favor by submitting a list that differs from their true preferences.

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Last Update: 28-Jul- 2014 at 21:38:03