Chicago Truck Drivers, Helpers & Warehouse Workers Union (Independent) Pension Fund v. CPC Logistics, Inc.

POSNER, Circuit Judge. This appeal from a decision upholding an arbitrator’s award is about what happens when an employer withdraws from a multiemployer defined-benefits pension plan, as the appellee, CPC, did in 2005. Multiemployer pension plans — which are governed, as single-employer plans are, by ERISA — are created by collective bargaining agreements to provide benefits to employees of many different firms. Thus they are found in industries such as construction and trucking in which workers do short-term, seasonal, or irregular work for many different employers over their working lives. 29 U.S.C. § 1002(37)(A); John H. Langbein et al., Pension and Employee Benefit Law 70-75 (5th ed.2010). When an employer withdraws from such a plan, the plan remains liable to the employees who have vested pension rights, though it no longer can look to the employer to contribute additional funds to cover these obligations. In an effort to prevent withdrawals that will shift the burden of funding the pension plan to the remaining employers and by doing so may precipitate additional withdrawals, provisions added to ERISA by the Multiemployer Pension Plan Amendments Act of 1980, 29 U.S.C. §§ 1381-1461, assess the employer with an exit price equal to its pro rata share of the pension plan’s funding shortfall. The shortfall (“unfunded vested benefits”) is the difference between the present value of the pension fund’s assets and the present value of its future obligations to employees covered by the pension plan. 29 U.S.C. §§ 1381, 1391. (If the present val *348 ue of the assets exceeds the present value of the plan’s future obligations, there is no shortfall.) Estimation of the shortfall depends critically on estimating the amount by which the fund’s current assets can be expected to grow by the miracle of compound interest. The higher the estimated rate of growth, the less the employers must put into the fund today to cover the future entitlements of the plan’s participants and beneficiaries. “[F]or a typical plan, a change (upward or downward) of 1 percent in the interest assumption (e.g. an increase from 6 to 7 percent) alters the long-run cost estimate by about 25 percent.” Dan M. McGill et al., Fundamentals of Private Pensions 612 (8th ed.2005); see also Artistic Carton v. Paper Industry Union-Management Pension Fund, 971 F.2d 1346, 1348 (7th Cir.1992). In addition to estimating the size of the plan’s funding shortfall, the pension plan must apportion responsibility for the shortfall among the employers participating in the plan. Each employer must pay his share to the fund if and when he withdraws, so that the plan can pay the employer’s share of the plan’s unfunded vested benefits as those benefits come due in the future. An employer who has just joined the plan may worry about inheriting withdrawal liability because the existing members failed to fund the plan adequately in prior years. To alleviate this worry, ERISA creates default rules (that is, rules that govern unless the plan provides otherwise) for assigning each participating employer a share of only so much of the plan’s funding shortfall as occurred while the employer was participating in the plan. 29 U.S.C. § 1391(b)(2)-(4); 29 C.F.R. § 4211.32; CenTra, Inc. v. Central States, Southeast & Southwest Areas Pension Fund, 578 F.3d 592, 599-600 and n. 7 (7th Cir.2009); Israel Goldowitz & Ralph L. Landy, “Special Rules for Multiemployer Plans,” in ERISA Litigation 1292-95 (Jayne E. Zanglein et al. eds., 4th ed.2011). The plan in this case used these rules to calculate the pro rata share of the funding shortfall to be borne by the withdrawing employer, appellee CPC. The rules calculate withdrawal liability in steps. The first is to determine annual “pools” of liability, each representing the change (which might be an increase or a decrease) in the plan’s total funding shortfall from one year to the next. The previous pools (that is, the previous annual changes in unfunded vested benefits) are then discounted by 5 percent a year (so, for example, a pool from seven years earlier would be discounted by 35 percent). As a result, after 20 years a pool no longer affects withdrawal liability. The rationale for discounting is that with the passage of