Relationship Between the Number of Residency Applications and the Yearly Match Rate: Time to Start Thinking About an Application Limit?

Abstract

Background: There has been an increase in the number of applications medical students have submitted for the National Residency Matching Program (NRMP). These additional applications are associated with significant costs and may contribute to match inefficiency.

Objective: We explored if match rates improved in years when an increased number of applications were submitted.

Methods: We analyzed yearly published data from the NRMP and the Electronic Residency Application Service for 13 specialties. A generalized linear model was used to assess the relationship between the annual match rate and the mean number of applications submitted per applicant, while controlling for the number of positions available and the number of applicants in the given year.

Results: Over the last 13 years there has been an increase in the mean number of applications submitted per applicant (P < .001). For the 13 assessed medical specialties, there was no statistically significant relationship between the mean number of applications per applicant per year submitted to the NRMP, and the annual match rate (odds ratios near 1.00 and nonsignificant, P values > .05).

Conclusions: There was no improvement in the match rate in years when medical students submitted an increased number of applications. Therefore, it would appear that the applicants do not benefit from the larger number of applications submitted. Further study is required to assess the cost and benefit of these additional applications.

FIGURE 1

The Prisoner's Dilemma Payoff Matrix In the prisoner's dilemma model, 2 criminal partners, Criminal A and Criminal B, are arrested and separated into individual holding cells for interrogation. There were no witnesses at the scene of the crime and, therefore, if both criminals remain silent and refuse to testify against one another they will only be convicted of a small charge, which carries a 3-year prison sentence. During interrogation, Criminal A is offered a plea deal and told that if he testifies against his partner (Criminal B) he will only be sentenced to 1 year in prison while his partner (Criminal B) will be sentenced to 15 years in prison. Criminal B is offered the same deal to testify against Criminal A. In the event that both criminals testify against one another they will each be sentenced to 10 years in prison. Individually, it appears to each criminal that testifying is always the best strategy. From Criminal A's perspective, if Criminal B stays silent, Criminal A is better off to testify instead of staying silent (will receive 1 year in prison instead of 3) and if Criminal B testifies, Criminal A is better off to testify instead of remaining silent (will receive 10 years in prison instead of 15). Criminal B has the same perspective. Given that it is always in the individual criminal's perceived best interest to testify, the result of this “economic game” is that both criminals will testify against one another and they will each wind up serving a 10-year prison sentence. They would have both been better off if they could have worked together and agreed to not testify against one another (3-year prison sentence each instead of 10). The prisoner's dilemma model thus demonstrates the counterintuitive phenomenon of all members of a group being individually worse off, when each member of the group acts in his or her self-interest. The reader is referred to the cited website for a further discussion and explanation of the prisoner's dilemma and game theory.

FIGURE 2

Mean Number of Applications Submitted During the Last 13 Years According to Specialty,