The Quiet Mathematics of an Insurance Appeal: A Working Cost-Benefit Worksheet

$900 expected recovery. Three hours of work. Three hundred dollars an hour. And she almost left it on the table because the denial felt small. The numbers belong to a 38-year-old paralegal in suburban Phoenix whose commercial carrier rejected a $1,200 outpatient ultrasound her primary-care physician had ordered three weeks earlier. In February she read the denial twice and gave her husband the reason most patients give. "It's twelve hundred dollars. It isn't worth my time." She put the letter in a drawer. Six weeks later, on the strength of an offhand comment from a coworker who had recently won her own appeal, she pulled the letter back out and ran the arithmetic she had skipped. The denial cited a missing prior-authorization code. Procedural denials of that type reverse in our internal data at roughly 75 percent. The denial amount multiplied by the reversal probability is $900. The appeal she eventually wrote took about three hours of evenings at the kitchen table. The implicit hourly rate was three hundred dollars. The check arrived eleven weeks later. She had nearly walked away from a quarter of a working month's net pay because she ran her math on the wrong number.

Patients make the keep-or-fight decision on the wrong number. They look at the absolute dollar amount and ask whether it is large enough to chase. The number that matters is the expected recovery, the denial amount discounted by the probability the appeal succeeds, set against an honest estimate of the time the appeal will take. A small denial with a high reversal probability is often worth fighting. A larger denial with no procedural or clinical foothold sometimes is not.

The expected-value framework, in plain numbers

Every appeal decision is a two-line calculation. The first line is the expected recovery. The second is the expected cost. The patient appeals when the first meaningfully exceeds the second.

Expected recovery is the denial amount multiplied by the probability of reversal. A $2,000 denial at a 60 percent reversal probability has an expected recovery of $1,200. The dollar size scales the figure linearly. The reversal probability scales it just as forcefully, which is why the procedural category of the denial matters more to the math than the patient usually realizes.

Expected cost is the hours the appeal will reasonably take, multiplied by the hourly value the patient assigns to her own time. The hourly value is not the day-job wage. It is the value she places on the evening or weekend hours the appeal will actually consume, which for most patients is higher than the day-job wage because those hours otherwise belong to family, rest, or other unpaid work. A conservative figure sits between $40 and $100 an hour.

The reversal-probability ranges anchoring the math are drawn from KFF analysis of Medicare Advantage prior-authorization data and state external-review datasets, which together represent the published external-review record across U.S. states. External review reverses denials at rates ranging from roughly 17 to 80 percent across U.S. states (Apellica's Apellica External Review Index Index, 2026), and the archetype-level pattern that emerges from the same source datasets is consistent. Lack-of-prior-authorization, coding errors, and step-therapy denials reverse most often when properly appealed. Out-of-network and coverage-exclusion denials sit in the middle. Medical-necessity denials reverse less often. Experimental or investigational denials reverse least often, and only when the appeal cites the carrier's own evidence framework. Patients should use the lower end of any published range when running their own numbers.

Three example calculations

The three examples below are composites drawn from common denial patterns.

The first is a $1,200 procedural denial. The carrier rejected an outpatient imaging study for lack of prior authorization. The treating physician's records establish that the service was medically appropriate and the prior-authorization step was missed at the clerical level. Denials of this kind reverse at roughly 75 percent when the appeal cites the right regulatory framework. Expected recovery is $900. The appeal takes approximately three hours to assemble, counting the time to read the denial, request the medical-policy bulletin and operative plan documents, draft the four-part letter, attach the records, and mail certified. Nine hundred dollars against three hours is $300 an hour. The patient appeals. The math is not close.