years, funded benefits are more likely to have been paid and so no longer be owing. Next, each discounted pool is apportioned among the employers participating in the plan on the basis of their contributions to the pension fund in the pool year and the four years preceding. The five-year window measures the size of an employer’s contributions to the fund relative to the other employers in the short term, on the theory, related to the 20-year discounting, that recent experience has greater predictive significance. The window is five years rather than just one in order to smooth trends in contribution, so that a year of anomalous contributions doesn’t drastically alter the allocation shares among employers. (Thus an employer who contributed a lot in 2004 but almost nothing from 2000 to 2003 would not be assessed a large chunk of the 2004 liability pool — the brief spike would be smoothed by the inclusion of the preceding years.) An employer’s withdrawal liability is the sum of his fractional share, calculated on *349 the basis of his last five years’ contributions, of the 20 pools. The table below presents a slightly simplified version of how CPC’s withdrawal liability was determined. The annual pool is calculated first. (Notice that for years in which the plan’s funding shortfall decreased — for example, 1985-1986 and 1995-1998 — the pools are negative. Each employer’s share of negative pools reduces his withdrawal liability.) The pools are discounted at 5 percent per year. The discounted pools are then divided among the employers on the basis of their relative contributions in the pool year and the four prior years (CPC made 3.67 percent of all contributions to the fund from 2000 to 2004 and 1.42 percent of all contributions from 1985 to 1989.) Its withdrawal liability (exit price) was thus the sum of its shares of each of the discounted pools from 1985 to 2004. 100% Minus Discounted CPC’s Relative CPC’s Share of Year Pool Discount Rate Pool Contribution Each Pool 2004 $56,171,305 x 100% = $56,171,305 x 3.67% = $2,061,487 2003 $39,092,526 x 95% = $37,137,900 x 2.75% = $1,021,292 2002 $8,587,297 x 90% = $7,728,567 x 1.65% = $127,521. 2001 $7,960,547 x 85% = $6,766,465 x 1.44% = $97,437 2000 $2,768,374 x 80% = $2,214,699 x 1.26% = $27,905 1999 $6,044,832 x 75% = $4,533,624 x 1.28% = $58,030 1998 -$14,106,445 x 70% = -$9,874,512 x 1.06% = -$104,670 1997 -$2,854,709 x 65% = -$1,855,561 x 0.82% = -$15,216 1996 -$3,878,390 x 60% = -$2,327,034 x 0.56% = -$13,031 1995 -$7,226,847 x 55% = -$3,974,766 x 0.49% = -$19,476 1994 $13,469,192 x 50% = $6,734,596 x 0.46% = $30,979 1993 $9,433,992 x 45% = $4,245,296 x 0.59% = $25,047 1992 $3,155,707 x 40% = $1,262,283 x 0.78% = $9,846 1991 $6,080,864 x 35% = $2,128,302 x 1.04% = $22,134 1990 $2,031,775 x 30% = $609,533 x 1.23% = $7,497 1989 $7,118,643 x 25% = $1,779,661 x 1.42% = $25,271 1988 $9,804,517 x 20% = $1,960,903 x 1.59% = $31,178 1987 $22,647,445 x 15% = $3,397,117 x 1.66% = $56,392 1986 -$13,247,195 x 10% = -1,324,720 x 1.61% = -$21,328 1985 -$381,233 x 5% = -$19,062 x 1.49% = -$284 CPC’s Withdrawal Liability: $3,428,013 Disputes over withdrawal liability are resolved by arbitration, 29 U.S.C. § 1401(a)(1); Chicago Truck Drivers v. El Paso CGP Co., 525 F.3d 591, 595 (7th Cir.2008), subject however to judicial review similar in scope to appellate review of district court decisions. Central States, Southeast & Southwest Areas Pension Fund v. Midwest Motor Express, Inc., 181 F.3d 799, 804-05 (7th Cir.1999); Board of *350 Trustees, Sheet Metal Workers’ National Pension Fund v. BES Services, Inc., 469 F.3d 369, 375 (4th Cir.2006). The arbitrator in the present case ruled that the pension plan’s trustees had overassessed CPC’s withdrawal liability by $1,093,000 (almost a third of its total assessment — the $3.4 million figure in the table). The district judge upheld the arbitrator’s ruling, and the plan and one of its trustees (but we can ignore him) appeal. Appellate review of the district court’s decision is plenary, in the sense that the court of appeals like the district court is reviewing the arbitrator’s decision, see CenTra, Inc. v. Central States, Southeast & Southwest Areas Pension Fund, supra, 578 F.3d at 602; Joseph Schutz Brewing Co. v. Milwaukee Brewery Workers’ Pension Plan, 3 F.3d 994, 1000 (7th Cir.1993), affirmed, 513 U.S. 414, 115 S.Ct. 981, 130 