Couples Match - “No Match” Code Questions

[psychtb]

Me and my partner have tentatively made 20 match pairs with the programs we are most interested with. After these 20 pairs we want to maximize our chance of matching at specific programs by using the “no match”code for a handful of programs for me and one program for her. Does the algorithm stop trying to match the unmatched partner if a pair with a no match code is successful?

Both of us intend to continue with matched programs after this if the no match code is unsuccessful. We also plan to rank all programs at the end with no match codes on both sides, as matching is more important for us than ending up in the same location or nearby location with one of us not matching. Summary of scenario below and both of us interviewed at quite a few places.

Summary
20 program match pairs
My few preferred programs - No Match code
No Match code - Partner’s preferred program
Remaining matched programs
All my ranked programs - No Match code
No Match code - All partner ranked programs

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[NotAProgDirector]

Yes, you can do this. Just make sure you know what it will do, and the choices you are making. The devil is in the details.

The alg will first try to put you into one of your 20 matched pairs. You both need to match for it to be successful. If that works out, then none of the rest matters. You should order these pairs in the order you both prefer.

The order of what comes next may matter quite a bit. Your plan is to list your preferred programs and no match for her. And then follow that by no match for you and her preferred program. Let's say that you prefer MGH and she prefers BWH - both in Boston so you're living in the same city. MGH-BWH would presumably be in your top 20. If you don't match to that combination, then either you're not matching to MGH, she is not matching to BWH, or both. If you now list MGH - XXX, then you will match at MGH if at all possible and she will get nothing. If you list XXX - BWH then you could get nothing and she will get BWH. It would not matter what order these come in, since they can't both be true at the same time -- if so, then you would have matched to MGH-BWH.

But let's say your preferred program is UCSF, and she did not get any SF interviews. And her preferred program is UW, and you got no Seattle interviews. In that case, it's quite possible that you could match to UCSF and she could match to UW -- but you don't want that. In that case, the order you put these options on the rank list will matter -- as whomever's option comes first would be the one you would get.

This problem goes away once you have listed all possible combinations - since at that point it's impossible for you both to match.

How many programs have you both interviewed for? The NRMP limits rank lists to 300, and you can easily run out of rank options. In this case the early "no match" choices will shorten your list of options. If you rank MGH - XXX and don't match to that, then you're not going to MGH no matter what and so you don't need to consider any combinations including it any lower on your rank list.

And you'll def want to weigh the impact of purposefully not matching on either of you. I believe you'd still be in SOAP if you choose the "no match" option, but you should probably check with the NRMP about that.

 

[psychtb]

Yes, you can do this. Just make sure you know what it will do, and the choices you are making. The devil is in the details.

The alg will first try to put you into one of your 20 matched pairs. You both need to match for it to be successful. If that works out, then none of the rest matters. You should order these pairs in the order you both prefer.

The order of what comes next may matter quite a bit. Your plan is to list your preferred programs and no match for her. And then follow that by no match for you and her preferred program. Let's say that you prefer MGH and she prefers BWH - both in Boston so you're living in the same city. MGH-BWH would presumably be in your top 20. If you don't match to that combination, then either you're not matching to MGH, she is not matching to BWH, or both. If you now list MGH - XXX, then you will match at MGH if at all possible and she will get nothing. If you list XXX - BWH then you could get nothing and she will get BWH. It would not matter what order these come in, since they can't both be true at the same time -- if so, then you would have matched to MGH-BWH.

But let's say your preferred program is UCSF, and she did not get any SF interviews. And her preferred program is UW, and you got no Seattle interviews. In that case, it's quite possible that you could match to UCSF and she could match to UW -- but you don't want that. In that case, the order you put these options on the rank list will matter -- as whomever's option comes first would be the one you would get.

This problem goes away once you have listed all possible combinations - since at that point it's impossible for you both to match.

How many programs have you both interviewed for? The NRMP limits rank lists to 300, and you can easily run out of rank options. In this case the early "no match" choices will shorten your list of options. If you rank MGH - XXX and don't match to that, then you're not going to MGH no matter what and so you don't need to consider any combinations including it any lower on your rank list.

And you'll def want to weigh the impact of purposefully not matching on either of you. I believe you'd still be in SOAP if you choose the "no match" option, but you should probably check with the NRMP about that.

I interviewed at around 40 places and my partner around 50. My partner interviewed at nearly all my places, other than a couple. If we don't match in our first 20 pairs we don't mind going to different places. I was just worried that if we failed on our first 20 rankings and the algorithm hit a successful "No match pair" the algorithm would stop for me or my partner depending who had "no match" selected. All the programs after our first 20 rankings and the "no match pairs" are different. I put an example below to illustrate our situation but with less pairs.

