concurring and dissenting in part:
I concur in the court’s opinion with the exception of Part II. In that Part, the court remands the Special Master’s benchmark determination — that is, his calculation of the hours claimants would have worked in the absence of discrimination. The questions my colleagues raise about the Master’s calculation are not unreasonable ones. But that is not the test on appeal. It does not matter that we might have made a different calculation had we been sitting as the triers of fact. See Anderson v. Bessemer City, 470 U.S. 564, 573-74, 105 S.Ct. 1504, 84 L.Ed.2d 518 (1985). Instead, to justify remand, appellants must demonstrate that the Master’s calculation was clearly erroneous. See id.; 9A Charles A. Wright & Arthur R. Miller, Federal Practice and Procedure § 2585, at 565 (2d ed.1995). Because they have not done so, I would affirm the Master’s determination rather than needlessly prolong this decades-old case.
I.
In order to determine the number of hours the claimants would have worked had they not been subject to discrimination, the Special Master consulted Local 201 pension records- to calculate the average number of hours a representative group of union workers actually worked during the relevant period. The court’s first objection to the Master’s méthodology is that he excluded from that group “those who for several years ... worked no hours at all.” J.A. 342-43. By not including these “zero-hour” workers in calculating the hours of an average worker, the court contends that “the Special Master remove[d] from the equation the risk of disabling injury, or of finding another more desirable job, or whatever other reason a person might not work full time.” Op. at . 1122.
The inclusion of zero-hour workers may be a reasonable way to account for the risk that an individual claimant would have stopped working even if he had been admitted to the union. But it is not the only, or even the most direct, way. The most direct way is simply to deny back pay to those claimants who actually did stop working, rather than build into the benchmark the statistical probability that a hypothetical claimant would have done so. Not unreasonably, the Special Master chose the direct approach.
The Master’s benchmark accounted for the risks of injury and attrition as follows. First, he included within the representative pool those workers whose hours had been reduced by short-term injuries or other absences. As the court notes in Part IV, the “Special Master’s proxy does ... factor in the ‘average number of days lost due to injury, sickness, and attrition.’” Op. at 1132 (quoting J.A. 341). Second, the Master excluded those who had worked zero hours “for several years,” because they were not representative of union members who were actually working during the relevant period. J.A. 342 — 43.1 *1142Finally, to ensure that a claimant who worked zero hours did not receive a windfall, the Master reduced the pay of claimants where there was “an ‘extensive period of unemployment due to injury [that] falls outside [the] statistical model of reasonable hours’ developed in the benchmark proxy.” Op. at 1122 (quoting J.A. 445).
I do not disagree that the Master appears to have performed this last calculus inconsistently. For that reason, I join Part IV.6 of the court’s opinion, which remands certain challenged back pay determinations for an “inquiry into whether each challenged award involves a claimant whose injury-time exceeds th[e] average.” Op. at 1132. But that limited remand is sufficient to remedy the error. As long as the Master denies claimants back pay for actual absenteeism “so extreme as to be beyond the proxy’s statistical average,” Op. at 1132, there is no reason to require him also to build the probability of lengthy absences into the benchmark. As the court itself notes in Part II, “[b]oth ... are means of discounting back pay awards to reflect unavailability for work during the liability period.” Op. at 1132. Even if the probability-based, zero-hour approach were preferable, it cannot be clearly erroneous for the Master to have chosen the direct-reduction approach instead. See Anderson, 470 U.S. at 574, 105 S.Ct. 1504 (“Where there are two permissible views of the evidence, the factfinder’s choice between them cannot be clearly erroneous.”).
II.
The court’s second criticism of the Special Master’s calculation is its asserted failure to recognize that the number of work-hours available for union members during the relevant period was a “fixed pie.” If the claimants had been admitted into the union, the court contends, that fixed pie of hours would have been divided among a greater number of workers. Hence, each union member would have worked fewer hours than union members actually worked during the period. There are two reasons to reject this critique.
First, defendants did not make this argument in their briefs before this court. Indeed, the term “fixed pie” cannot be found anywhere therein. See Def. Br. at 24-32; Def. Reply Br. at 4-6. We routinely and for good reason refuse to consider contentions not raised in a party’s briefs. See Boggs v. Rubin, 161 F.3d 37, 42 (D.C.Cir.1998) (holding that “[w]e will not consider at this late stage an argument that the appellant failed to raise” in his briefs); Diamond Walnut Growers, Inc., v. NLRB, 113 F.3d 1259, 1263 (D.C.Cir.1997) (en banc) (“[I]t is well-established ... that we do not consider arguments not presented to us.”). Although it is not impossible to tease the recipe for a fixed-pie argument out . of a single sentence in which defendants described the calculations performed by their own expert, their briefs did not argue that a fixed-pie problem rendered the Special Master’s calculations clearly erroneous. As we haye said in another context, a reviewing body “need not sift pleadings and documents to identify arguments that are not stated with clarity by a petitioner.” Bartholdi v. FCC, 114 F.3d 274, 279 (D.C.Cir.1997) (internal quotations omitted); see also United States v. Gilliam, 167 F.3d 628, 640 n.10 (D.C.Cir.1999) (“[T]he court will not construe the briefs to raise an argument that is hinted at but never stated.”).2
Second, there is substantial support in the record for the Master’s conclusion that “there really [was] no fixed pie” of available hours. J.A. 339. As the court explains, the Local referred work to both union members and non-union workers. The defendants’ expert assumed that had claimants become members of the union, they would have displaced non-union workers first. There would thus be no fixed-pie problem, the expert said, as long as the hours referred to non-union workers in a given year were more than the potential “claimant hours” — which he defined as the product of the number of eligible claimants and the mean hours worked by union members that year. J.A. 1383 (report of defendants’ expert).