L.Ed.2d 932 (1995); Central States, Southeast & Southwest Areas Health & Welfare Fund v. Cullum Cos., 973 F.2d 1333, 1335 (7th Cir.1992), and thus not deferring to the district court’s ruling. This is the same pattern that is observed when a court of appeals reviews a decision by a district court to which an administrative law judge’s decision denying social security disability benefits has been appealed. McKinzey v. Astrue, 641 F.3d 884, 889 (7th Cir.2011); O’Connor-Spinner v. As true, 627 F.3d 614, 618 (7th Cir.2010). It is the arbitrator’s decision, like the administrative law judge’s, that receives judicial deference, from both the district court and the court of appeals. Hideous complexities lurk in the briefs in this appeal-. Many appellate lawyers write briefs and make oral arguments that assume that judges are knowledgeable about every field of law, however specialized. The assumption is incorrect. Federal judges are generalists. Individual judges often have specialized knowledge of a few fields of law, most commonly criminal law and sentencing, civil and criminal procedure, and federal jurisdiction, because these fields generate issues that frequently recur, but sometimes of other fields as well depending on the judge’s career before he became a judge or on special interests developed by him since. But the appellate advocate must not count on appellate judges’ being intimate with his particular legal nook — with its special jargon, its analytical intricacies, its commercial setting, its mysteries. It’s difficult for specialists to write other than in jargon, and when they don’t realize the difficulty this poses for generalist judges neither do they realize the need to write differently. Federal pension law is a highly specialized field that judges encounter only intermittently. Yet the lawyers in this case made no allowance for our lacking their specialized knowledge. Consider this extract from the statement of facts in the appellant’s opening brief (record citations and footnotes omitted): Most multiemployer pension plans retain one plan actuary, and ask it to provide calculations for two purposes: (1) calculations which ERISA and the Internal Revenue Code (the “Code”) require the actuary to certify on Schedule B to the plan’s annual report; and (2) calculations the plan can use as the foundation for determining withdrawal liability.... The Fund’s actuary, the Segal Company (“Segal”), ... calculated UVB for withdrawal liability purposes using a series of steps rather than simply using the UVB from its Schedule B report. Segal’s approach, known as the “Segal Blend,” is to combine the interest rate from its Schedule B funding report with the average interest rates then current for annuities. Over the years Segal thus provided the Fund with one UVB for *351 funding and another for withdrawal liability. In 1993 ... the Supreme Court issued a decision that prompted Segal to issue a guidance memorandum to its actuaries dated March 29, 1994. The memorandum advised Segal actuaries that the Court’s decision in Concrete Pipe and Prods, v. Construction Laborers Pension Trust, 508 U.S. 602 [113 S.Ct. 2264, 124 L.Ed.2d 539] (1993), raised the question whether it was permissible for an actuary to have different numbers for the UVB in the withdrawal liability report and the Schedule B report. The memorandum suggested that client plan trustees be asked to make a decision telling Segal what to do and attached templates for memoranda to be provided to client trustees and plan counsel and a “Questions and Answers” section for actuaries to use in advising their clients on the decision. The gist of the templates was to advise client plans that Segal’s use of different assumptions in the two reports may create litigation risk for the clients. Two solutions were proposed for consideration. First, the trustees could direct Segal to continue to use the Segal Blend approach for withdrawal liability, which would continue to produce two different numbers for the plan’s unfunded vested benefits each year, one for the funding report and one for the withdrawal liability report. Second, the trustees could direct Segal to modify the steps used to determine the UVB for withdrawal liability: first calculate the UVB using the Blend assumptions, and then determine the UVB using the funding assxxmptions, with the latter