Thread by @KevinCChiang

✨NRMP Match Tweetorial✨

Hey #MedStudentTwitter! It’s February—time for rank order lists! I’ve seen misconceptions about the Match, so here’s a #tweetorial about the Match & ROLs, including history, algorithms, and applicant considerations! #Match2021 #PedsMatch21 #MedTwitter

1. As complex as the Match seems, it wasn’t always that way. In the early to mid-1900s, there were more internship spots than candidates, and hospitals competed to acquire us applicants! By the 1940s, students were receiving offers as early as the start of 3rd year! Crazy, right?

2. Students could only have one offer at a time and would often have to make a decision on whether to accept it or turn it down within 24-48 hours. In 1945, a “Cooperative Plan” provided more uniformity to the process, but the system was still dysfunctional.

3. Medical schools agreed not to release student information before a set date, but hospitals quickly discovered that if their initial offers were rejected, students whom they would want to offer positions to next had often already accepted other positions.

4. This led to a system with offers that applicants would have to respond to immediately, which caused chaos and led to missed and broken agreements. This kind of behavior had been previously seen in markets in medicine, psychology, and law and led to market failure.

5. F. J. Mullin, dean at the University of Chicago School of Medicine proposed a new plan: a clearinghouse that used rank-order lists made by students and hospitals to create matches. (Today, this clearinghouse is the NRMP.) However, the Mullin-Stalnaker algorithm was flawed.

6. In this algorithm, hospitals ranked students in pools, with up to X students per pool if they had X available spots. The algorithm prioritized 1-1 matches, then 2-1 matches (student ranking hospital as #1 and hospital ranking student as #2), 1-2, 2-2, etc. See a problem?

7. Students who ranked “reach” programs #1 could miss out on their #2 if the #2 program filled all their spots with 1-1 and 2-1 matches. Thus, students could be punished for highly ranking a preferred program that they might not be very competitive for!

8. Changes were subsequently made in 1952, leading to the Boston Pool algorithm, in which students were tentatively matched to hospitals and removed from a hospital’s rank-order list when they were tentatively matched at a program they preferred over said hospital.

9. The Boston Pool algorithm was an important step in the evolution of the Match because it produced stable outcomes, which is where there aren’t students and hospitals not matched with one another who would both prefer each other to their matches.

10. In 1962, David Gale & Lloyd Shapley proved it's always possible to solve the stable marriage problem for N men & N women with all matches stable. It wasn’t until 1984 that Alvin Roth noticed the Gale-Shapley algorithm principles were those used by the NRMP since the 1950s.

11. This idea of “deferred acceptance” has continued to be an essential part of the algorithm. In 1998, the Roth-Peranson algorithm was developed to improve the efficiency of the matching process and accommodate the idea of couples matching.

12. As a side note, the work of Roth, Gale, and Shapley has been influential in a variety of other settings as well, such as improving New York’s public high school admission system and creating algorithms for systems like kidney matching and online auctions.

13. In fact, in 2012, Alvin Roth and Lloyd Shapley were awarded the Nobel Prize for Economic Sciences “for the theory of stable allocations and the practice of market design.”

14. Anyways, Roth and Peranson showed that in limited cases (<0.1%), an applicant-proposing algorithm leads to more favorable matches for most applicants who would be affected by an applicant vs. program-proposing algorithm. This is part of why today’s algorithm is what it is.

15. So why is this important? Well, it means that applicants can focus on creating their ROLs solely based on PERSONAL PREFERENCE rather than trying to “strategize” based on how they believe programs will rank them.

16. There are more intricacies to the applicant-proposing algorithm. For those interested, I recommend Alvin Roth’s full “Report on the design and testing of an applicant proposing matching algorithm, and comparison with the existing NRMP algorithm”.
stanford.edu/~alroth/phase1…

17. Looking ahead, one interesting thing to consider is the question: Are we willing to sacrifice stable matching for the sake of ensuring more applicants are matched through the algorithm (minimizing how many applicants have to SOAP)?