The second is a $4,500 medical-necessity denial. The carrier rejected a specialty procedure as not meeting medical-policy criteria, citing a bulletin without identifying the specific criterion the patient failed. Denials of this type reverse in the 45 to 55 percent range when the appeal aligns the clinical record to the carrier's own published criteria and cites peer-reviewed evidence at the level the policy identifies as sufficient. At 55 percent, expected recovery is $2,475. The appeal takes longer because the clinical narrative has to be constructed and the evidence stack compiled. A reasonable estimate is six hours, an hourly equivalent of $412. The patient appeals. The larger denial amount more than compensates for the lower reversal probability.

The third is a $300 coding-error denial. The carrier rejected a small outpatient service on the basis of an incorrect procedure code. Denials of this type reverse at roughly 80 percent because the underlying problem is clerical. Expected recovery is $240. The appeal is short, perhaps two hours, counting the call to the provider's billing office, a brief letter, and submission. The hourly equivalent is $120. This case is borderline. A patient who values her evening hours at $40 an hour appeals comfortably. A patient who values them at $150 an hour does not. The math respects the answer either way.

The stay-in-the-process multiplier

The reversal probabilities above are for internal appeals. When the case moves to external review by an Independent Review Organization for ACA and ERISA plans, or to the Independent Review Entity for Medicare Advantage, the reversal probability typically rises by ten to twenty percentage points. The IRO has no financial relationship with the carrier and the decision binds the carrier on ACA-regulated coverage. A medical-necessity denial that reverses at 55 percent on internal appeal often reverses at 65 to 70 percent on external review. The marginal cost of the second stage is lower because the four-part letter, the medical-policy bulletin, the clinical narrative, and the evidence stack are already assembled. The patient who appeals once and stops walks away from the highest-probability stage of the process.

Hidden value beyond the immediate denial

The expected-recovery line captures only the dollars at stake on the specific denial. Three additional categories of value sit outside that line.

The first is precedent value. A reversed denial on a recurring service alters the carrier's posture on the patient's future claims. Subsequent claims for the same service, code, and diagnosis tend to clear without the friction that produced the original denial. The expected value of the first appeal includes the avoided costs of the appeals the patient never has to file.

The second is plan-language forcing. The statutory right to request the operative plan documents and clinical criteria applied exists under 29 CFR 2560.503-1(h)(2)(iii) for ERISA plans and 45 CFR 147.136(b)(2)(ii)(C) for ACA plans, and the carrier must produce within 30 days. Patients who never appeal never exercise that right. Patients who do frequently discover that other services they assumed were not covered actually are, or that exclusions cited in casual carrier communications do not exist in the operative document. The forcing function, covered in Apellica's earlier piece on the 30-day rule, has value beyond the case that triggered it.

The third is deterrent value. Carriers operate utilization-management programs calibrated against the appeal rate. Patients with one or more successful appeals on file experience marginally lower denial rates on subsequent claims, controlling for service mix. The effect is small per claim, meaningful in aggregate over years.

When the math says do not appeal

The honest application of the framework produces cases in which the answer is to let the denial stand. Four situations recur.

The first is very small dollar amounts. A denial under $100 with a reversal probability of 70 percent produces expected recovery under $70. Even at two hours and a $40 hourly value, expected cost is $80. The math does not pencil out unless the denial reflects a recurring service for which precedent value matters more than immediate recovery. For one-off small denials, the patient is rational to walk away.

The second is denials with no procedural irregularity and no clinical basis to challenge medical necessity. A service excluded in unambiguous language, with no overlap with any federally mandated coverage category, with the patient's record matching the exclusion exactly, has a reversal probability low enough that expected recovery does not justify the time. These cases are less common than they look, because plan documents are inconsistent and federally mandated coverage categories are broader than carriers represent. But they exist.

The third is cases in which the underlying service is covered by a different plan the patient holds. Patients with dual coverage, spousal plans, or coordination-of-benefits situations frequently spend appeal time fighting a denial that resolves faster through a re-submission under the secondary plan. The re-file route often wins.

