CMS publishes two numbers for every hospital. One you can compute in your head. One its model actually uses. Here is all 2,316 of them, and the distance between.
Every hospital in this file publishes number of discharges and number of readmissions. Divide one by the other and you have a readmission rate. It is clean, it is arithmetic, and it looks like an answer.
CMS does not use it. It publishes a second number — a predicted rate from a hierarchical model that risk-adjusts for the patients and shrinks small hospitals toward the national mean. That is the number attached to the money.
The question is not whether you're skeptical of the model. It's whether you'd have thought to ask on a number that came out this clean.
Both numbers, all 2,316 hospitals
≥ 25
Hospitals shown
2,316
Spread (SD)
5.6 pts
Range p10–p90
—
Highest rate
—
Each dot is one hospital. Horizontal axis is heart-failure discharges (log scale); vertical is 30-day readmission rate. The shaded band is where 95% of hospitals would fall from chance alone if every hospital in the country readmitted at the national pooled rate of 19.69%.
Highest 8 — raw rate
Lowest 8 — raw rate
Drag the minimum-discharge slider. The leaderboard is the test. At ≥25 discharges the top of the list is a list of small hospitals. Push the threshold to 500 and the entire cast changes — not because those hospitals improved, but because the arithmetic stopped being loud.
How far the number moves
The distance between the two published numbers, by how many patients the hospital had. This is computed live from the same 2,316 rows.
HF discharges
n
SD, raw
SD, adjusted
Median move
Largest move
“Move” is the absolute difference in percentage points between the rate you can compute and the rate CMS publishes. It is not error correction in one direction — it is risk adjustment and shrinkage together.
The bottom row is the honest one. At 600+ discharges, the model barely touches the number: the median move is under half a point. The arithmetic and the model agree, because there is enough signal for them to agree about. Everything above that row is the model telling you the raw number was mostly noise — and the raw number never looked like noise.
What this benchmark does not see
It is missing about a quarter of the hospitals, on purpose. In the HRRP file, 36% of rows have no ratio at all and 55–56% have no discharge count — suppressed. The 2,316 here are the ones CMS was willing to publish complete. Every plot on this page is a plot of the hospitals that cleared a reporting threshold.
The denominator is not your heart failure patients. HRRP counts Medicare fee-for-service only. Medicare Advantage enrollees — now more than half of Medicare — are not in it. A hospital's published readmission rate is a rate for a shrinking slice of its own panel.
Risk adjustment sees claims, not lives. The model adjusts for coded comorbidities. It does not see housing, transport, pharmacy access, or whether anyone was home. CMS itself conceded the point in FY2019 by stratifying hospitals into peer groups by dual-eligible share — an admission that the unstratified model had been reading poverty as quality.
The window is 2021–2024. Three years of discharges that include the tail of COVID staffing collapse. Averaged, it looks like a steady state. It was not one.
Watch which number gets quoted. The raw rate is the one that's easy to compute, easy to chart, and easy to put in a press release or a slide. The ratio is the one that moves money. They are not the same number and at small hospitals they are not close.
Why this is on a page about a play
Today's newsletter is about a phrase Washington had worn smooth — the calm light — that surfaced on its own in the worst room of his career, because he had said it enough times on ordinary days.
The clinical version is what's the worst thing this could be, asked on five hundred chest walls that turn out to be pulled muscles, so that it asks itself on the one that isn't.
The version you need when you build is how would I know if this were wrong? — and the cruelty of it is the timing. Nobody asks it of a number that looks broken. You need it for a number like the one at the top of this page: arithmetic, published by CMS, correct in every digit, and off by twenty-three points.