Calculating Matching percentage - ATTENTION ALL Math Athletes

[arafatni]

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Hi guys,

I wanted someone that is good with probabilities calculate chance of matching. YES I KNOW THERE IS NRMP calculator and matching outcomes. problems with them is that the sample size is small and too much variety. Also , you cant use it if you say you have feeling where program will rank you. I mean if you know you are ranked lower third vs upper third vs not ranked . That is why mathematical formula is great. this is how i came up with my calculations. PLEASE PLEASE LOOK AT IT AND criticize IT SO WE CAN COME UP WITH ALMOST PERFECT FORMULA. according to Nrmp report, in all specialities on avg programs rank 13 times the spots they have available . that being said i know programs for a fact rank as much 20 times. if we assume 13 times that roughly gives us 8% rounded to nearest hundredth. so what does this mean? it means people ranked in last percentile have 8% chance of matching at the program vs people at first percentile have 100% chance of matching vs middle percentile have 50% chance of matching that program . Also, your number of contagious ranking in one speciality you can multiply number of interviews by 8% that gives you chance matching to a program( not a specific one) . let say i had 12 interviews for family , then i have 12 x 8% =96% chance of matching family ( assuming i was ranked in the last percentile). so i am asking if ppl can modify this formula and think of how they can make it more accurate . if someone already had a similar topic please post the link below.

Thank You

 

[deleted859689]

The limit does not exist.

Edit: I feel like your using NRMP data wrong. There’s a correlation between program invites received vs match rate. I have no idea what voodoo is going on above. I wish you the best matching as a US-IMG

 

[arafatni]

The limit does not exist.

Edit: I feel like your using NRMP data wrong. There’s a correlation between program invites received vs match rate. I have no idea what voodoo is going on above. I wish you the best matching as a US-IMG

Thank you for your reply . Please elaborate what do you mean by limit ?

 

[deleted859689]

 

[arafatni]

I got 8 % by dividing 1/13.
As for percentile. We assume program has 1 spot and they rank 13 ppl. Number 1 has 100% , number 2 has 92 %, Number 3 has 84 % , number 4 has 76%, number 5 has 68%, number 6 has 60%, number 7 has 52%, number 8 has 44% , and so on.

 

[arafatni]

Thank you clearly now I am sure I am dealing with a troll . Honestly I am hear you see how we can calculate things .

 

[deleted859689]

https://www.nrmp.org/wp-content/uploads/2018/06/Charting-Outcomes-in-the-Match-2018-IMGs.pdf

You've read this right?

 

[arafatni]

https://www.nrmp.org/wp-content/uploads/2018/06/Charting-Outcomes-in-the-Match-2018-IMGs.pdf

You've read this right?

Yes but this data doesn’t consider where the program rank you .

 

[VincentAdultman]

There’s so many things that you can be don g with your time that would be more enjoyable and rewarding than whatever ....that is.

 

[arafatni]

https://mk0nrmp3oyqui6wqfm.kinstacd...n-Match-Results-2019-Main-Residency-Match.pdf where I got 1:13

 

[arafatni]

OP go outside.

Thank you, planing to head out . I don’t understand why these posts always end up either as a joke or becomes troll Fight . I hope we can all Grow up .

 

[deleted859689]

Thank you, planing to head out . I don’t understand why these posts always end up either as a joke or becomes troll Fight . I hope we can all Grow up .

There are plenty of metrics to measure chances of matching (# of programs invited to/applied to, Step scores, etc.) with actual data to pull from. You realise the NRMP matches based on a computer generated algorithm - you expect this forum to give you an exact formula that spits out your match chances?

 

[arafatni]

There’s so many things that you can be don g with your time that would be more enjoyable and rewarding than whatever ....that is.

True. And I am . This forum or this only takes fraction of my time. This doesn’t change a fact It will make me happy million other ppl stressing over matching this year. With that I am done . I ll come back on tomorrow hopefully some serious ppl will come in .

 

[libertyyne]

Your feeling where a program will rank you is about as terrible a metric you could use to generate a formula for likelihood of match.

NRMP already generates charts that display what number of interviews or step score correlated highly with ability to match. Go look at those, draw a line on how many interviews you recieved/ attended and draw a line on your step score. Now average those two numbers have you have a real estimate of where previous candidates are in terms of liklihood of matching.

or you know you could just look at charting outcomes interactive.