X - No match Code
Me: Left Side. A & B are my preferred programs.
Partner: Right side. C is partner's preferred program.
Some of our preferred programs are relatively close by so we can rank some of them in different combinations.
D, E, F are programs we both interviewed at and would be happy to match there.

A - A
B - B
C - C
A - B
B - A
A - C
C - A

A - X
B - X
X - C

Would the algorithm halt here if one of the no match pairs is selected above?

D - D
E - E
F - F

We want to put a bunch of no match pairs at the bottom so we can both match even if it is elsewhere.

D - X
E - X
F - X

X - D
X - E
X - F
X - Programs I did not interview at.

 

[NotAProgDirector]

YES. The alg will stop and that will be it. One of you will be unmatched.

You absolutely don't want to do this.

With 40 and 50 places, you will not be able to rank all combinations. With 40 and 50 exactly, there would be ((40-1)x(50-1))-1 combinations. That's 1,910 combinations. You only get 300 ranks max.

There is no way to submit a couple rank list for some number, and then uncouple if it doesn't work out. You'll get 300 joint ranks and have to make the best of it. Or submit separate lists and hope for the best.

 

[NotAProgDirector]

Sorry, got my math wrong.

It's ((40+1)x(50+1))-1 = 2,090 combinations. No practical difference, but I hate being inaccurate

 

[HemeOncHopeful19]

Sorry, got my math wrong.

It's ((40+1)x(50+1))-1 = 2,090 combinations. No practical difference, but I hate being inaccurate

As penance I would be interested to see you solve for the minimum number of programs OP and their friend could have interviewed at to max out the algorithm at 300.

 

[NotAProgDirector]

If we assume they get the same number of interviews each:
((n+1)x(n+1))-1=300
(n+1)^2=301
n+1=SQRT(301) = 17.35 (ignoring the negative sqrt since that would be meaningless in this case)
n = 16.35. Since interviews are integers only, it's 16
(16+1)x(16+1)-1=288
If one of them has 17 interviews, it's 305 ranks, just a bit too much.

If we assume they have the same 4:5 ratio:
((4n+1)x(5n+1))-1=300
(4n+1)(5n+1)=301
20n^2+9n+1=301
20n^2+9n-300=0
Now need the quadradic equation:
-9+/-SQRT(9^2-4(20)(-300)) / 2(20)
-9+/-SQRT(24081) / 40
-9 +/- 155 / 40 --- No point in the negative root, so choose the plus
146 / 40 = 3.65 = n
Therefore one would have 4 x 3.65 = 14.6, and the other would have 5 x 3.65 = 18.25
((14+1)x(18+1))-1 = 284
But it turns out that due to rounding, can fit one more. 14 and 19:
((14+1)x(19+1))-1 = 299

 

[NotAProgDirector]

Oh wait, you asked for MINIMUM.

Let x=one partner's number of interviews.
Let y=other partner's number of interviews

(x+1)(y+1)-1=300
xy + x + y + 1 -1 = 300
xy+y=300-x
y=(300-x)/(x+1)

Brute force is the best way to solve this:

x	y	x+y	Ranks
1​	149​	150​	299​
2​	99​	101​	299​
3​	74​	77​	299​
4​	59​	63​	299​
5​	49​	54​	299​
6​	42​	48​	300​
7​	36​	43​	295​
8​	32​	40​	296​
9​	29​	38​	299​
10​	26​	36​	296​
11​	24​	35​	299​
12​	22​	34​	298​
13​	20​	33​	293​
14​	19​	33​	299​
15​	17​	32​	287​
16​	16​	32​	288​

Both 16/16 and 15/17 give you equally the smallest number of combined ranks of 32

 

[TelemarketingEnigma]

Op, please please please make sure you fully understand how the match algorithm works before you submit your rank list

here's the NRMP's video on how it works:

it's clear that you have a fundamental misunderstanding about what "no match" means here. You should only use that option if staying in the same location together with one partner going unmatched is more important to you than both partners matching, but in different locations. there is no separate rank list that the unmatched partner gets to continue on with if you hit that rank. it stops there. your lists are one and the same.

 

[NotAProgDirector]

@psychtb

Sorry for derailing your thread into match-math insanity.

Let us know if we can answer anything else.

As I mentioned earlier on the thread, you and your partner have a tough choice to make. You've been incredibly successful with an insane number of interviews. Unfortunately, this leaves you with a new problem. The couple's match will only let you rank 300 options which is absolutely not all of them. With 40 and 50 interviews, you've almost certainly gone on too many and there isn't much point to ranking all of them, so you could pick your top choices and use the couple's match. Or, you can just rank individually and hope for the best, but then you will be able to rank every program.

The second video mentioned above is here:



Let us know what you decide to do!