Inefficiencies in Residency Matching Associated with Gale-Shapley Algorithms.

Purpose: To investigate emerging trends and increasing costs in the National Residency Matching Program (NRMP) and San Francisco Residency and Fellowship Match Services (SF Match) associated with the current applicant/program Gale-Shapley-type matching algorithms.

Design: A longitudinal observational study of behavioral trends in national residency matching systems with modeling of match results with alternative parameters.

Methods: We analyzed publicly available data from the SF Match and NRMP websites from 1985 to 2020 for trends in the total number of applicants and available positions, as well the average number of applications and interviews per applicant for multiple specialties. To understand these trends and the algorithms' effect on the residency programs and applicants, we analyzed anonymized rank list and match data for ophthalmology from the SF Match between 2011 to 2019. Match results using current match parameters, as well as under conditions in which applicant and/or program rank lists were truncated, were analyzed.

Results: Both the number of applications and length of programs' rank lists have increased steadily throughout residency programs, particularly those with competitive specialities. Capping student rank lists at 7 programs, or less than 80% of the average 8.9 programs currently ranked, results in a 0.71% decrease in the total number of positions filled. Similarly, capping program rank lists at 7 applicants per spot, or less than 60% of the average 11.5 applicants ranked per spot, results in a 5% decrease in the total number of positions filled.

Conclusion: While the number of ophthalmology positions in the US has increased only modestly, the number of applications under consideration has increased substantially over the past two decades. The current study suggests that both programs and applicants rank more choices than are required for a nearly-complete and stable match, creating excess cost and work for both applicants and programs. "Stable-marriage"-type algorithms induce applicants and programs to rank as many counter-parties as possible to maximize individual chances of optimizing the match.