For medical school, you apply to multiple schools, hopefully get several acceptances, and choose the program you like most. For residency, it’s not so straightforward. Instead, you’ll be using the NRMP Match and its Nobel Prize-winning algorithm. Here’s how it works.
To properly understand how the Match works, we first need to understand the issues that it addresses. Before the National Resident Matching Program (NRMP), there was a straightforward traditional application system, just like you would use for applying to medical school. Back then, hospitals benefited from filling positions as early as possible, and applicants benefited from delaying acceptances.
These factors led to offers being made for positions up to two years in advance before starting residency. In response, medical schools began releasing transcripts and letters of recommendation only during the students’ final year.
Competition then took another form, in which programs issued “exploding” offers, requiring medical students to accept or reject a residency offer within 24-48 hours. There were other problems too. Competitive applicants would hold onto multiple program offers or would renege on accepted offers when a better one came along. Programs were pressured to extend early offers to secure the best candidates.
In short, it was a mess.
Enter the NRMP Match, designed to promote an even playing field. The NRMP has been running since 1952, and the matching algorithm it uses predates the formal mathematics behind it by a decade.
In 1962, mathematicians David Gale and Lloyd Shapley published a paper proving that a stable matching always exists in two-sided markets. When Gale eventually wrote to the NRMP to ask whether their algorithm matched his theory, he found out it essentially already did.
Alvin Roth later built on that work to redesign the algorithm, and he and Shapley were awarded the Nobel Prize in Economics in 2012 for their contributions to stable allocation theory and market design. David Gale, who co-authored the foundational 1962 paper, passed away in 2008 and was not eligible for the prize.
Each September, fourth-year medical students apply to residency using ERAS, the Electronic Residency Application Service. From October to January, they’ll be offered interviews at various residency programs.
In February, both the residency programs and the applicants will submit their Rank Order List (ROL). A rank list is an ordered list, in decreasing preference, of the programs an applicant would like to attend, or a list of the applicants a program would like to recruit.
Let’s take a look at how this works in real life. Say we have five applicants and three residency programs, and each submits their own rank lists. The algorithm is applicant-proposing, meaning it prioritizes what the applicants submit, rather than the programs.
First, the algorithm will start with John, who ranked City first. City ranked him as well, at number two. He’s now tentatively matched at City. We say tentatively because if another applicant is higher ranked in the program, the algorithm may bump the lower-ranked candidate, depending on the number of available seats.
Next, we’ll go to Charlene, who also ranked City first. City ranked her third, so she’ll tentatively match there for now. Zach ranked City first, and City ranked him 5th. Since the two seats are already tentatively assigned to other applicants, the algorithm cannot assign Zach to City. Instead, it moves to his number two position, County. County ranked him, so he’s tentatively matched there for now.
Linda ranked Private first, but Private didn’t rank her, so the algorithm will go to her number two. She ranked City next, but she’s at number four, and the two seats are already claimed by applicants higher on City’s list. The algorithm moves to her third choice, General, and tentatively matches her there for now.
Mark ranks City first, and City ranked him first as well. A match made in heaven. This is a confirmed match, not a tentative one, as there’s no possibility of another applicant being ranked higher at City. In doing so, Charlene got bumped off. The algorithm will try to match her to a second program, but Private didn’t rank her. She ends up going unmatched.
In the end, here are the final match results. John and Mark both ended up at their number one-ranked program, so big congratulations to them. Zach and Linda didn’t match at their number one picks, but they still matched, and that’s a reason for celebration as well.
Unfortunately, Charlene and Private both end up going unmatched. You’ll note that both had shorter rank lists. This isn’t a coincidence. Generally speaking, you’re less likely to successfully match with a shorter rank list for two reasons.
First, statistically, there are fewer opportunities for a match to occur with a shorter list. Second, more competitive and desirable applicants are usually offered more interviews. Not only are they ranked higher on the program’s list, but they also have longer lists because they attended more interviews.
The walkthrough above covers the straightforward case: one applicant, one rank list. Couples matching is where things get considerably more complicated.
If you and your partner are both entering the Match, you can participate as a couple by linking your rank lists. Instead of ranking individual programs, you submit paired combinations. For example, you might rank “Program A + Program B” as your first choice, “Program A + Program C” as your second, and so on. The algorithm evaluates your paired preferences simultaneously and seeks the highest-ranked combination in which both of you can match.