 

[CherryRedDracul]

To OP: What data do you want to integrate into your calculator that Charting the Outcomes has not factored in?

 

[7331poas]

There are plenty of metrics to measure chances of matching (# of programs invited to/applied to, Step scores, etc.) with actual data to pull from. You realise the NRMP matches based on a computer generated algorithm - you expect this forum to give you an exact formula that spits out your match chances?

I think the real oddity here is why a premed feels the need to come onto the med student forum and argue about how someone uses their free time.

 

[NotAProgDirector]

according to Nrmp report, in all specialities on avg programs rank 13 times the spots they have available . that being said i know programs for a fact rank as much 20 times. if we assume 13 times that roughly gives us 8% rounded to nearest hundredth. so what does this mean? it means people ranked in last percentile have 8% chance of matching at the program vs people at first percentile have 100% chance of matching vs middle percentile have 50% chance of matching that program.

Well, it's certainly true that the higher you are on a program's list, the more likely you are to match. In fact, if you're ranked #1 on any program's list, you're guaranteed to match -- either at that program, or at one higher on your rank list. But there's no way of knowing where you're ranked on a program's list.

Also, your number of contagious ranking in one speciality you can multiply number of interviews by 8% that gives you chance matching to a program( not a specific one) . let say i had 12 interviews for family , then i have 12 x 8% =96% chance of matching family ( assuming i was ranked in the last percentile).

This is incorrect, and is a classic statistics problem. Let's say you have 12 interviews, but you're ranked at the bottom of everyone's list. You will not have a 96% chance of matching. If rank lists were random assortments, then yes.

A simpler but similar statistics problem: let's say there are 10 marbles in a bag, 1 green and 9 red. You pick a marble at random, then replace it into the bag. If you draw 10 marbles this way, what's the chance of picking the green marble at least once? By your logic, there's a 10% chance of picking the green marble in each draw. You draw ten times. 10 x 10% = 100%. So it's guaranteed! But obviously, it isn't. This problem is solved the other way -- the chance of picking a red marble is 0.90. Picking ten red marbles in a row is (.90)^10 = .35 (rounded). Therefore, the chance of picking at least one green marble in ten tries is 1 - 0.35 = 65%.

Your match math is equally faulty. If you have 12 interviews, but you're at the bottom of everyone's rank list so you have an 8% chance of matching (of which I'm not sure is accurate, but good enough for this discussion), then the chance of not matching if you rank a single program is 92%, and not matching at 12 programs is (0.92)^12 = 37%, so the chance of matching is actually 64%. But even that math is suspect, because I don't think there's any way to say that your chances of matching are actually 8% to begin with, and you can only match to a single program (the marble answer above states that there is a 65% chance of drawing AT LEAST one green marble, but maybe more).

 

[Tenk]

Lemme do a number crunch real quick. Yeah, I’m coming up with 32.33(repeating of course) chance of matching for you.

 

[Seihai]

Well, it's certainly true that the higher you are on a program's list, the more likely you are to match. In fact, if you're ranked #1 on any program's list, you're guaranteed to match -- either at that program, or at one higher on your rank list. But there's no way of knowing where you're ranked on a program's list.



This is incorrect, and is a classic statistics problem. Let's say you have 12 interviews, but you're ranked at the bottom of everyone's list. You will not have a 96% chance of matching. If rank lists were random assortments, then yes.

A simpler but similar statistics problem: let's say there are 10 marbles in a bag, 1 green and 9 red. You pick a marble at random, then replace it into the bag. If you draw 10 marbles this way, what's the chance of picking the green marble at least once? By your logic, there's a 10% chance of picking the green marble in each draw. You draw ten times. 10 x 10% = 100%. So it's guaranteed! But obviously, it isn't. This problem is solved the other way -- the chance of picking a red marble is 0.95. Picking ten red marbles in a row is (.95)^10 = .60 (rounded). Therefore, the chance of picking at least one green marble in ten tries is 1 - 0.60 = 40%.

Your match math is equally faulty. If you have 12 interviews, but you're at the bottom of everyone's rank list so you have an 8% chance of matching (of which I'm not sure is accurate, but good enough for this discussion), then the chance of not matching if you rank a single program is 92%, and not matching at 12 programs is (0.92)^12 = 37%, so the chance of matching is actually 64%. But even that math is suspect, because I don't think there's any way to say that your chances of matching are actually 8% to begin with, and you can only match to a single program (the marble answer above states that there is a 40% chance of drawing AT LEAST one green marble, but maybe more).

