Small classroom market: match
The match
The match rate, the positions filled, which choice applicants matched to, the match rate by the length of the rank order list, who matched where (applicant strength against program quality, with the sorting), which programs filled their positions, the checks of the match, and who matched by group and strength.
What to do here
- The tabs above lead to the population, the views before interviews, the applications, the match, and the lists of applicants and programs.
A saved run of the simulator: everyone who opens it sees this same market. Simulated from the assumptions in the parameters; not a prediction of any real applicant's or program's match.
The match
Applicant-proposing deferred acceptance, the mechanism of the NRMP. The match rate counts the applicants who submitted a rank order list, as NRMP reports do; 0 applicants had no interview and so no list.
Which choice did applicants match to?
Matched applicants by where they had ranked their program on their own rank order list: first choice, second, and so on, with every choice after the tenth counted together. Each bar is a share of the matched applicants; a tall first bar means most got their first choice. Hover a bar for the number of applicants. Choices are places on the list the applicant submitted, which holds only programs they interviewed at: a first choice here is not always the program they wanted most before interviews. Applicants who did not match are not shown.
Learn more in the helpOf 50 matched applicants, 9 (18.0%) matched to their first choice and 33 (66.0%) to one of their first three.
The numbers
| Choice | Applicants | Share of matched |
|---|---|---|
| 1st choice | 9 | 18.0% |
| 2nd choice | 16 | 32.0% |
| 3rd choice | 8 | 16.0% |
| 4th choice | 10 | 20.0% |
| 5th choice | 2 | 4.0% |
| 6th choice | 3 | 6.0% |
| 7th choice | 2 | 4.0% |
| 8th choice | 0 | 0.0% |
| 9th choice | 0 | 0.0% |
| 10th choice | 0 | 0.0% |
| 11th choice or lower | 0 | 0.0% |
Rank order lists
- Mean list length, matched applicants
- 6.24
- Mean list length, unmatched applicants
- 5.00
- Applicants with a list
- 60 of 60
Does a longer rank order list help?
Applicants with a rank order list, by the number of programs on it, and in each group the share who matched. Each bar is all the applicants whose list has that many programs; the green part matched. As in the real Match, the share usually climbs steeply over the first few programs ranked and then levels off. Hover a bar for the numbers. A longer list is a sign of a stronger application, not only a cause of matching: a list is as long as the applicant's interviews, and strong applicants get more of them. A bar that stands for a handful of applicants can be far off. Applicants without a list are left out.
Learn more in the helpOf 60 applicants with a rank order list, 50 matched (83.3%): 0.0% of the 1 who ranked 1 program, and 100.0% of the 9 who ranked 8 programs.
The numbers
| Programs ranked | Applicants | Matched | Not matched | Match rate |
|---|---|---|---|---|
| 1 program | 1 | 0 | 1 | 0.0% |
| 2 programs | 1 | 1 | 0 | 100.0% |
| 3 programs | 1 | 1 | 0 | 100.0% |
| 4 programs | 11 | 9 | 2 | 81.8% |
| 5 programs | 5 | 2 | 3 | 40.0% |
| 6 programs | 9 | 7 | 2 | 77.8% |
| 7 programs | 23 | 21 | 2 | 91.3% |
| 8 programs | 9 | 9 | 0 | 100.0% |
How this match was checked
| Check | Result |
|---|---|
| Blocking pairs: an applicant and a program that rank each other above their match | 0 |
| Programs matched to more applicants than they have positions | 0 |
| Matches that are not on both rank order lists | 0 |
| List entries without an interview | 0 |
| Rank order lists whose ranks are not exactly 1, 2, ..., k | 0 |
| Applicant list entries beyond rank 300 (the NRMP limit) | 0 |
| Both proposing sides match the same applicants and fill each program equally (rural hospitals) | not run |
| No applicant prefers the program-proposing result (applicant optimality) | not run |
The last two checks run when Compare both sides proposing is on in the match settings. The engine is also checked on hundreds of random markets against an independent solver (docs/VALIDATION.md).
Who matched where
Do stronger applicants match to better programs?
Applicants in five groups by strength percentile (the rows, the top 20% at the top) and where each group ended up (the columns): not matched, or matched to a program in each fifth of the programs by quality, from the bottom 20% to the top 20%. Each cell is its share of the row's applicants, darker for more: blue for matches, grey for not matched. Read along a row: it adds up to 100%. In a perfectly sorted market the dark cells run along the diagonal, from the weakest applicants, unmatched or at the lowest programs, to the strongest at the best programs; the more a row spreads out, the less strength decides where its applicants match. Sorting, in the summary, is the rank correlation between an applicant's strength and the quality of the program they matched to (close to 1 when the strongest applicants are at the best programs, in order; 0 = no relation). Hover a cell for its number of applicants. Applicants do not rank programs by quality alone: with tastes of their own (agreement below 1) a market that works well is still not perfectly sorted. Strength and quality are the latent values, which the other side sees only through its own noisy view. The fifths of programs hold equal numbers of programs, not of positions. Sorting cannot quite reach 1, because the applicants of one program share its quality: the fewer and larger the programs, the lower its ceiling (0.99 with 8 programs of 6 positions).
Learn more in the helpSorting is 0.67: the rank correlation between an applicant's strength and the quality of the program they matched to (close to 1 when the strongest applicants are at the best programs, in order; 0 = no relation). Of the top 20% of applicants by strength, 41.7% matched to a program in the top 20% by quality and 0.0% did not match; of the bottom 20%, 50.0% matched to a program in the bottom 20% and 50.0% did not match.
