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OPINION

ROSEMARY M. COLLYER, United States District Judge

Seemingly intended to test the mathematical acumen of counsel and court, this case arises .out of the legislative and regulatory thicket that is Medicare reimbursement. At issue is a congressional mandate that requires the Secretary of Health and Human Services to. adjust annually one component of the Medicare reimbursement formulas in a budget neutral manner, so that it is not the cause of either higher or lower overall Medicare hospital reimbursements from one year to the next. Plaintiffs are hospitals that serve rural communities or the uninsured poor; they sue the Secretary for shortchanging their reimbursements in specific fiscal years. Plaintiffs allege that the Secretary has deprived them of millions of dollars in Medicare reimbursements by improperly achieving budget neutrality through changes to their reimbursement rates rather than through adjustments to the mandated component of the rate formula. Unsurprisingly, the Secretary disagrees. Out of the parties’ arguments concerning numerators, denominators, and quotients, a more familiar question has emerged; is the Secretary’s methodology a rational interpretation of the Medicare Act to which the Court should defer? Because the Court answers this question affirmatively, it will grant summary judgment to the Secretary.

I. FACTS

On February 7, 2011, sixty-two sole community hospitals (SCHs) and Mediearede-pendent, small rural hospitals (MDHs) filed a three-count Complaint against Kathleen Sebelius, in her official capacity as Secretary of Health and Human Services (HHS). Only Counts II and III are relevant here: Plaintiff Hospitals contend that the Secretary erroneously calculated their Medicare reimbursements starting in Fiscal Year 2009. See Compl. [Dkt. 1], They claim that the Secretary has failed to follow clear congressional directions in the Medicare Act, see 42 U.S.C. § 1395ww(d)(4)(C)(iii), and, in so doing, her erroneous calculations are both ultra vires and arbitrary and capricious in violation of the Administrative Procedure Act (APA), 5 U.S.C. §§ 701 et seq. See Compl. ¶¶ 28-29, 33-34. Accordingly, the Court must embark upon a journey through the “labyrinthine world of Medicare.” Adirondack Med. Ctr. v. Sebelius, 740 F.3d 692, 694 (D.C.Cir.2014).

A. Basics of Medicare Reimbursements

The Centers for Medicare and Medicaid Services (CMS), a division of HHS, administers Medicare under the executive management of the Secretary, see 42 U.S.C. §§ 1395 et seq. To incentivize hospitals serving Medicare patients to control costs, Congress revised the Medicare reimbursement scheme in 1983 and established the Inpatient Prospective Payment System (IPPS). See Methodist Hosp. of Sacramento v. Shalala, 38 F.3d 1225, 1227 (D.C.Cir.1994) (describing the transition in 1983 to IPPS and explaining that it was “designed ... to encourage health care providers to improve efficiency and reduce operating costs”). Under IPPS, the Secretary informs all hospitals, before a fiscal year begins, of the “rates at which their services will be reimbursed, regardless of costs actually incurred.” Id.; see also 42 U.S.C. § 1395ww(d). This litigation concerns two of the factors used in calculating prospective Medicare reimbursement rates: Diagnosis-Related Groups (DRG) and Budget Neutrality Adjustments (occasionally, BNA).

1. Diagnosis-Related Groups

As the Circuit has succinctly explained, “a DRG is a category of inpatient treatment.” Adirondack Med. Ctr., 740 F.3d at 694 n. 1. It attempts to account for the fact that “the costs of treating patients vary based on the patients’ diagnoses.” Cape Cod Hosp. v. Sebelius, 630 F.3d 203, 205 (D.C.Cir.2011). Accordingly, Medicare patients are assigned a DRG based on their diagnosis at the time of discharge. Each DRG is associated with “a particular “weight’ [that] represents] the relationship between the cost of treating patients within that group and the average cost of treating all Medicare patients.” Id. at 205-06 (citing 42 U.S.C. § 1395ww(d)(4)). There are hundreds of different DRGs, see State of Florida, Office of Attorney General, Department of Legal Affairs v. Tenet Healthcare Corp., 420 F.Supp.2d 1288, 1293 (S.D.Fla.2005), with individual weights ranging from less than 1.000 to more than 7.000 and an average weight, in theory, of 1.000, Tr. of Feb. 25, 2013 Hr’g [Dkt. 38] at 8.T-3. In other words, if the theoretical DRG weight for the average cost of a patient’s in-hospital' treatment were 1.000, then “a case using twice as many resources as the average case would be assigned the value of 2, and a case using only half the resources as the average case would have a weight of 0.5.” Am. Health Lawyers Ass’n, supra, § 3 — 2(b). The upshot of applying a DRG weighting factor is that “a hospital -will be paid more for patients diagnosed with a heart condition requiring surgery than for those diagnosed with a sprained ankle.” Def. Mot. for Summ. J. [Dkt. 23] at 4.

