Issue 055 - Public health - Healthcare throughput
How much healthcare is associated with 7 million Medicaid enrollees?
AP reports that recent Medicaid changes in the 2025 federal budget law are projected to leave more than 7 million people without health insurance as work requirements and related changes take effect. This problem treats the policy as a scale question: how much healthcare use is associated with a population that large?
The problem
Estimate the annual volume of healthcare currently used by a population of 7 million people.
Express that volume in terms of doctor or outpatient visits per year, emergency-room visits per year, and total clinician-hours required to provide that care.
You will need to estimate how frequently the average person visits a doctor, how often they use an emergency department, how long a typical medical encounter requires from physicians, nurses, or other clinical staff, and whether Medicaid recipients use healthcare at the same rate as the general population.
The calculation does not assume that all of this care would disappear if coverage were lost. Some care could be forgone, delayed, paid out of pocket, covered by another source, or shifted toward emergency and uncompensated care. The purpose is simply to establish the approximate scale of healthcare associated with the affected population.
Because Fermi problems target an order of magnitude, I normally use no more than two significant digits and write most calculations in scientific notation; the Fermi reference explains both conventions.
Before checking sources
Matt's first pass
I estimated that the average Medicaid recipient might visit a doctor or outpatient clinician about 2.5 times annually, and might visit the ER once every 5 years.
With 7 million individuals at that rate, that would be about 1.8 x 10^7 clinician/outpatient visits and 1.4 x 10^6 ER visits.
outpatient visits
~= 7 x 10^6 people x 2.5 visits/person-year
~= 1.8 x 10^7 visits/year
ER visits
~= 7 x 10^6 people x 0.2 visits/person-year
~= 1.4 x 10^6 visits/yearNext I assumed clinicians spend on average about 2 hours per visit, on the aggregate of those scheduled doctor's visits, outpatient visits, and ER visits combined.
So about 1.9 x 10^7 combined visits x 2 hours each gives about 3.8 x 10^7 hours, or 38 million hours, spent by clinicians on those 7 million Medicaid recipients annually.
combined visits
~= 1.8 x 10^7 + 1.4 x 10^6
~= 1.9 x 10^7 visits/year
clinical time
~= 1.9 x 10^7 visits/year x 2 h/visit
~= 3.8 x 10^7 h/yearIf we are only considering full-time workers, at 2,000 hours annually, that is about 19,000 full-time clinicians.
full-time clinician equivalents
~= 3.8 x 10^7 h/year / 2 x 10^3 h/worker-year
~= 1.9 x 10^4 worker-yearsScale-check note
This page is published as an unscored policy scale check because the hook is a U.S. law and healthcare-policy issue. It is excluded from Matt's numerical Calibration Score averages, but the estimate is still compared with sourced reference numbers below.
Grounding facts
AP reports that Medicaid changes in the 2025 federal budget law are expected to leave more than 7 million people without health insurance from Medicaid changes, while CBO's supplemental estimate for P.L. 119-21 says the Medicaid provisions will increase the uninsured population by 7.5 million in 2034.
CDC FastStats reports about 1.0 billion physician office visits, or 320.7 visits per 100 people, using 2019 National Ambulatory Medical Care Survey data. A separate CDC data brief reported 267 office-based physician visits per 100 people in 2018. A Fermi peg of about 3 office visits per person per year is reasonable.
CDC FastStats reports 155.4 million emergency-department visits, or 47.3 visits per 100 people, using 2022 National Hospital Ambulatory Medical Care Survey data. A CCW Medicaid emergency-department analysis found that about 17% of Medicaid enrollees had at least one ED visit in the year it studied, with most users having one visit and some having multiple visits.
There is no single authoritative clinician-hours-per-visit number for this mixed bundle, so the corrected calculation below uses a transparent staffing model: roughly 1 clinician-hour for an ordinary office or outpatient encounter and roughly 4 clinician-hours for an emergency-department encounter, counting physician, nurse, and other clinical labor together.
After checking sources
Check and recalibrate
Start with outpatient and office-based care. General U.S. office-visit data point toward about 2.7 to 3.2 physician office visits per person per year, before adding hospital outpatient, urgent care, behavioral health, or other non-office settings. For a simple scale check, use 3 outpatient or office-style visits per person-year:
outpatient/office visits
~= 7 x 10^6 people x 3 visits/person-year
~= 2.1 x 10^7 visits/yearFor emergency-department use, the general-population CDC rate is about 0.47 ED visits per person-year. Medicaid-specific analysis suggests many enrollees have no ED visit in a given year, but the users who do visit may have more than one. A practical range for this Fermi problem is about 0.25 to 0.5 ED visits per person-year:
ED visits, lower case
~= 7 x 10^6 people x 0.25 visits/person-year
~= 1.8 x 10^6 visits/year
ED visits, higher case
~= 7 x 10^6 people x 0.5 visits/person-year
~= 3.5 x 10^6 visits/yearMatt's outpatient count was a bit low and his emergency-department count was probably low, but both were in the right order of magnitude. The total encounter count is better thought of as roughly 20 million to 25 million outpatient or office-style visits plus about 2 million to 4 million emergency-department visits per year.
Now convert those visits into clinical labor time. If ordinary outpatient encounters average about 1 clinician-hour across the full clinical team, and ED visits average about 4 clinician-hours, the total clinical time is:
outpatient clinical time
~= 2.1 x 10^7 visits x 1 h/visit
~= 2.1 x 10^7 h/year
ED clinical time
~= 2 x 10^6 to 4 x 10^6 visits x 4 h/visit
~= 0.8 x 10^7 to 1.6 x 10^7 h/year
total clinical time
~= 3 x 10^7 to 4 x 10^7 h/yearThat translates to:
full-time worker equivalents
~= 3 x 10^7 to 4 x 10^7 h/year / 2 x 10^3 h/worker-year
~= 1.5 x 10^4 to 2 x 10^4 worker-yearsThe best Fermi answer is therefore roughly tens of millions of visits and about 30 million to 40 million clinician-hours per year, equivalent to around 15,000 to 20,000 full-time clinician-years.
That does not mean losing coverage removes that amount of care from the healthcare system. The care can shift across time, payer, setting, and severity. The scale lesson is that a 7-million-person coverage population corresponds to a healthcare workload large enough to resemble the annual clinical labor of a mid-sized city's healthcare workforce.
Post-check reflection
Matt's reflection
Looks like all my estimates were a bit off, but often in opposite directions so they tended to cancel out.
Ultimately if the question is order of magnitude of annual clinician visits represented by Medicaid recipients, tens of millions is the right answer. Even though I underestimated the annual count of the types of visits and overestimated time spent by a clinician, the rough FTE of clinicians needed to cover that time was on the right order of magnitude as well.
Recommended memory peg
For healthcare-throughput problems, remember: 3 office visits per person-year, roughly 0.5 emergency-department visits per person-year, and 2,000 work-hours per full-time worker-year. For a 7-million-person population, that puts healthcare use in the range of tens of millions of encounters and tens of millions of clinician-hours per year.
Reader results
Bars show how submitted estimates sort into the answer choices from the gut-check prompt.