Actuarial value as the plan-paid share of total allowed cost

Divides the plan's total payment for covered care by the total allowed cost of that care, both summed over a standard population for one benefit year. The population is held as G spending groups of n_g people with the same allowed cost per person, the layout of the article's worked example and of a continuance table. With one person in every group the formula is the article's ratio of summed plan payments to summed allowed costs over N people, and it equals 1 minus the members' share of total allowed cost.

Signature

AV = sum_(g=1)^G [n_g * P_g] / sum_(g=1)^G [n_g * X_g]
Inputs
InputsDefinitionUnit
n_gNumber of people in spending group g of the standard population, one value per groupcount
P_gAmount the plan pays per person in group g under its cost-sharing rulescurrency per person
X_gAllowed cost of covered care per person in group g over the benefit year, equal to the plan payment plus the member's cost sharingcurrency per person, for example dollars
Output
AVShare of the total allowed cost of covered care paid by the plan for the standard populationproportion, usually reported as a percentage
  • G Number of spending groups, equal to the length of the n_g, X_g and P_g lists (count)

Function

Actuarial value calculation function for health plan cost sharing

Maps a health plan's cost-sharing rules and the allowed costs of a standard population over one benefit year to the share of those costs that the plan pays. Each person's allowed cost is split into the cost sharing paid by the member and the remainder paid by the plan, and the plan's total is divided by the total allowed cost. The records follow the notation of the Actuarial Value article, where X is allowed cost, S is cost sharing and P is the plan payment. Premiums appear in neither term.

Computational function

  • Computational function: plan design and spending distribution to actuarial value

    Takes a plan design, the deductible, the member's coinsurance rate and the out-of-pocket maximum, together with a spending distribution for the standard population, and returns the actuarial value. It applies the member cost-sharing formula HE-FM-AV-002 to the allowed cost of each spending group, takes the plan payment as the remainder and then forms the ratio HE-FM-AV-001, so its inputs are the plan terms rather than the plan payments that the ratio needs. This is the core of what the federal AV Calculator does with its continuance tables, without the copayment, service-type and interpolation steps.

    Inputs and outputs: D: Annual deductible; required, zero or above. Unit: currency.; c: Member coinsurance rate after the deductible, as a decimal; required, zero or above and no more than 1. Unit: proportion.; M: Annual out-of-pocket maximum, not below D; required. Unit: currency.; n_g: Number of people in each spending group; required, one value per group. Unit: count.; X_g: Allowed cost per person in each spending group; required, one value per group. Unit: currency per person.; G: Number of spending groups. Unit: count.; S_g: Member cost sharing per person in each group, returned. Unit: currency per person.; P_g: Plan payment per person in each group, returned. Unit: currency per person.; AV: Actuarial value of the design for the population. Unit: proportion, usually reported as a percentage.

    Assumption: Everyone in a group has the same allowed cost, the plan has one deductible, one coinsurance rate and one out-of-pocket maximum with no copayments, and spending does not change with the design. The federal calculator instead uses finer spending buckets and metal-level continuance tables that allow for induced demand.

    Worked example (Illustrative $2,000 deductible plan over five spending groups): The article's plan and population give member payments of $500 to $6,000 per person, plan payments of $0 to $144,000 and an actuarial value of about 0.7396 (74.0%). D = 2000; c = 0.2; M = 6000; n_g = [40, 30, 20, 8, 2]; X_g = [500, 2500, 8000, 30000, 150000]; G = 5; S_g = [500, 2100, 3200, 6000, 6000]; P_g = [0, 400, 4800, 24000, 144000]; AV = 0.7396

    Worked example (Deductible cut to $1,000): The same population with a $1,000 deductible gives an actuarial value of about 0.7899 (79.0%), with spending held fixed. D = 1000; c = 0.2; M = 6000; n_g = [40, 30, 20, 8, 2]; X_g = [500, 2500, 8000, 30000, 150000]; G = 5; S_g = [500, 1300, 2400, 6000, 6000]; P_g = [0, 1200, 5600, 24000, 144000]; AV = 0.7899

    Worked example (No cost sharing gives full cover): With a zero deductible, zero coinsurance and a zero out-of-pocket maximum the plan pays every allowed cost and the actuarial value is 1, a limiting case that checks the implementation. D = 0; c = 0; M = 0; n_g = [40, 30, 20, 8, 2]; X_g = [500, 2500, 8000, 30000, 150000]; G = 5; S_g = [0, 0, 0, 0, 0]; P_g = [500, 2500, 8000, 30000, 150000]; AV = 1

    Excel: =LET(t,Allowed-(1-Coins)*(Allowed>Deductible)*(Allowed-Deductible),s,t-(t>OOPMax)*(t-OOPMax),SUMPRODUCT(People,Allowed-s)/SUMPRODUCT(People,Allowed)) With the people per group in People and the allowed cost per person in Allowed (ranges of the same size) and the plan terms in Deductible, Coins and OOPMax, the formula returns the actuarial value in Excel 2021 or Microsoft 365. Inside LET, t is the deductible plus coinsurance before the cap and s is the capped member payment for each group.

    R: actuarial_value <- function(n, x, D, c, M) { s <- pmin(M, pmin(x, D) + c*pmax(0, x-D)); sum(n*(x-s)) / sum(n*x) } Vectorised over the groups with pmin and pmax; n and x are numeric vectors of the same length.

    Python: def actuarial_value(n, x, D, c, M): s = [min(M, min(xi, D) + c*max(0, xi-D)) for xi in x]; return sum(ni*(xi-si) for ni, xi, si in zip(n, x, s)) / sum(ni*xi for ni, xi in zip(n, x)) Takes lists of group sizes and allowed costs and needs no imports.