The fourth is cases at or beyond the deadline. The 180-day clock for ACA and ERISA appeals, the 60-day clock for Medicare Advantage, the four-month external-review window, all enforce. An appeal filed after the deadline is rejected procedurally. Expected value collapses to zero when the clock has run.

Exhibit 1: Expected-value matrix

The matrix below crosses denial amount against reversal probability and reports expected recovery in each cell. The highest-EV zone sits in the $1,000 to $10,000 denial range at reversal probabilities of 50 percent and above. The do-not-appeal zone sits in the bottom-left corner.

| Denial amount | 35% reversal | 50% reversal | 65% reversal | 75% reversal | 85% reversal | |---|---|---|---|---|---| | $200 | $70 | $100 | $130 | $150 | $170 | | $500 | $175 | $250 | $325 | $375 | $425 | | $1,200 | $420 | $600 | $780 | $900 | $1,020 | | $2,500 | $875 | $1,250 | $1,625 | $1,875 | $2,125 | | $5,000 | $1,750 | $2,500 | $3,250 | $3,750 | $4,250 | | $12,000 | $4,200 | $6,000 | $7,800 | $9,000 | $10,200 |

Action title for designer: "The expected-recovery cell is the only number that matters. A $500 denial at 75 percent reversal beats a $5,000 denial at 35 percent reversal on every dimension except the headline number patients fixate on."

Exhibit 2: Distribution of denial amounts in Apellica's caseload

The bulk of denials sit in the $500 to $5,000 band, which is also where the expected-value math is most favorable. Denials below $200 produce little expected recovery. Denials above $25,000 are rarer but disproportionately important when they arise.

| Denial amount band | Approximate share of caseload | Median time to assemble appeal | |---|---|---| | Under $200 | roughly 8% | roughly 1.5 hours | | $200 to $499 | roughly 14% | roughly 2 hours | | $500 to $1,499 | roughly 27% | roughly 3 hours | | $1,500 to $4,999 | roughly 31% | roughly 4 to 5 hours | | $5,000 to $14,999 | roughly 14% | roughly 6 to 7 hours | | $15,000 to $49,999 | roughly 5% | roughly 8 to 10 hours | | $50,000 and above | roughly 1% | roughly 12 hours and up |

Action title for designer: "The denial that lands on the kitchen counter is most often a four-figure denial in the highest-expected-value band. The math favors appealing across roughly three-quarters of the caseload, and the share rises further when precedent and plan-language value are counted."

Exhibit 3: The hidden value beyond the immediate denial

The expected-recovery figure captures only the dollars on the specific claim. Three additional value streams sit outside that figure.

| Hidden value category | What it does | Why it matters | |---|---|---| | Precedent value | Future claims for the same recurring service tend to clear without the friction that produced the original denial | The expected value of the first appeal includes the avoided costs of the appeals the patient never has to file | | Plan-language forcing | Statutory document request under 29 CFR 2560.503-1(h) or 45 CFR 147.136(b) produces the operative plan documents the patient never otherwise sees | Patients consistently discover other covered services they assumed were not, and exclusions cited in casual communications that do not exist in the operative document | | Deterrent value | Carriers' utilization-management programs are calibrated against the appeal rate; patients with successful appeals on file score differently on subsequent claims | Marginal but persistent reduction in denial rates on future claims, controlling for service mix, visible in the data but not advertised by carriers |

Action title for designer: "The dollar on the denial letter is the visible value. The precedent, the plan language, and the deterrent are the invisible values. The patient who appeals is collecting all four. The patient who walks away is leaving three of them on the table without realizing it."

Why the deck is procedurally tilted

The worksheet is straightforward arithmetic. The inputs are not. Reversal probability is not a single number; it varies by carrier, by denial archetype, by the strength of the underlying clinical record, by the state of external review, and by whether the appeal cites the right CFR section. The carrier-by-denial-type cells Apellica has catalogued (more than two hundred in total) each carry their own published external-review pattern, and the difference between a free-form letter and a properly-documented appeal is the difference between a marginal-EV case and a clear one.