Starting in Fiscal Year 1988, Congress required the Secretary to adjust DRG weighting factors “at least annually ... to reflect changes in treatment patterns, technology ..., and other factors which may change the relative use of hospital resources.” 42 U.S.C. § 1395ww(d)(4)(C)(i). Then, in Fiscal Year 1991, see Decl. of Tzvi Hefter [Dkt. 40] ¶ 4, Congress directed the Secretary to ensure that the annual adjustments to DRG weighting factors not result in an overall increase in projected aggregate IPPS payments, 42 U.S.C. § 1395ww(d)(4)(C)(iii). Specifically, the annual DRG recalibration must “be made in a manner that assures that the aggregate payments ... for discharges in the fiscal year are not greater or less than those that would have been made for discharges in the year without such adjustment.” Id. The parties agree that this subsection of Medicare stands for the proposition that other factors might increase the cost of Medicare reimbursements but the Secretary must ensure that annual changes to DRG weights have a budget-neutral effect.

In connection with recalibrating DRG weights each year, the Secretary “normalizes” the weights so that the “average case weight after recalibration is equal to the average case weight prior to recalibration.” Rulemaking R. (74 Fed.Reg. 24080 (May 22', 2009)) [Dkt. 20] at 106. The Secretary has determined, however, that normalization alone does not achieve budget neutrality for recalibrated DRGs. See id. (“While [normalization] is intended to ensure that reealibration does not affect total payments to hospitals, ... [the Secretary’s] analysis ... indicate^] that "the normalization adjustment does not achieve budget neutrality with respect to aggregate payments to hospitals.... ”). As a result, the Secretary calculates an additional adjustment — a so-called Budget Neutrality Adjustment — to satisfy the congressional directive that changes to DRG weighting factors not increase projected aggregate IPPS payments. Id.

2. The Budget Neutrality Adjustment

The Secretary calculates the Budget Neutrality Adjustment by way of payment simulations. She computes a budget neutrality factor by comparing “estimated aggregate payments using the current year’s relative weights and factors to aggregate payments using the prior year’s relative weights and factors.” Id. As the Secretary explained in the preamble to the notice of a final rule revising IPPS and Fiscal Year 1991 rates, which she published in the Federal Register in 1990, this “methodology effectively isolate[s] the impact of changes in the relative weights,” and, therefore, “provide[s] a proper basis for computing the [BNA] factor.” 55 Fed. Reg. 35990, 36074 (Sept. 4,1990).

In 1993, in conjunction with publishing notice in the Federal Register of a final rule that altered certain aspects of IPPS and Fiscal Year 1994 rates, the Secretary addressed the cumulative application of the Budget Neutrality Adjustment. The preamble to the 1993 Final Rule explained that in calculating and applying the budget neutrality factor for a future fiscal year, no attempt is made to remove the effect of prior years’ neutrality adjustments. See 58 Fed.Reg. 46270, 46346 (Sept. 1, 1993). In the Secretary’s view, a cumulative Budget Neutrality Adjustment is mandated by the language of 42 U.S.C. § 1395ww(d)(4)(C)(iii) and the nature of the hospital-specific rate. “She do[es] not remove the prior budget neutrality adjustments] because the statute requires that aggregate payments after the changes in the DRG relative weights ... equal estimated payments prior to the changes. If [the Secretary] removed the prior year adjustment, [she] would not be able to satisfy this condition.” Id. If the adjusted DRG weights were not further adjusted for budget neutrality, then, according to the Secretary, “the hospital-specific amounts would be artificially high” which would “result[] in higher aggregate payments than permitted under the statute.” Rulemaking R. at 106.

