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Odds of getting accepted to a medical school. A simple mathematical model.

  • By @NoviceDad
  • •
  • 02 May, 2021
  • •

A simple Binomial probability distribution based mathematical model can highlight the impact of number of schools a student applies to his/her/their odds of obtaining an acceptance.

A common question we get is “What is the probability of getting accepted into a medical school?” Getting into a medical school depends on several factors – GPA, test scores, essays, letters of recommendations, yield management decision of colleges, your luck, and more.

A related question is “What can we do to increase out odds of getting accepted?” i.e. things that we can control and possibly influence. One factor under the control of students is the number of colleges to apply and the list of colleges to apply.

A mathematical model can offer some guidance into number of schools to apply. One way to look at the mathematics of acceptance is to rely on Binomial probabilities. We present a simplified model which one looks at the number of applications and its impact on potential medical school acceptance.

Let us denote p as the acceptance rate at a university i.e. success.
For my example, I have assumed this to be constant and equal to 2.4% (that is approximately the average acceptance rate based on AAMC application data).

Thus, p = 0.024

Let us denote q as the failure rate.

Now, we know
q = 1 - p
q = 1 - 0.024
q = 0.976

Probability of getting AT LEAST 1 acceptance = 1 - probability of getting ZERO acceptances

Binomial probability is given by this formula: nCr * p^n * q^(1-n)

Where

n = number of program one applies to

r = number of acceptances

nCr = Binomial coefficient in combination format

Let’s assume you apply to 15 programs, n = 15
Probability of getting ZERO acceptance means r = 0

Probability of getting ZERO acceptance = P(r = 0)

P(r=0) = 15 C 0 * (0.024)^0 * (0.976)^15

P(r=0) = 0.69461997

Probability of getting AT LEAST 1 acceptance = P(r >=1) = 1 - P(r=0)

P(r>=1) = 1 - 0.69461997
P(r>=1) = 0.30538003 OR 30.54%

If you apply to 15 colleges, there is 30.54% chance you will get at least 1 acceptance.

Here is the probability of getting AT LEAST 1 acceptance for various N (number of applications): Please refer to chart below.


NOTE:

  1. You need to apply to 29 colleges for your probability to be greater than 50%.
  2. You need to apply to 21 colleges for your probability to be nearly 40%

One can use different probabilities and play around with this model. But the key to remember is that this is just based on mathematical model - in actual practice, a lot of factors are in play!

While this is a simple exercise, we should ideally do conditional probability – probability of getting accepted conditional on getting an interview. Also this simple model does not factor any impact of GPA, test scores, and other factors. It is just to highlight how the number of applications may impact your odds.

The number of schools to apply will remain a decision that parents and students have to take. Models can show some insights but the decision on how many schools to apply needs to factor in individual circumstances, effort, cost, and time availability.

 

PS: The contents of this article were shared in one of the public forums last year as part of forum discussions.

2021 BS/MD Program List

By Priti Shah • 02 May, 2021

NOTE: Universities change their programs and/or criteria constantly. In many cases, they may discontinue their BS/MD program. This list is for informational purposes only. Please contact the respective university to find out about the current program and associated requirements.

The list is in alphabetical order by state.

Why BS/MD?

By @NoviceDad • 08 May, 2020

If you are sure about pursuing Medicine as a career, should you opt for BS/MD programs or pursue the traditional pre-med / Medical route?

At the outset, let me share a statistic: Less than approx. 5% of all medical school students come through the BS/MD route. So clearly, a very small minority of student population is opting for BS/MD. But do not let that statistic mislead you. Why? Because universities offer <5% seats to their BS/MD programs. If they offer more seats, this percentage would be a lot higher.

The above dilemma becomes more important if you have secured an offer of admission from an Ivy-league level university. We must guard against one important thought-process - "If you can get an admission to Ivy-league undergrad then you can surely get admission into the "top ranked" medical school." Most general folks are unfamiliar with the medical school admissions process and therefore they can get into the above thought process.

And add to that the potential scope of obtaining merit based scholarships while pursuing the traditional route. 

Yes, with good grades, great MCAT score (>515), a resume complete with research, shadowing, volunteer and other factors, will get you a medical school admission. It may or may not be the same "Ivy-league kind" of schools.

What I am sharing here are some of the RISKS involved in the traditional pre-med / Medical route:

1) Potential to complete your medical school in an accelerated manner: Many BS/MD programs are accelerated 7 year programs. A few are 8 year programs. 6 year programs have become rare after the recent change in MCAT examination. This means you can save one full year from the long-drawn process (11+ years) to become a medical doctor.

2) Gap year(s): Even if you are from an Ivy League with great MCAT scores, we have numerous number (not outliers) of cases where students have had to take a gap year to strength their application. According to Association of American Medical Colleges (AAMC), 63.4% of matriculating students into a medical school had a gap year in 2018 and that percentage has been steadily increasing every year. To me, this represents a VERY HUGE risk as there is approximately 63% chance, you or your child may be hit with a gap year. And yes, if you get an admission after a gap year, you will be counted in the ~95% of the matriculants to a medical school via the traditional route.

3) “Non-traditional” students: These are students with 2 or more gap years. It appears that "Ivy League" medical schools are matriculating more and more non-traditional students. Nearly 68% of students that matriculated into University of Pennsylvania’s Medical School are non-traditional. At Northwestern University, that percentage is lower but still significant at 23%. This trend is creating an extra pressure among students to take additional gap years to keep up with the competition.

4) Low GPA: For traditional route, the impact of grade deflation or student not able to cope up with college due to bad selection of courses or other distractions is very real. FOR BS/MD, most colleges are flexible and supportive of their students. For example, at NU, you can take an extra-year in undergrad to pull-up your GPA to meet the HPME requirements. You do NOT have that luxury in a traditional route.

5) The Myth that "since I can into Ivy League undergrad, I can definitely get into "Ivy League" medical school": This myth has been broken so many times that there are "skeletons of students aspirations" lying around.

6) Plan B: Selecting a "proper" undergrad is important - many kids take biology as their undergrad for both BS/MD and traditional route. If you look at career prospects for biology majors, you will quickly come to a conclusion, they are limited. So it would not have mattered if you did biology major at Princeton or Rutgers. On the other hand, if a student has interest in mathematics or computer science, doing that minor / double major would open up many options - even if you did that at Rutgers. So, undergrad college + major are both important. In that case, one has to plan for Plan B in the first year of college itself. That means - more work because you may have to load yourself with more coursework to do a meaningful minor or double major. How many parents/ kids are thinking about this?

So, the question of ask – are you comfortable with the risks with the traditional pre-med/ Medical route?

It boils down to that!

List of BS/MD Programs

By Priti Shah • 04 May, 2019

NOTE: Universities change their programs and/or criteria constantly. In many cases, they may discontinue BS/MD program. This list is for informational purposes only. Please contact the respective university to find out about the current program and associated requirements.

List is in alphabetical order.

BS/MD Interviews - yours to lose!

By @NoviceDad • 23 Jan, 2019
Understand what BS/MD interviews are about, including interview types and useful tips.
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