setting an upper limit for the UVB. Using the lower number for the UVB each year, Segal reasoned, would eliminate the risk that an employer wouid complain that the UVB was too high.... [The trustees chose the latter option, passing a resolution] that the UVB would continue to be determined based upon the Segal Blend (“best estimate”) approach, subject to the directive that the UVB not be higher than the UVB reported by Segal to the IRS in Schedule B for that year. As it happened, CPC’s withdrawal liability assessment was significantly impacted by two factors. First, in 2004 the Fund repealed the 1997 resolution adopting the “cap” on the Segal Blend method, returning to always using the Segal Blend to determine UVB, resulting in the recapture of unfunded vested benefit liabilities of the Fund not previously recognized due to the operation of the cap. At precisely the same time, CPC’s share of the Fund’s total contribution base increased dramatically, from 1.26% in 2000 to 3.67% in 2004. The combination of these two factors served to create significantly higher liability for CPC than if it had happened to withdraw in a different year.... Here is a parallel discussion in the appellee’s brief (again we omit record citations and footnotes): In a memorandum dated Wednesday, April 4, 1997, the Client Relationship Manager from the Segal Company to the Fund ... discussed the Supreme Court’s 1993 decision in Concrete Pipe and Produces ] of California Inc. v. Construction Laborers Pension Trust for Southern California, 508 U.S. 602 [113 S.Ct. 2264, 124 L.Ed.2d 539] (1993). The memorandum advised that the Se-gal Blend remained the actuary’s best estimate for the interest assumption to be used in the calculation of the Fund’s UVBs for withdrawal liability purposes, and suggested that the Fund consult with legal counsel on the impact of the continued use of the Segal Blend.... *352 [The manager testified] that the memorandum provided the trustees “with an option to cap the unfunded liability.”. ... As a result ... the trustees required the actuary to apply a “cap” to the UVBs used to calculate the withdrawal liability pools from 1996 until 2004. As indicated in Segal’s withdrawal liability reports during the years that the cap applied, the cap limited UVBs “to be no greater than the vested liability calculated using the same investment return used for funding less the actuarial value of assets.” Thus, the funding interest assumption was used to calculate the UVBs that were the basis [of] the pool in all years when it produced lower UVBs than the Segal Blend interest assumption .... Evidence at the arbitration hearing confirmed that the trustees capped UVBs for the deliberate purpose of lowering withdrawal liability in order to attract employers to the Fund. Segal Chief Actuary Thomas Levy testified Segal came up with the Concrete Pipe option in 1996 because employers had come to Segal with concerns that “changing economic circumstances” would “severely adversely affect the willingness” of employers to support their plans, because it resulted in higher withdrawal liability assessments.... [Plan] Trustee William Carpenter conceded that the reason for adopting the cap was to lower withdrawal liability due to concerns at the time that higher withdrawal liability would put off employers and prospective employers who might come into the Fund. The trustee’s cap was removed in the 2004 withdrawal liability report.... [T]he trustees decided to remove the cap in order to raise withdrawal liability for departing employers and enhance the viability of the Fund at a time when the Fund was experiencing declining assets and declining membership. The selective decisions to cap and then uncap the UVBs had a significant impact on CPC’s assessed withdrawal liability. When the trustees uncapped UVBs in 2004, the UVBs nearly doubled from $67 million in 2003 to $117 million in 2004. Without the cap, portions of this increase in the UVBs would have been included in several of the earlier pools (and would have been subject to the statutory 5% per year reduction). Also significantly for CPC, much of the change attributed to 2004 would have been allocated to prior years when CPC’s relative percentage of contributions was lower. Employers, such as CPC, who had a larger percentage of the 2004 pool than they had during previous years, were