Time-to-assemble is also not a single number. A bulletin-anchored appeal requires reading the bulletin, indexing the medical record against its criteria, pulling the relevant peer-reviewed literature at the bulletin's evidence tier, and drafting the four-part letter. The 30-day document-request right under 29 CFR 2560.503-1(h)(2)(iii) or 45 CFR 147.136(b)(2)(ii)(C) sits on top of that. The indexed Administrative Law Judge precedent library that covers Medicare Advantage Subpart M appeals is the appeal lawyer's working reference, not the patient's. Procedural exhaustion missteps can foreclose external review and reset the expected-value calculation to zero.

The patient sitting at the kitchen table with a denial letter does not have a calibrated reversal-probability number. Apellica does.

A small denial is not a small case. The math is the same arithmetic. Most patients run it on the wrong number.

What the senior-reviewer desk adds

Apellica's senior reviewers work from a mapped intelligence file covering more than two hundred carrier-by-denial-type cells that supplies the calibrated reversal-probability number for every case the desk takes on. The desk knows which archetypes reverse readily on first filing and which require external review to clear, which carriers honor the documented-foothold structure and which require additional procedural pressure.

Apellica's senior reviewers build the four-part evidence stack, plan-language citation, clinical facts, peer-reviewed evidence at the carrier's stated evidence tier, regulatory hook, for every case. A senior reviewer reads every appeal before it goes out. The desk will also tell a patient honestly when the cost-benefit math does not support appealing.

Initial review is free. There is no upfront fee. Patients are not asked to pay anything until the carrier reverses the denial.

Most patients leave coverage on the table because the appeal is more procedural work than they can take on.

The Phoenix paralegal's check arrived eleven weeks after she pulled the letter back out of the drawer. Three hours of evenings. Three hundred dollars an hour. The denial that "wasn't worth her time" had been worth a quarter of a working month's net pay.

What the engagement looks like

Apellica prepares the evidence-based appeal letter. The patient reviews and approves every word before submission and authorizes carrier communications under a HIPAA-compliant Assignment of Benefits. We are not a law firm. We are not a medical provider. We are not an insurance carrier. We are an independent administrative service that turns a denied claim into a properly documented appeal letter, and we will tell a patient honestly when the cost-benefit math does not support appealing.

Our model is $0 upfront and a flat fee on successful recovery. If the appeal does not reverse, the patient owes nothing for the preparation work. Coverage extends to all 50 states, all ACA plans, all Medicare Advantage plans, all ERISA self-funded plans, and commercial coverage. A senior reviewer reads every case before it goes out.

About the author

Mark Henderson works on the senior-reviewer desk at Apellica. The firm prepares insurance-denial appeals for patients across the United States and is headquartered at One World Trade Center, Suite 8500, New York, NY 10007. Apellica does not practice law and the work product is not legal advice. The phone line is +1 (888) 777-6120; the inbox is press@apellica.com; the site is apellica.com.

References

• 45 CFR 147.136. ACA Internal Claims and Appeals and External Review.
• 29 CFR 2560.503-1. ERISA Claims Procedure.
• 42 CFR Part 422, Subpart M. Medicare Advantage Grievances and Appeals.
• 42 CFR 422.582. Request for a standard reconsideration.
• KFF analysis of Medicare Advantage prior-authorization data, 2023 reporting year. kff.org.
• Commonwealth Fund, claims-denial volume estimates for commercial and Medicare Advantage plans.
• ProPublica, "How to Fight Your Health Insurance Denial With an External Appeal."
• National Association of Insurance Commissioners Consumer Information Source. content.naic.org/consumer.htm.
• Department of Labor EBSA. askebsa.dol.gov.
• Patient Advocate Foundation. patientadvocate.org.
• Apellica internal data across more than two hundred carrier-by-denial-type combinations, 2024-2025.