Examination of two charts prominently displayed in defendants’ own brief reveals *1143that in fact, the number of hours the Local referred to non-union workers did exceed the number of potential claimant hours every year through 1981. Def. Br. at 15, 28. That is because in each of those years the union referred in excess of 100,000 hours to nonunion workers, more than enough to accommodate 173 claimants without displacing any union members.3 Hence, even assuming that the union could not have attracted additional work for additional members, there simply was no fixed-pie problem through 1981.4 If there were an error in the Master’s calculation, then, it would apply only to awards for years after 1981 — and only one claimant received such an award. At most, the fixed-pie theory would necessitate a remand of the award to Eldridge Harmon, who received $2,075 for 1985-86.
But the court is also factually incorrect in stating that “[t]here is no evidence in the record to suggest that there was additional work in the D.C. area for Local 201 rodmen” beyond that actually handled by its union members and nonunion referrals. Op. at 1123. Defendants’ own briefs provide the contrary evidence, demonstrating that during the entire relevant period, Local 201 had more job requests from employers than both its union and non-union workers could absorb. Defendants state that from 1972 to 1975, “Local 201 was unable to fill 4,432 jobs due to an insufficient number of workers seeking jobs through the hiring hall.” Def. Br. at 14 (citing J.A. 274-75). And from 1976 to 1986, “Local 201 was unable to fill 1,649 jobs.” Id. at 15; see also id. at 60 (“Even after the 1972-75 ‘full employment’ period, Local 201-referral jobs went unfilled for lack of applicants.”). Defendants’ evidence makes clear that this circumstance existed in every year for which there are records, see J.A 275, despite the fact that the “union never deliberately let a job go unfilled.” Def. Br. at 14. Hence, the defendants’ own briefs provide the “'prima facie showing that additional hours were available to Local 201” upon which the court insists. Op. at 1124.5
Finally, the fact that the union had to turn down jobs also undermines the court’s declaration that “[cjommon sense and experience suggest that a union will attempt to bring as many projects as possible under union con-trol_” Op. at 1123. That may be the case where a union and its non-union referrals are able to handle all the work they can bring in. But where a local is already turning down unsolicited job referrals, it has no incentive to bring still more projects under its control. Under these circumstances, neither common sense nor experience militates against the Master’s finding that there was no fixed pie. J.A 339.6
*1144III.
The burden is on the appellants to establish that the decision below was clearly erroneous. See Bellevue Gardens, Inc. v. Hill, 297 F.2d 185, 187 (D.C.Cir.1961); 9A Charles A. Wright & Arthur R. Miller § 2585, at 565. Because they have not met that burden, there is no reason for us to prolong the final resolution of plaintiffs’ back pay awards by remanding the Special Master’s benchmark determination for further consideration.
. It is important to note that the Special Master did not exclude all zero-hour workers from the proxy group — he excluded only those who had worked zero hours “for several years." J.A. 342-43. Similarly, defendants’ own expert excluded some, but not all, zero-hour workers from his preferred benchmark proxy — he excluded “zero-hour rodmen who had died, retired, were incarcerated or permanently disabled.” Op. at 1122 (citing J.A. 1381). Neither the court nor defendants explain why the exclusions made by defendants’ expert were permissible, while those made by the Master were clearly erroneous.
. To a lesser extent, the zero-hour argument discussed above suffers from the same disability. Although one of defendants' briefs did use the term "zero-hour” (once), it did so only in describing the work of defendants’ expert. It did not expressly argue that the failure to include zero-hour workers rendered the Master’s benchmark clearly erroneous.
. The chart on page 15 of defendants’ brief discloses the number of hours the union referred to non-union workers in each year. The chart on page 28 shows the mean union-member hours for each year as determined by defendants' expert. When the latter figures are multiplied by the 173 putative class members, the resulting claimant hours are less than the non-union hours for every year through 1981.
. This roughly accords with the concession of defendants’ own expert that in the 1970s there would have been sufficient hours available for the claimants had they been admitted to the union. See J.A. 339 (citing expert’s testimony).
. The court states that the fact that jobs went unfilled does not necessarily mean that the union had enough work for the claimants, since it might be explained merely by "[flluctuations on a given day that would result in a specific job referral being listed as unfilled.” Op. at 1123. But this theoretical possibility, like the year-to-year disparities to which the court also points, is hardly sufficient to justify a conclusion that the Master’s determination was clearly erroneous. See Anderson, 470 U.S. at 573-74, 105 S.Ct. 1504. The court also contends that defendants "made a prima facie showing that the hours were not available” for the claimants, based on evidence of "the declining hours referred out of the hall and [on] evidence [defendants] introduced of the declining market share available to the union.” Op. at 1123. But it is the gross hours potentially available for the claimants, not the evidence of trends and percentages, that is relevant to the validity of the fixed-pie theory.
.For the same reasons, and contrary to the court’s contention, the Special Master did not shift the burden of proof to defendants by characterizing the fixed-pie theory as "at best speculative.” J.A. 340. Indeed, the defendants’ expert himself described the theory in words of speculation. See J.A. 1383 (stating that the benchmark "may require [an] adjustment ... [to] reflect[] the fixed number of union-referred hours”) (emphasis added); id. at 1384 (stating that a fixed-pie adjustment would be required "if there are no permitmen and travelers working in a given year”) (emphasis added).