disproportionately affected by the 2004 pool. Specifically, the concomitant result of the cap on the interest assumption in prior years and subsequent removal of the cap in 2004 was that the “sum allocable” to CPC for the 2004 pool was $2,075 million, compared to $1.45 million for all of the 19 previous pools combined. Because CPC was a larger contributor to the Fund in 2004 than it had been in prior years, if the trustees had used Segal’s best estimate assumptions for all years, CPC’s allocable share of the 2004 pool would have been only $353,452, resulting in a reduction of $1,093 million in CPC’s overall assessment. All this was terribly opaque to us because the parties had failed to provide context — failed to explain what exactly the pools are, why interest rates are important to withdrawal liability, what the “funding interest assumption” is, and why what they confusingly call a “cap” on the Segal Blended Rate (confusingly because in most years the “cap” required as we’ll see the *353 substitution of a higher rate than the Blended Rate) caused a loss to CPC when the “cap” was removed. And so at the oral argument one of the judges felt compelled to ask one of the lawyers, pleadingly, whether she could explain in words of one syllable what the case was about. She was a good lawyer and tried, but, perhaps surprised by the question, failed. We have had to fall back on a remark by Justice Holmes: “I long have said there is no such thing as a hard case. I am frightened weekly but always when you walk up to the lion and lay hold the hide comes off and the same old donkey of a question of law is underneath.” Holmes-Pollock Letters: The Correspondence of Mr. Justice Holmes and Sir Frederick Pollock, 1874-1932, vol. 1, p. 156 (Mark De Wolfe Howe ed.1941) (letter to Pollock of Dec. 11, 1909). We have applied ourselves to tugging the hide off this lion in search of the donkey underneath. We think we have found the donkey. We said earlier that estimating the interest rate at which the pension fund’s assets are likely to grow is required for determining withdrawal liability. Consider a plan that has $1 million in assets and expects to have a $5 million benefit obligation 20 years from now. If its assets are assumed to grow over this period at an annual rate of 6 percent, its funding shortfall — the difference, discounted to present value, between the $5 million it will owe and the assets it will have as a result of the compounding of the 6 percent interest — will be $505,971. If the plan’s assets and benefit obligation are unchanged at year’s end, its funding shortfall will have grown to $599,099, the increase being attributable to the fact that the benefit will be one year closer to falling due. The plan’s withdrawal liability pool will thus be $93,124, the amount by which the funding shortfall increased. If an 8 percent interest rate were assumed instead, the initial shortfall would be only $9,482, increasing to $93,559 at year’s end, creating a withdrawal liability pool of $84,076. Estimating the growth of the fund’s assets is required not only for determining withdrawal liability but also for determining whether employers are contributing to the fund the minimum amount required by ERISA in order to reduce the probability that the Pension Benefit Guaranty Corporation may have to make up for the fund’s not being able to pay vested benefits; for the Corporation is the insurer of those benefits, though only to a limited extent. (In fact, the Corporation has been helping the fund in this case remain solvent. See “PBGC Divides Chicago Trucker Pension Plan to Extend its Solvency,” May 26, 2010, www.pbgc.gov/news/press/releases/pr 10-35.html (visited Aug. 3, 2012).) Employers must pay a penalty in the form of a tax if they fail to contribute the required minimum amount. 