The numbers
| Applicants by strength | Applicants | Not matched | Matched to a program, by its quality percentile | ||||
|---|---|---|---|---|---|---|---|
| 0–20 | 20–40 | 40–60 | 60–80 | 80–100 | |||
| Top 20% | 12 | 0 (0.0%) | 1 (8.3%) | 2 (16.7%) | 3 (25.0%) | 1 (8.3%) | 5 (41.7%) |
| 60th–80th percentile | 12 | 1 (8.3%) | 2 (16.7%) | 3 (25.0%) | 4 (33.3%) | 2 (16.7%) | 0 (0.0%) |
| 40th–60th percentile | 12 | 1 (8.3%) | 6 (50.0%) | 2 (16.7%) | 3 (25.0%) | 0 (0.0%) | 0 (0.0%) |
| 20th–40th percentile | 12 | 2 (16.7%) | 6 (50.0%) | 1 (8.3%) | 2 (16.7%) | 1 (8.3%) | 0 (0.0%) |
| Bottom 20% | 12 | 6 (50.0%) | 6 (50.0%) | 0 (0.0%) | 0 (0.0%) | 0 (0.0%) | 0 (0.0%) |
Which programs fill their positions?
The positions of the programs in each fifth by quality, from the bottom 20% of programs to the top 20%, and the share of them the match filled. Each bar is all the positions of its group; the green part is filled. A bar with grey at the top has unfilled positions: hover it for the positions, how many were filled, and how many of the group's programs have an unfilled position. In the real Match, unfilled positions go to the scramble after the match (SOAP), which is not simulated.
Learn more in the helpThe match filled 50 of 50 positions (100.0%). Programs in the bottom 20% by quality filled 100.0% of their positions and those in the top 20% 100.0%; 0 of 8 programs have an unfilled position.
The numbers
| Programs by quality | Programs | Positions | Filled | Unfilled | Share filled | Programs with an unfilled position |
|---|---|---|---|---|---|---|
| Bottom 20% | 2 | 21 | 21 | 0 | 100.0% | 0 |
| 20th–40th percentile | 1 | 8 | 8 | 0 | 100.0% | 0 |
| 40th–60th percentile | 2 | 12 | 12 | 0 | 100.0% | 0 |
| 60th–80th percentile | 1 | 4 | 4 | 0 | 100.0% | 0 |
| Top 20% | 2 | 5 | 5 | 0 | 100.0% | 0 |
Who matched
Do stronger applicants match more often?
Applicants in ten groups by strength (deciles: 1 is the weakest tenth, 10 the strongest) and, in each, the share who matched, who submitted a rank order list but did not match, and who had no list (no interview, or no program they would rank). Each bar is all the applicants of its decile; the green part matched. Hover a bar for the numbers and for the match rate among applicants with a list, the rate NRMP reports use and the one in the table below. Strength is the applicant's latent strength, which each program sees only through its own noisy view.
Learn more in the helpOf the weakest tenth of applicants by strength, 33.3% matched; of the strongest tenth, 100.0%. Of all 60 applicants, 50 matched (83.3%) and 0 had no rank order list.
The numbers
| Strength decile | Applicants | Matched | Not matched | No rank order list | Share matched | Match rate with a list |
|---|---|---|---|---|---|---|
| 1 | 6 | 2 | 4 | 0 | 33.3% | 33.3% |
| 2 | 6 | 4 | 2 | 0 | 66.7% | 66.7% |
| 3 | 6 | 5 | 1 | 0 | 83.3% | 83.3% |
| 4 | 6 | 5 | 1 | 0 | 83.3% | 83.3% |
| 5 | 6 | 5 | 1 | 0 | 83.3% | 83.3% |
| 6 | 6 | 6 | 0 | 0 | 100.0% | 100.0% |
| 7 | 6 | 5 | 1 | 0 | 83.3% | 83.3% |
| 8 | 6 | 6 | 0 | 0 | 100.0% | 100.0% |
| 9 | 6 | 6 | 0 | 0 | 100.0% | 100.0% |
| 10 | 6 | 6 | 0 | 0 | 100.0% | 100.0% |
| Group | Applicants | With a list | Match rate | Mean choice matched | Interviews (mean) |
|---|---|---|---|---|---|
| us_md | 26 | 26 | 88.5% | 2.48 | 6.27 |
| us_do | 11 | 11 | 90.9% | 2.70 | 6.09 |
| us_img | 5 | 5 | 80.0% | 3.50 | 6.40 |
| non_us_img | 15 | 15 | 66.7% | 3.30 | 5.27 |
| other | 3 | 3 | 100.0% | 5.33 | 7.00 |
| Decile | Applicants | With a list | Match rate | Mean choice matched | Interviews (mean) |
|---|---|---|---|---|---|
| 1 | 6 | 6 | 33.3% | 2.50 | 4.50 |
| 2 | 6 | 6 | 66.7% | 5.00 | 6.17 |
| 3 | 6 | 6 | 83.3% | 2.60 | 5.33 |
| 4 | 6 | 6 | 83.3% | 4.20 | 6.17 |
| 5 | 6 | 6 | 83.3% | 5.20 | 6.33 |
| 6 | 6 | 6 | 100.0% | 3.00 | 5.83 |
| 7 | 6 | 6 | 83.3% | 1.40 | 4.50 |
| 8 | 6 | 6 | 100.0% | 2.17 | 6.83 |
| 9 | 6 | 6 | 100.0% | 2.33 | 7.00 |
| 10 | 6 | 6 | 100.0% | 1.67 | 7.67 |
Strength deciles group applicants by their latent strength: 1 is the weakest tenth, 10 the strongest.