Yes, conditional probability. That’s what I based my analysis for the BS/MD few years ago. The condition there seems to be essays which beget the interviews more than GPA and test scores, which they all have stellar figures in.
Whatever analysis you mentioned, seems to have been already done by these smart college kids, that’s perhaps the reason for the magic number for applications in traditional route being in the 25-30 range.
But again, it is not that straightforward, wish it was. The big condition there is the competition from others from one’s own undergrad institution. Recently heard of someone with a stellar MCAT, good GPA from a reputed undergrad and involved heavily in some medical device related enterprise, applying to some 30 odd programs, getting invited to 4 or 5 interviews and only 1 final acceptance.
If you notice in my calculations, 29 is the number of applications to increase the odds to >50%
However, the number of applications seems more a function of competition within the same college - UCLA undergrads on an average send out ~30 applications (while the national average across all colleges is ~17).
It is interesting to see how the # of applications increase as you progress
High School to College (regular undergrad) = 8-15
Traditional med. school = 15-30
Residencies = 50-80+
Yes, Binomial probability distribution is used for option pricing such as Black- Schole’s option pricing model.
This is a good attempt. For n= 17, it gives 33.8% which underestimates the value derived from data 40.9% (total # of matriculants/total number of applicants).
From wikipedia,
In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own boolean-valued outcome: success/yes/true/one (with probability p) or failure/no/false/zero (with probability q = 1 − p). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment and a sequence of outcomes is called a Bernoulli process; for a single trial, i.e., n = 1, the binomial distribution is a Bernoulli distribution. The binomial distribution is the basis for the popular binomial test of statistical significance.
The binomial distribution is frequently used to model the number of successes in a sample of size n drawn with replacement from a population of size N. If the sampling is carried out without replacement, the draws are not independent and so the resulting distribution is a hypergeometric distribution, not a binomial one. However, for N much larger than n, the binomial distribution remains a good approximation, and is widely used.
FYI -
Black-Scholes formula is derived from partial differential equations and the distribution used in normal distribution (not binomial distribution).
However, this is not relevant for this group.
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As I mentioned, this is mathematical simplified model. Ideally, one needs to do conditional probability and also factor in more attributes/ parameters.
I believe this simplified model is based on sound probability theory.
But, let’s remember, the number of schools to apply will remain a decision that parents and students have to take. Models can indicate some insights but decision on how many to apply needs to factor in individual circumstances, effort, cost and time availability.
I am open to discuss other models if you or others have. We can create a separate thread for that, so that we do not side-track from the focus of this thread.
I suggest we focus our attention to questions prospective students and their parents have on the application process/ issues concerning them.
Also the model’s yield or prediction can depend on whether or not the students will be open to applying to both MD and DO schools (which in turn depends on the residency match statistics in a few years from now after the recent unified process).
There is a binomial distribution based derivation for Option pricing from first principles. Black-Scholes model has many different derivations. You welcomed comment in your post initially. Agreed there is need to discuss advanced Stochastic/Differential Equation based Financial models here.
All this started with mention of approximately 41% acceptance to at least one medical school via regular roue, which is an accepted data. There is data published by AAMC for allopathic MD admission on two popular attributes GPA and MCAT for different ranges.
Let us move on.
It is mostly risk-averse folks who prefer BSMD as a bird-at-hand option. The number of seats under bsmd will not increase rather decrease and demand increases every year driven by fear of not getting into a medical school. This will increasingly become a diminishing return effort.
Could you please elaborate on the last sentence? Did you mean both MDs and DOs will compete for the same residency matches? Pardon my ignorance, but what was the recent unification process that happened? Ty
This year, i.e. 2020 was the first match process as part of SINGLE combined residency match for both MD and DO students.
Till last year, DO students technically had TWO options to match - DO residencies via COMLEX and MD residency via USMLE/NRMP. Over the past few years, more and more DO were matching into the MD residency and the two accreditation entities decided to merge into one.
Now MD students can match into traditional DO residencies and vice versa.
Additional 3,000+ spots have opened up as a result for MD students.
The probability used by @NoviceDad of 0.024 in above calculation only applies to MD admissions. AAMC only deals with allopathic medical schools. There is no where DO schools in this data. This is irrelevant to the discussion about the probability of getting into at least one allopathic medical school of 41% as per AAMC data. Now students can apply to residency slots via one merged process( i.e. a simple unified residency applications process). This unification has no bearing on the model using AAMC data and has no use here. The value of 0.024 is not dependent on any DO school admissions. Residency matching is a totally independent process than admission to MD or DO school.
On a slightly less mathematical note (unless we count subtracting an application from the to do pile), my son submitted his first college application tonight! While not for a BSMD, it is one of his traditional undergrad choices. We are pretty excited in our house.
I thought the 0.024 you used (2.4% chance) is rather selective and so used twice that since usually the ratio of acceptance to the seats in medical schools is usually 2-3 times.
So using 0.05, meaning 95% chance of not getting any response for a given application, the number of applications for a 50% chance of landing in at least one med school acceptance turns out to be 14 [ 1 - (0.95)^14 (where ^=raised to the power of)]
For a 70% chance it is 24 i.e 1 - (0.95)^24
However depending on one’s confidence level, can plugin higher values and see, like 0.9 or 0.85 etc
However this is just to give a mathematical probability as you already pointed out. Lot of factors come into play during the actual selections (some of which I have listed earlier in the thread).
Also as cited above an outstanding candidate in every respect applied to 30+ med schools (not a UCLA undergrad but similar in reputation) to land with just one selection (not any fancy one). Perhaps would have got in more if gap year(s) taken.