26 U.S.C. § 412, § 4971(a)(2), (b)(2); Langbein et al., supra, at 220-35. The plan in our case retained a prominent pension benefits actuarial firm — the Segal Company — to determine whether the plan met its minimum funding requirements for avoiding the tax penalty and also what the withdrawal liability of each of its participating employers would be if one or more of them withdrew from the plan in the coming year. Both funding calculations depended critically on the interest rate used to estimate the plan’s ability to meet its future obligations. During the period relevant to this case, ERISA required the plan actuary, in calculating interest rates as in making other actuarial determinations (such as how the plan’s liabilities would grow in the future, which will depend on the rate at which employees with vested benefits retire and die as well *354 as on the rate at which future employees will work long enough for their benefits to vest), to use assumptions which, “in the aggregate, are reasonable” and “which, in combination, offer the actuary’s best estimate of anticipated experience under the plan.” These requirements apply to determining both adequacy of funding to avoid the tax penalty, 26 U.S.C. § 412(c)(3)(A)(ii), (B) (revised by the Pension Protection Act of 2006 in respects not material to this case), and withdrawal liability. 29 U.S.C. § 1393(a)(1). Despite the identical statutory text (the text we just quoted) for both calculations, the Segal Company used different formulas to arrive at its “best estimate” of the two rates. It called its best estimate of the interest rate for tax purposes the “funding interest assumption” and for withdrawal-liability purposes the “Segal Blended Rate.” We’ll call the funding interest assumption the “Funding Rate.” The different methods yielded different interest rates. The Blended Rate was based in part on current rates for annuities (and in part on the Funding Rate— hence “blended”). These rates were shorter-term and more variable than rates used for the Funding Rate because they were used to calculate the employer’s liability at a specific time (namely the coming year). What might happen in later years to affect the fund’s assets and liabilities — critical considerations in determining whether the pension plan was sufficiently funded to avoid the penalty tax — was irrelevant. If the short-term rates used in calculating the Blended Rate exceeded the long-term interest rates used to calculate the Funding Rate, making the Segal Blended Rate higher than the Funding Rate, the effect would be to reduce withdrawal liability, because the higher the assumed interest rate in calculating withdrawal liability the faster the funds’ assets would be estimated to grow and so the lower its future liabilities would be projected to be. When developed (in the 1980s, shortly after the Multiemployer Pension Plan Amendments Act was passed), an era generally of high interest rates, the Segal Blended Rate usually did generate a higher interest-rate estimate than the Funding Rate, making the estimate of the plan’s shortfall smaller for withdrawal-liability purposes than for penalty-tax purposes. Minimizing withdrawal liability was attractive to Segal’s multiemployer-plan clients because it made it easier for them to induce employers to join such a plan — easier because they could expect to be charged a lower exit price if they later withdrew. But the two rates had reversed by the mid-1990s. The Segal Blended Rate was now lower than the Funding Rate, resulting in higher withdrawal-liability estimates than if the Funding Rate had been used. Remember that the lower the interest rate used to calculate the future growth of fund assets, the lower the estimate of what those assets will be worth in the future, just as the slower a child grows each year, the shorter he will be as an adult. In 1997 Segal told the pension plan’s trustees that they could if they wanted direct Segal to ignore the Segal Blended Rate and instead use the Funding Rate— which now as we said exceeded the Segal Blended Rate — to calculate withdrawal liability. Segal didn’t say the Funding Rate was as good an estimate as Segal’s own “best estimate” for withdrawal-liability purposes; it stuck to its best estimate; it just said that the pension plan could choose between the two rates in calculating employers’ withdrawal liability. Language in the Supreme Court’s decision in Concrete Pipe & Products of California, Inc. v. Construction Laborers Pension Trust, 508 U.S. 602, 632-33, 113 S.Ct. 2264, 124 L.Ed.2d 539 (1993), could be *355 read to suggest that having two different interest-rate assumptions — one for withdrawal liability and one for avoiding the tax penalty — might make a plan vulnerable to claims that either or both were “unreasonable” within the meaning of 29 U.S.C. § 1393(a)(1). The danger was remote; the Court had indicated that “supplemental” assumptions that might cause the rates to diverge were permissible. 