    Test (Plan and member totals add to total allowed cost): With helper columns PlanPays and MemberPays holding P_g and S_g for each group, the plan and member totals add to the total allowed cost. Expected result: TRUE. Excel check: =ABS(SUMPRODUCT(People,PlanPays)+SUMPRODUCT(People,MemberPays)-SUMPRODUCT(People,Allowed))<1E-6

    Test (No member pays more than the out-of-pocket maximum): The largest member payment in any group does not exceed the maximum. Expected result: TRUE. Excel check: =MAX(MemberPays)<=OOPMax

    Common error (Leaving out the group sizes): Dividing the sum of plan payments per person by the sum of allowed costs per person, without weighting by n_g, gives about 0.907 for the article's plan instead of 0.740, because the two very high spenders then count as much as the 40 low spenders.

    Source: Centers for Medicare & Medicaid Services, Center for Consumer Information and Insurance Oversight. Final 2027 Actuarial Value (AV) Calculator Methodology. Washington, DC: CMS; 25 February 2026. Sections Constructing Continuance Tables (a continuance table describes the distribution of claims spending, ranked by allowed charges and grouped by ranges of spending) and Calculating AV, Steps 2 and 4 to 9.

    S_g = min(M, min(X_g, D) + c * max(0, X_g - D)); P_g = X_g - S_g; AV = sum_(g=1)^G [n_g * P_g] / sum_(g=1)^G [n_g * X_g]

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Implementations

  • Excel

    Actuarial value from spending-group ranges with SUMPRODUCT

    With the people per group in a range named People, the allowed cost per person in Allowed and the plan payment per person in PlanPays, all of the same size, Excel returns the actuarial value as a proportion. The cell can be formatted as a percentage.

    =SUMPRODUCT(People,PlanPays)/SUMPRODUCT(People,Allowed)

Assumptions

  • Fixed standard population for actuarial value

    The population and its allowed costs are fixed by the regulator or analyst for the benefit year, not taken from the plan's own members, so plans with different designs are ranked on the same spending. In the US the standard population is the one built into the HHS AV Calculator for that benefit year.

  • Allowed costs of covered services only in actuarial value

    Both totals cover the allowed costs of covered services, and the US calculator estimates in-network spending only. Premiums, provider networks, excluded services and out-of-network charges enter neither term.

  • Spending held fixed when the plan design changes

    The formula takes allowed costs as given. When a design is changed, the article's example keeps spending fixed, whereas the federal calculator switches to the continuance tables for the plan's metal level to allow for induced demand, so its result would differ.

Worked examples

  • Actuarial value of an illustrative $2,000 deductible plan

    A standard population of 100 people in five spending groups faces a deductible of $2,000, member coinsurance of 20% and an out-of-pocket maximum of $6,000. The plan pays $588,000 of $795,000 in allowed costs, an actuarial value of about 0.7396 (74.0%), between the silver and gold targets. All figures are illustrative.

    n_g = [40, 30, 20, 8, 2]; X_g = [500, 2500, 8000, 30000, 150000]; P_g = [0, 400, 4800, 24000, 144000]; G = 5; AV = 0.7396

  • Actuarial value after cutting the illustrative deductible to $1,000

    Cutting the deductible to $1,000 with the other terms unchanged raises the plan payment to $1,200 per person in the moderate group and $5,600 in the higher group, and the plan's total to $628,000. The actuarial value rises to about 0.7899 (79.0%). Spending is held fixed, as in the article.

    n_g = [40, 30, 20, 8, 2]; X_g = [500, 2500, 8000, 30000, 150000]; P_g = [0, 1200, 5600, 24000, 144000]; G = 5; AV = 0.7899

Common errors

  • Averaging each person's plan share instead of dividing totals

    Averaging the plan's share of each person's allowed cost gives about 0.251 in the article's example, against an actuarial value of about 0.740. Spending is skewed, so the ten heaviest users dominate the totals while 90 of the 100 people have less than 74% of their own costs paid and 40 have nothing paid. The actuarial value is a population average and does not predict what any one member will pay.

  • Comparing actuarial values from different standard populations

    A change in the claims data behind the standard population, or a new calculator version, changes the result for an unchanged plan design. Actuarial values from different benefit years or calculator versions therefore cannot be compared as if the plans had changed.

Sources

  • US regulatory definition of the percentage of total allowed costs

    Code of Federal Regulations. Title 45, section 156.20, definition of percentage of the total allowed costs of benefits: anticipated covered medical spending for EHB coverage paid by a health plan for a standard population, computed in accordance with the plan's cost sharing, divided by the total anticipated allowed charges and expressed as a percentage. Electronic Code of Federal Regulations, text current to 29 September 2026.

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  • CMS 2027 AV Calculator numerator and denominator

    Centers for Medicare & Medicaid Services, Center for Consumer Information and Insurance Oversight. Final 2027 Actuarial Value (AV) Calculator Methodology. Washington, DC: CMS; 25 February 2026. Section Calculating AV, Step 2 (the denominator is the average allowed cost over all enrollees) and Step 9 (the numerator of plan-covered expenses is divided by the denominator).

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  • Simulation showing actuarial value overstates realised coverage

    Polyakova M, Hua LM, Bundorf MK. Marketplace plans provide risk protection, but actuarial values overstate realized coverage for most enrollees. Health Affairs. 2017;36(12):2078-2084. Abstract: for most consumers the share of covered spending paid by the plan is likely to be well below its actuarial value.

    View source →

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