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question about sf match stats and algorithm

Discussion in 'Ophthalmology: Eye Physicians & Surgeons' started by toomanyeyes, Jan 3, 2009.

  1. toomanyeyes

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    Hey everyone!

    Happy new year!

    I had two questions about SFMatch.

    1) In the stats that they show for ophthalmology, there's an entry under Positions called "Avg. Offers - Average # of offers per applicant" Are they referring to interview offers? Or how far they had to go down the rank list on average for a match to occur? I wasn't sure what "offers" they were referring to.

    2) Is the SFMatch algorithm the same as the NMRP algorithm? The Stable Marriage algorithm where the applicants are proposing to the programgs?

    Thanks!
     
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  3. MacularStar

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    I believe they mean average interview offers. The average number of interview offers each applicant receives is ~4. As far as I know the matching algorithm is the same as NRMP... there is a description of how it works on the SF match website. Never heard of the "stable marriage" method. Maybe I missed the boat... as far as I know there is no "proposing" involved in the residency match :). Each program ranks their interviewees 1, 2, 3, etc. and each applicant ranks the programs where they interviewed and liked. Then a computer program "matches" both parties based on their rank lists. Most programs do not tell their applicants where they are on their rank list and vice versa. Some applicants have an attending/mentor call their top program(s) to convey strong interest, but the jury is out as far as how much this actually matters.
     
  4. toomanyeyes

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  5. EyeDocx2

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    Actually, it seems different:

    The hospitals/residents problem — also known as the college admissions problem — differs from the stable marriage problem in that the "women" can accept "proposals" from more than one "man" (e.g., a hospital can take multiple residents, or a college can take an incoming class of more than one student). Algorithms to solve the hospitals/residents problem can be hospital-oriented (female-optimal) or resident-oriented (male-optimal).
     
  6. MacularStar

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    Interesting... but in the Gale-Shapley algorithm women do receive multiple proposals from men... isn't the H/R algorithm different because women accept multiple marriages to men?

    From the description on the SF match site regarding the process it sounds male (applicant) optimal. What do you all think?
     
  7. OphthoGal

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    The "Avg. # of offers per applicant" is definitely not the average number of interviews per applicant. I did not apply for match, my wife did (I am posting under her name), and we too were confused about what this mysterious number meant, but after reading the commentary on the different types of algorithms used, it makes a lot of sense now (if my understanding described below is correct). The "Avg. # of offers per applicant" is a number generated by the ranking algorithms. It is not that straightforward to understand, but here is my best shot:

    In the Gale/Shepley Algorithm allowing for multiple "marriages" (hospital/residency problem) the scenario is something like this (you may want to read the wikipedia article to better understand this):

    1) Each program offers a spot to their top ranked applicant. The program and this applicant are now "engaged".

    2) Each program then offers the second ranked student on their list a spot. If that student is not "engaged", the student and this program become "engaged". If the student is already "engaged" one of two things can happen: i) if the new program is ranked higher on the students list than the program he is currently "engaged" to, the student breaks the engagement with the old school and becomes "engaged" to the new school, ii) if the new program is ranked lower on the students list than the school he is currently "engaged" to, the student rejects the proposal. Regardless of whether the student accepts or rejects the offer, it is counted as an offer in the "Avg. # of offers per applicant" statistic.

    3) Step (2) is repeated until each program has filled their max number of residency positions. Obviously programs cannot offer a spot to someone if they have already filled their maximum quota. However, if a program loses an engagement because an applicant breaks off an engagement because they get a better offer, than that program must offer a spot to the next highest ranked applicant on their list. This process continues until there are no spots available or the programs that do not have full quotos run out of ranked students. The total number of offers given out to students are averaged and this is the number reported.

    I think that the number they are reporting is in fact what I have described above, so I hope the analysis I have provided is clear. The reason I know that this number is definitely not the number of interviews per applicant is rather straightforward. There are ~450 ophtho spots each year, and most programs interview 8-12 applicants per spot (some do more), or, for simplicity, about 10 interviews per spot. That means that a safe estimate for the number of interviews conducted each year is about 4500 interviews. Meanwhile, if we multiply the number of CAS participants (usually about 750-800) and multiply it by the reported "Avg. # of offers per applicant" (about 4-4.4), we only get about 3000-3500 interviews accounted for. Since it is obvious that the number of offers that can be given out is less than the number of interviews, these numbers are consistent with the argument that the value reported for "Avg.# of offers per applicant" is not the number of interviews but, in fact, something along the lines of what I have describe above.
     

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