508 U.S. at 633, 113 S.Ct. 2264. Nevertheless Segal was worried, and at its suggestion the plan’s trustees directed Segal to calculate both the Segal Blended Rate and the Funding Rate and then use the higher of the two (which remember would generate a lower withdrawal liability) each year. The Funding Rate was higher in every year from 1996 to 2004 except 2000 when the Segal Blended Rate was higher and hence was used by the plan instead. The trustees’ decision was questionable. ERISA requires that the computation of withdrawal liability be based on “the actuary’s best estimate of anticipated experience.” 29 U.S.C. § 1393(a)(1) (emphasis added); cf. Citrus Valley Estates, Inc. v. Commissioner, 49 F.3d 1410, 1414 (9th Cir.1995); Rhoades, McKee & Boer v. United States, 43 F.3d 1071, 1075 (6th Cir.1995); Wachtell, Lipton, Rosen & Katz v. Commissioner, 26 F.3d 291, 296 (2d Cir.1994). The actuary is a professional, assumed to be neutral and disinterested; a plan’s trustees, in contrast, may, whether for short-term reasons, pressures from employers or unions, or lack of relevant expertise, want unreasonably high or unreasonably low interest-rate assumptions, contrary to 29 U.S.C. § 1393(a)(1). On the one hand, the higher the interest rate assumed, the faster the fund will be predicted to grow and so the smaller will be the liability of withdrawing employers; this in turn may encourage employers to join the plan. On the other hand, the lower the interest rate assumed, the greater the funding shortfall, enabling the plan to impose greater withdrawal liability on any withdrawing employer. That will discourage withdrawals, and also alleviate current funding shortfalls by replenishing the fund with large withdrawal payments by those employers who do withdraw. In 2004 the plan’s trustees directed the Segal Company to revert to using the Se-gal Blended Rate to calculate the plan’s unfunded vested benefit pools for withdrawal-liability purposes. That rate was lower than the Funding Rate (as it had been in every year since 1996 except 2000), but the plan’s priorities apparently had changed, from attracting more employers with the prospect of low withdrawal liability (by assuming a high interest rate and therefore a rapid growth in the fund’s assets) to extracting higher exit prices from employers who withdrew (by assuming a low interest rate and in consequence a sluggish rate of asset growth and so a larger shortfall.). The reversion to the Segal Blended Rate in 2004 was a major factor in causing the plan’s unfunded vested benefits to leap from $67 million to $117.2 million that year. It was the plan’s use of the higher Funding Rate from 1996 to 2003, coupled with the reversion to the lower Segal Blended Rate thereafter, that increased CPC’s withdrawal liability by $1,093,000 from the amount it would have owed had the Segal Blended Rate been used throughout the period. For CPC had been hit by a one-two punch. The higher rate in 1996-2003 had, by shrinking the pools and thus withdrawal liability, induced a number of employers to withdraw, so that in 2004 CPC found itself allocated a higher share of the 2004 pool. The change in interest-rate assumptions particularly distorted the 1996 and 2004 pools because the funding shortfalls *356 calculated at the beginning and end of those years were based on different interest rates. Since the withdrawal liability pool is the growth of the funding shortfall, a mid-year change in the assumptions can have a dramatic effect even if the plan’s financial performance is unchanged. Recall how in our earlier example the constant use of an 8 percent interest rate generated a withdrawal liability pool of $84,076, while use of a 6 percent rate generated a pool of $93,124. If that hypothetical plan calculated its initial funding-shortfall using an 8 percent interest rate and switched to a 6 percent interest rate for its year-end calculation, its withdrawal liability pool would balloon to $589,617. Had CPC withdrawn from the plan before 2004, it would have benefited from the fact that the pools had shrunk in those years, when the Funding Rate had (in all but 2000) been used in place of the Segal Blended Rate, since it would have paid less in withdrawal liability upon leaving the fund. But it had stuck around, and the earlier shrinkage had caused the 2004 pool to soar in size in order to compensate. Foisting a larger share of the larger 2004 pool on CPC increased the company’s withdrawal liability still further. Remember that ERISA requires the plan’s trustees to base its calculation of withdrawal liability on the actuary’s “best estimate.” 