18. So how does the match algorithm work?! I created a diagram that I’ve included below that depicts the basics of the algorithm for INDIVIDUAL applicants. It’s actually more complicated (when considering couples and supplementary ROLs), but this should give you a general sense.

19. In essence, individual applicants will “propose” down their ROL, starting from the top. If the program has a spot available, or they rank the applicant higher than their lowest ranked “match”, the applicant becomes “tentatively matched” to that program.

20. If at any point an applicant is “displaced” (bumped off of the bottom of a program’s tentative match list), they will propose down their ROL again until they get another tentative match, or exhaust their entire list, in which case they would be unmatched.

21. The NRMP and Med School Insiders provide a couple of videos that I think do a pretty good job of describing how the algorithm works and providing examples if you feel that may help you understand the process better:
nrmp.org/matching-algor…

22. So what does this mean from a practical standpoint?! Rank based on where YOU want to go, not based on where you think programs will rank you on their lists or where you think you are “most likely” to match. This is part of the purpose of an applicant-proposing algorithm.

23. In fact, trying to “strategize” your ROL in such a manner has been shown in studies and analysis of the algorithm to potentially worsen the quality of your matching outcomes.

24. There’s a lot to potentially consider when making ROLs: benefits, salary, geography, program size, curriculum structure, research, schedule, patient volume, reputation, fellowship opportunities, program leadership, resident “vibe”, significant other, gut feeling, etc.

25. Based on ACGME guidelines, much of resident education is standardized. Given this standardization, a lot of your decision comes down to personal factors and what you value as important to you.

26. Consider maximizing your contiguous ranks to improve your chances of matching, but there may be a point of diminishing returns. For example, the graphics below show that for US MD seniors applying to pediatrics, you almost guarantee yourself a match with 10+ programs ranked.

27. Of course, this kind of data also varies quite a bit from specialty to specialty, as you might expect. It’s tempting to rank every program you interview at, but also ask yourself whether you would be happy at each program you rank and can imagine being there for X years.

28. Imagine opening an envelope or email on Match Day and seeing the name of each program on your ROL. What is your reaction? If you have a particularly negative reaction, perhaps you should consider why you are ranking that program.

29. At the same time, many applicants don’t have many interviews or programs to consider ranking. You should weigh the advantages and disadvantages of ranking vs. not ranking enough programs based on your individual situation and historical specialty-specific match data.

30. What about ROLs for those couples matching? Are there any special considerations to make?
Partners who are couples matching are treated in the algorithm only as a couple. If they don’t match as a couple, the algorithm does not run their ROLs separately to try to match them.

31. The algorithm works essentially the same as how it works for individuals, except both partners must be able to tentatively match for the couple to be tentatively matched. If one or neither match can be made, the algorithm moves on to the next ranking down their paired lists.

32. Interestingly, introducing couples to the algorithm can create situations in which there is no stable solution, but as far as I know, these cases are rare, and the NRMP match algorithm has not yet run into major problems with this in practice.

33. With regards to cost, the $85 registration fee allows up to 20 unique programs on your rank list (30 for each person in couples). Each program over this limit (up to a maximum of 300) costs an additional $30. There are additional fees every 50 ranks over 100 too.

34. It’s important to realize it’s 30 UNIQUE programs for couples, meaning couples can list different combinations (e.g. AA, AB, BA, BB) and have a list longer than 30 entries without additional fees as long as there are 30 or fewer unique programs on each person’s list.

35. There is also a “No Match” code that can listed such that one partner would match at a program and the other would not match. These are often listed at the bottom of the ROLs so that the algorithm tries matching them together first before proceeding to the “No Match” options.

36. The NRMP has a couple of videos that may be helpful for getting a better understanding of couples in the match and the matching algorithm for couples. They can be found here: nrmp.org/couples-match-…

Phew! That was a lot of information. At the end of the day, I’d say the biggest takeaway from all of this is that when making your ROL, rank programs based on YOUR preference and where YOU want to go. Wishing all of my fellow applicants the best as we get closer to Match Day!