This is a great way of explaining it, and I concur.

OP, your math is nonsensical to the point where correcting it isn't even fruitful over completely scrapping it and starting over. Furthermore, almost everything you're looking to calculate is already laid out in the document in what I would argue is a clear fashion.

 

[arafatni]

Well, it's certainly true that the higher you are on a program's list, the more likely you are to match. In fact, if you're ranked #1 on any program's list, you're guaranteed to match -- either at that program, or at one higher on your rank list. But there's no way of knowing where you're ranked on a program's list.



This is incorrect, and is a classic statistics problem. Let's say you have 12 interviews, but you're ranked at the bottom of everyone's list. You will not have a 96% chance of matching. If rank lists were random assortments, then yes.

A simpler but similar statistics problem: let's say there are 10 marbles in a bag, 1 green and 9 red. You pick a marble at random, then replace it into the bag. If you draw 10 marbles this way, what's the chance of picking the green marble at least once? By your logic, there's a 10% chance of picking the green marble in each draw. You draw ten times. 10 x 10% = 100%. So it's guaranteed! But obviously, it isn't. This problem is solved the other way -- the chance of picking a red marble is 0.90. Picking ten red marbles in a row is (.90)^10 = .35 (rounded). Therefore, the chance of picking at least one green marble in ten tries is 1 - 0.35 = 65%.

Your match math is equally faulty. If you have 12 interviews, but you're at the bottom of everyone's rank list so you have an 8% chance of matching (of which I'm not sure is accurate, but good enough for this discussion), then the chance of not matching if you rank a single program is 92%, and not matching at 12 programs is (0.92)^12 = 37%, so the chance of matching is actually 64%. But even that math is suspect, because I don't think there's any way to say that your chances of matching are actually 8% to begin with, and you can only match to a single program (the marble answer above states that there is a 65% chance of drawing AT LEAST one green marble, but maybe more).

thank you for your response. finally somebody with math knowledge and it makes so much sense.

 

[arafatni]

To OP: What data do you want to integrate into your calculator that Charting the Outcomes has not factored in?

it doesn't consider where you are ranked on the program's list .

 

[arafatni]

Lemme do a number crunch real quick. Yeah, I’m coming up with 32.33(repeating of course) chance of matching for you.

hahaha thank you ! i let you know if i matched .

 

[OneTwoThreeFour]

it doesn't consider where you are ranked on the program's list .

That is an unknowable value (regardless of whatever post-interview communication you received) so can't be reliably factored in. Particularly not for every applicant.

 

[arafatni]

That is an unknowable value (regardless of whatever post-interview communication you received) so can't be reliably factored in. Particularly not for every applicant.

very true unknowable .... but i was gonna assume the worst ( well not the worst because worst is not getting ranked at all) that i was ranked dead last

 

[OneTwoThreeFour]

very true unknowable .... but i was gonna assume the worst ( well not the worst because worst is not getting ranked at all) that i was ranked dead last

But how would you even know if you were dead last vs first vs DNR. You could be DNR at every place you interview in which case your chance to match would be 0%. You could be ranked #1 at every place you go and your chances would be 100%. But since programs do not release how many people they rank nor do they communicate openly about how far down their rank list they go, trying to factor in their opinion of each applicant is a fool's errand.

Thousands of people have tried to figure out ways to make themselves feel better about their odds of matching between January and March. None have "cracked the code". If you are truly worried you won't match your time would be better spent researching the SOAP programs from last year. If you aren't actually worried and are just obsessing over an inscrutable process, go outside and do something fun.

 

[arafatni]

But how would you even know if you were dead last vs first vs DNR. You could be DNR at every place you interview in which case your chance to match would be 0%. You could be ranked #1 at every place you go and your chances would be 100%. But since programs do not release how many people they rank nor do they communicate openly about how far down their rank list they go, trying to factor in their opinion of each applicant is a fool's errand.