29 U.S.C. § 1393(a)(1). Segal maintains, and the plan does not dispute, that the Segal Blended Rate, not the Funding Rate, was its best estimate of the right interest rate to use to calculate withdrawal liability. The arbitrator therefore sensibly concluded that the pools had not been calculated “on the basis of ... actuarial assumptions ... which, in combination, offer the actuary’s best estimate of anticipated experience under the plan” in years when the Funding Rate was used in lieu of a lower Segal Blended Rate. There is no evidence either that the offer of a choice was made for any reason other than Segal’s anxiety about having calculated two interest rates or that it was accepted for any reason other than the trustees’ desire to attract employers to the fund by manipulating withdrawal liability. Hence there is no basis for the plan’s invocation of Combs v. Classic Coal Corp., 931 F.2d 96 (D.C.Cir.1991), which reversed an arbitrator’s rejection of a withdrawal-liability calculation because he had considered only the reasonableness of the interest rate, ignoring the plan’s argument that its calculation of the withdrawal liability was still “reasonable ... in the aggregate,” 29 U.S.C. § 1393(a)(1), because of offsetting actuarial assumptions. Nothing in the present case offsets the malign consequences of the trustees’ directing Segal to use the Funding Rate instead of the Segal Blended Rate, when the latter was the actuary’s best estimate of the rate to use. The plan cites 29 U.S.C. § 1393(b)(1), which states that “the plan actuary may rely [in calculating withdrawal liability] on the most recent complete actuarial valuation used for purposes of’ 26 U.S.C. § 412, the section of the tax code governing calculation of a pension plan’s minimum funding requirements — a calculation based on the Funding Rate. The plan argues that the provision creates a safe harbor, insulating its use of the Funding Rate for calculation of withdrawal liability from challenge. But the provision we quoted does not override the statutory requirements that the calculation of withdrawal liability be based on reasonable actuarial assumptions and the plan actuary’s best estimate. Masters, Mates & Pilots Pension Plan v. USX Corp., 900 F.2d 727, 731-32 (4th Cir.1990); see Goldowitz & Landy, supra, at 1294. The Funding Rate could be appropriate for use in calculating withdrawal liability, *357 but was not in the circumstances of this case. Moreover, the plan’s resolution directing Segal to switch from one method of estimating the interest rate to another and back again compounded the damage to CPC, and also violated the “best estimate” requirement, which exists to maintain the actuary’s independence. Cf. Citrus Valley Estates, Inc. v. Commissioner, supra, 49 F.3d at 1414; Rhoades, McKee & Boer v. United States, supra, 43 F.3d at 1075; Wachtell, Lipton, Rosen & Katz v. Commissioner, supra, 26 F.3d at 296. The fact that Segal proposed the switch from the Segal Blended Rate didn’t mean that the Funding Rate had become its best estimate; Segal was explicit that it was not its best estimate. It was a result either of its having been confused by the Supreme Court’s decision in the Concrete Pipe case or of pressure from the pension plan. Finally, the plan argues that its calculation of withdrawal liability is shielded by the limited scope of the arbitrator’s review of determinations by a plan’s trustees. But the trustees were not entitled to disregard a statutory directive, specifically the directive in section 1393(a)(1) that they base their estimate of withdrawal liability on the actuary’s “best estimate” of future fund performance. An actuarial determination that violates ERISA by not being based on the actuary’s best estimate is unreasonable, hence reversible by the arbitrator. 29 U.S.C. § 1401(a)(3)(B)(i); Concrete Pipe & Products of California, Inc. v. Construction Laborers Pension Trust, supra, 508 U.S. at 634-36, 113 S.Ct. 2264. The district court’s judgment upholding the arbitrator’s decision is Affirmed.