The tradeoff is real. Couples who link their lists are essentially narrowing the pool of viable outcomes, which makes the algorithm’s job harder. Research has consistently shown that couples have a lower match rate than individual applicants, and the more geographically restrictive your paired list, the greater that risk becomes. This is not a reason to avoid couples matching if it applies to you, but it is a reason to build your list strategically, cast a wide geographic net, and include more combinations than you think you need.
If you’re applying as a couple, the rank list strategy advice in this article still applies to each of you individually. Rank your true preferences, don’t try to game the algorithm, and don’t cut your list short. For couples, that last point is especially important.
Rank lists are submitted by both applicants and programs at the end of February. Match Day occurs in the second half of March. It’s a formal celebration at all medical schools around the country. Students open an envelope that holds the name of the residency program they will be training at for the next 3-7 years.
Going unmatched is not the end of the road. During Match Week, unmatched applicants enter SOAP, the Supplemental Offer and Acceptance Program, a compressed four-round process where unfilled positions and unmatched applicants have a second chance to connect. The entire window runs Monday through Thursday, so speed and preparation matter more than you might expect. In 2025, 92% of positions placed in SOAP were ultimately filled, so outcomes are far from hopeless.
The strategy going into SOAP is different from the Main Match, and the stakes of each decision are higher given the compressed timeline. For a full breakdown of how SOAP works, what to do if you find yourself in it, and how to maximize your chances, read our complete SOAP guide.
Now that you understand the basics of the Match and how the algorithm works, let’s debunk some of the common myths that lead applicants astray.
Since matching at a program is a binding commitment, it’s important to rank only programs where you would be happy to train. When I was applying to plastic surgery residency, there were a couple of programs I didn’t rank because I knew I wouldn’t be happy there. It’s ultimately a personal decision, and for me, I would have rather gone unmatched than train at those programs.
It’s also important to note that programs will only rank applicants they have interviewed, so there’s no benefit to listing programs at which you weren’t offered interviews.
Prior to 1998, the NRMP matching algorithm favored residency programs over applicants, meaning the algorithm proposed matches based on program preferences rather than applicant preferences. In 1995, the NRMP Board commissioned a review of the algorithm, leading to a redesigned applicant-proposing version developed by Alvin Roth and Elliott Peranson.
That new algorithm was formally adopted in 1997 and first used in the Match in March 1998. It’s been this way ever since, so it’s time to retire the conspiracy theories.
Don’t wait until the last minute to make any changes to your rank list. Similarly, don’t wait until the last minute to finalize your rank list.
It’s important to weigh multiple factors to make the rank list that will result in you being happiest come Match Day. If any part of the process is rushed, a rash decision is highly likely to lead to regret.
The most pervasive myth is that the order of your rank list should depend on where you think you have been ranked highly, rather than on your true order of preference. By understanding how the algorithm works, it becomes clear that you should rank programs in your order of preference, meaning if you want to go to Prestigious Program X, rank them number one, even if you think they didn’t rank you as highly.
Trying to outsmart the system by ranking a program higher because you think they also ranked you higher doesn’t actually improve your match outcomes. It’s actually just more likely to result in you going to a program you’re not as happy with.
The only time this sort of game theory actually comes into play is under two conditions, both of which must be met. First, you’re applying to smaller specialties, like plastic surgery, ENT, interventional radiology, and several others, where the faculty and programs are well connected. And second, you or your advocate informs your #1-ranked program that you’ve ranked them as such.
There are several rules and restrictions around this, so only proceed with professional guidance. Programs like matching with students who have ranked them highly can sometimes sway a program’s rank list by a couple of spots. It won’t move an applicant from the bottom of the list to the top, but it can move you from number 3 to number 2, and that can be the difference between you matching there or not.
This is a much more advanced topic that depends on multiple specific factors for each student, and for that reason, I won’t discuss it further in this guide. Rather, this advanced theory and application of rank list strategies is best suited to one-on-one guidance from a physician with real experience on residency admissions committees.
Understanding how the Match algorithm works is only half the battle. The other half is making sure you’re competitive enough for the algorithm to work in your favor in the first place.
The Match is applicant-proposing, which means it will always try to place you at your highest-ranked program where you’ve also been ranked. But it can only work with what you bring to the table. A strong rank list strategy means nothing if programs aren’t ranking you highly to begin with.
That’s where your competitiveness in your chosen specialty becomes the real variable. Step scores, research output, clinical experience, and geographic flexibility are factors that vary significantly by specialty, and most applicants don’t have a clear picture of where they actually stand until it’s too late to do much about it.
Use the Residency Specialty Chance Predictor to get a personalized read on your competitiveness before you build your rank list. It takes less than a minute, and knowing where you stand early gives you time to actually do something about it.
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