Thousands of people have tried to figure out ways to make themselves feel better about their odds of matching between January and March. None have "cracked the code". If you are truly worried you won't match your time would be better spent researching the SOAP programs from last year. If you aren't actually worried and are just obsessing over an inscrutable process, go outside and do something fun.

thank you. I don’t see why Some of you attacking me . Ok as a curious person and lover of math . I thought it would be fun and maybe helpful to figure it out . anyhow thanks for your input

 

[CyrilFiggis]

thank you. I don’t see why Some of you attacking me . Ok as a curious person and lover of math . I thought it would be fun and maybe helpful to figure it out . anyhow thanks for your input

People are criticizing you because you are using a poor metric for your analysis. The NRMP has provided data for many of the statistical confounders and even then things are case by case. So it is pretty impossible to “figure out” even with historical and quantifiable data, even more so with your suppositions.

 

[arafatni]

People are criticizing you because you are using a poor metric for your analysis. The NRMP has provided data for many of the statistical confounders and even then things are case by case. So it is pretty impossible to “figure out” even with historical and quantifiable data, even more so with your suppositions.

yes thank you . I made it clear that i wanted to be criticized in my original post so i know how i can improve on my calculations. ( if it can even be done)

 

[arafatni]

People are criticizing you because you are using a poor metric for your analysis. The NRMP has provided data for many of the statistical confounders and even then things are case by case. So it is pretty impossible to “figure out” even with historical and quantifiable data, even more so with your suppositions.

only one post so far had legit criticized me and i thanked for them the rest were just told me to give up , go outside , forced me to read NRMP reports ( which i highly agree with but i want to look the problem from different perspective) , or just trolled me like a child .

 

[libertyyne]

only one post so far had legit criticized me and i thanked for them the rest were just told me to give up , go outside , forced me to read NRMP reports ( which i highly agree with but i want to look the problem from different perspective) , or just trolled me like a child .

Quantifying your feelings about performance is very subjective and not easily quantifiable. Furthermore, Everyone has a different perspective and ability to quantify their performance and where they stand.

For example, If I feel I really did well after each exam , yet I ended up failing each exam. On the flip side I have a friend who thinks he did poorly after each exam and he ends up acing every exam. This self assessment is also problematic because of things like the dunning kruger effect where people overestimate their competence all the time.

This makes your approach problematic to say the least, and nonsensical to be frank.Since using a random number generator is likely to provide more accurate predictions.

The future is not predictable, but the best thing we have are the NRMP reports which are fairly good at giving you a general idea of where candidates stand in terms of likelihood of matching historically, much better estimate of where a person is in terms of likelihood of match compared to what you are proposing.

If you do want to investigate additional metrics something like figuring out how many candidates a program interviews and on average how far down they have to go on their rank list to fill are probably a better starting point. But the problem with this approach are the yearly variations in fill rank per program.

 

[arafatni]

Quantifying your feelings about performance is very subjective and not easily quantifiable. Furthermore, Everyone has a different perspective and ability to quantify their performance and where they stand.

For example, If I feel I really did well after each exam , yet I ended up failing each exam. On the flip side I have a friend who thinks he did poorly after each exam and he ends up acing every exam. This self assessment is also problematic because of things like the dunning kruger effect where people overestimate their competence all the time.

This makes your approach problematic to say the least, and nonsensical to be frank.Since using a random number generator is likely to provide more accurate predictions.

The future is not predictable, but the best thing we have are the NRMP reports which are fairly good at giving you a general idea of where candidates stand in terms of likelihood of matching historically, much better estimate of where a person is in terms of likelihood of match compared to what you are proposing.

If you do want to investigate additional metrics something like figuring out how many candidates a program interviews and on average how far down they have to go on their rank list to fill are probably a better starting point. But the problem with this approach are the yearly variations in fill rank per program.

thank you very true. Last paragraph is exactly how I am gonna approach even though I am making lot of assumptions . Metrics is based on assumptions. Thank you for your input I appreciate it.

 

[Cornfed101]

You do realize that the guys that developed the match algorithm won the Nobel prize for economics right? It wasn't something you could learn from a stats class.

 

[VincentAdultman]

only one post so far had legit criticized me and i thanked for them the rest were just told me to give up , go outside , forced me to read NRMP reports ( which i highly agree with but i want to look the problem from different perspective) , or just trolled me like a child .

I think this is a silly exercise that will get you nowhere and do little to soothe your anxiety.

You’re gonna do what you’re gonna do

 

[GoSpursGo]

I think this thread has run its course. As I think has been stated multiple times, there are too many assumptions that need to be made based on a total lack of data to make this a fruitful exercise.