Thus, the Secretary has applied a cumulative Budget Neutrality Adjustment in each successive fiscal year for more than two decades. Stated differently, since 1994, the Secretary has not removed the effects of prior years’ Adjustments when calculating the Budget Neutrality Adjustment for the upcoming fiscal year. It is the manner in which the Secretary applies the annual Budget Neutrality Adjustment to the hospital-specific rate by which Plaintiffs are reimbursed which is at the heart of this case.

B. Medicare Reimbursement Formulas

Each Plaintiff Hospital in the instant litigation has been designated either an SCH or an MDH under Medicare. See 42 ' U.S.C. § 1395ww(d)(5)(D)(iii) (defining SCH); id. § 1395ww(d)(5)(G)(iv) (defining MDH). SCHs and MDHs are reimbursed for inpatient treatment based on the “federal rate” or the “hospital-specific rate.”

1. The Federal Rate

Most IPPS hospitals are reimbursed under the “federal rate.” See 42 C.F.R. § 412.64. To calculate the federal rate, “Medicare authorities first construct a standard nationwide cost rate ... based on the average operating costs of inpatient hospital services.” Methodist Hosp., 38 F.3d at 1227. This figure, which is known as the “average standardized amount,” or, more simply, the “standardized amount,” averages the operating costs of all IPPS hospitals, including SCHs and MDHs. See 42 C.F.R. 412.64(g). Each year, the standardized amount is updated for inflation, based on an “applicable percentage increase,” 42 U.S.C. § 1395ww(b)(3)(B), that is taken from a “market basket index,” 42 C.F.R. § 412.64(d). Once an updated standardized amount is calculated, the Secretary multiples it by the Budget Neutrality Adjustment for the upcoming year. See 42 U.S.C. §§ 1395ww(d)(3)(C); see, e.g., 58 Fed.Reg. at 46358 (explaining the calculation of the federal rate for Fiscal Year 1994 and noting that the Budget Neutrality Adjustment “is applied to the standard Federal payment rate”). To calculate the actual reimbursement to most IPPS hospitals for specific inpatient care, the product of'the standardized amount and the Budget Neutrality Adjustment is multiplied by the DRG weight that corresponds to the patient’s diagnosis at discharge. See 42 U.S.C. § 1395ww(d)(3)(D). The result is the amount of reimbursement the hospital will receive under the federal rate for the patient’s in-hospital care, regardless of actual cost.

2. The Hospital-Specific Rate

Because SCHs and MDHs provide critical services to the underserved and uninsured, Congress has adopted special payment provisions for them. Adirondack Med. Ctr., 740 F.3d at 694. However, reimbursement calculations for SCHs and MDHs are different. “Reimbursements for [SCHs] are fairly straightforward— such hospitals are paid the higher of either the federal rate or the hospital-specific rate.” Id. at 695 n.2. Reimbursement to MDHs is slightly more complicated. MDHs receive a rate that “is calculated by taking the federal rate and adding 75% of the difference between the federal rate payment and the hospital-specific rate payment.” Id.; see 42 U.S.C. §§ 1395ww(d)(5)(D) & (G); 42 C.F.R. §§ 412.92, 412.108. The hospital-specific rate is particular to each of Plaintiff Hospitals. It “is calculated with a base amount derived not from national data, but from historic operating costs at [the] individual hospital.” Adirondack Med. Ctr., 740 F.3d at 695.

Calculating the hospital-specific rate for an SCH or MDH is a relatively simple, three-step process. First, the hospital’s historic average cost per patient in a particular base year is divided by the average patient DRG weight for that base year, repeated for each base year authorized by Congress. See, e.g., 42 C.F.R. §§ 412.73(a)-(b), 412.75(b)-(c), 412.77(c)-(d), 412.78(c) — (d), 412.79(b)-(c); 412.92(d); 412.108(c). Second, the highest resulting quotient is multiplied by an update factor. See Joint Statement [Dkt. 36] at 2. (“[T]o account for inflation ... between the base year period and the payment year period, CMS applies an update factor to the hospital’s average case-mixed adjusted base-period operating cost per discharge.”). That product is further multiplied