How the Match Algorithm Works

The Match is a computer process, not a negotiation. Your list of programs and every program's list of applicants go in, and the NRMP's algorithm produces one result for each applicant. It is applicant-proposing, which means it works from your list down and favors your preferences wherever a program also wants you. This page explains how it works and why the advice is to rank by true preference.

The short version #

NRMP describes the algorithm as one that tries to place each applicant into the program ranked highest on the applicant's list, then moves down the list if that is not possible. Matches are tentative while the algorithm runs and become final and binding once all rank order lists have been considered. Research underlying the algorithm contributed to the 2012 Nobel Prize in Economic Sciences, as noted in NRMP's applicant materials.

Step by step #

1. Each applicant has an ordered list. Your Rank order list contains the programs you would train in, from most to least preferred.
2. Each program has an ordered list and a number of positions. Programs rank the applicants they would accept and have a fixed quota.
3. The algorithm starts with your first choice. If the program ranks you and has an open position, you are tentatively matched. If the program is full but ranks you above someone already tentatively matched, you take that place and the other applicant is bumped.
4. Bumped or unplaced applicants move down. They try their next choice, and the same rule applies.
5. This repeats until no one can move. At that point all tentative matches become final.

This is the logic known as deferred acceptance. Nothing is final until the end, which is why a program can hold you tentatively and still drop you for someone it prefers more.

A worked example #

Suppose three applicants (A, B, C) and two programs (X with one position, Y with one position).

Program X ranks B, then A, then C. Program Y ranks A, then C, then B.

• Round 1: A and B both propose to X. X prefers B, so B is tentatively placed and A is rejected. C proposes to Y and is tentatively placed.
• Round 2: A moves to Y. Y ranks A above C, so A takes the place and C is bumped.
• Round 3: C moves to X. X ranks B above C, so C is rejected. C has no more choices and is unmatched.

Final result: B matched to X, A matched to Y, C unmatched. Notice that each applicant ended up with the best program that would also take them, given the others' lists.

Why ranking true preferences is optimal #

For an individual applicant, listing programs in your real order of preference is the best strategy. In plain terms:

• Your list is consulted from the top. A lower choice only matters if every higher choice has rejected you or filled with candidates the program prefers more.
• Moving a program up cannot help you get a program above it, and ranking a "safer" program higher than a program you prefer can only cause you to end up in the safer one, even if the preferred one would have taken you.
• Leaving a program off only removes options. If you would train there rather than go unmatched, rank it.
• You cannot see how programs ranked you, so guessing "who likes me" and reordering is a bet on information you do not have.

Two caveats are honest to state. First, the guarantee is about the individual applicant under the standard rules; couples ranking pairs and unusual cases involve additional constraints (see below). Second, ranking truthfully does not create matches that programs did not rank: you can only match where a program ranked you.

What the algorithm does not do #

• It does not give extra credit for being "loyal" or telling a program you will rank it first. NRMP policy allows expressing interest, but programs may not ask you to disclose your ranking or imply your ranking depends on a statement of intent.
• It does not fill unfilled positions. Those go to SOAP after the algorithm runs.
• It does not consider anything outside the lists: scores, visas and connections matter only to the extent they shaped the lists.

Couples #

Two applicants can participate as a couple and submit linked lists. NRMP's materials say a couple will match to the most preferred pair of programs on their combined lists that can accommodate both. In the 2026 Match there were 1,258 couples, and 93.0 percent had at least one partner match. Couples have more complex strategy and constraints. Read NRMP's couples guidance before ranking.

Why this matters for IMGs #

IMGs often have fewer interviews and fewer ranked programs. The algorithm cannot add programs that did not interview you, so the lever is upstream: applying broadly enough and presenting a profile that earns interviews. NRMP's 2026 Charting Outcomes report for non-U.S. citizen IMGs found that matched applicants had a median of 5 contiguous ranks in their preferred specialty, compared with 2 for those who did not match. See building your rank order list for how to use this in practice, and Match Week for what happens after you certify your list.