Modeling the Urology Residency Application and Match Process: A Mathematical Argument for Application and Interview Caps

To develop a mathematical model to predict the effects of an application and interview cap on the urology match success rate.

Using 2020-2021 AUA data, we created a mathematical model in MATLAB that simulated 481 applicants applying to a total of 357 training positions distributed across 143 urology residency programs. Applicants were divided into top (16%), middle (68%), and bottom (16%) strata based on a normal distribution. Programs were divided into 3 equally sized strata (1/3, 1/3, 1/3) based on Doximity rankings. Outcomes include results of a simulated AUA Match: percentage of training positions filled, percentage of interview spots filled, percentage of applicants matching from each stratum, applicant preference distribution (the percentage breakdown of applicants matching at their first, second, third, fourth, or >fourth choice), and cost/time savings of a capped application process.

Based on the results of our simulated model, match parameters were optimized with caps of 50 applications and 20 interviews per applicant. Programs filled all training positions and nearly all interview spots. Top applicants matched more frequently than middle applicants who matched more frequently than bottom applicants. Applicant preference distribution remained stable with these caps compared to the true match results.

Application and interview caps of 50 and 20, respectively, would reduce average applications by at least 39% from the 2021-2022 cycle. This would lead to over 17,000 fewer applications, $832 saved per applicant, and over 4400 hours of time saved across all Urology programs.