Full opinion text
OPINION KAREN NELSON MOORE, Circuit Judge. In 2004, Defendant-Appellant City of Akron administered promotional examinations for firefighters for the ranks of Lieutenant and Captain. The Plaintiffs-Appel-lees are Akron firefighters who took the examinations, but were not promoted. They filed this lawsuit, alleging that the promotional process disparately impacted firefighters over the age of forty in violation of the Age Discrimination in Employment Act, 29 U.S.C. § 621 et seq., and Ohio Revised Code §§ 4112.02, .14, and .99. In addition, they allege that the Lieutenant promotional process adversely impacted African-American applicants, and the Captain promotional process adversely impacted Caucasian candidates in violation of Title VII, 42 U.S.G. § 2000e et seq., and Ohio Revised Code § 4112.02(A). On December 23, 2008, a jury found that the two promotional processes adversely impacted applicants over the age of forty, and that the exams and promotional processes were not justified by business necessity. On October 2, 2009, the district court entered findings of fact and conclusions of law consistent with the jury’s verdict with respect to the Plaintiffs’ Title VII race-discrimination claims, finding that Akron’s promotional process adversely impacted African-American Lieutenant candidates and Caucasian Captain candidates. Following the parties’ post-judgment motions, the district court ordered a new trial on the sole issue of damages. On August 30, 2013, -after a retrial, the district court entered an award of back pay in the amount of $616,217.75. On March 27, 2014, the district court entered a permanent injunction and appointed a court monitor. The parties have been litigating this case with remarkable vigor and venom since 2008. After two trials and multiple appeals, the parties remain unwilling to settle their differences. Akron now appeals the liability judgment, back-pay award, permanent injunction, and the appointment of a court monitor. The Plaintiffs have cross-appealed the district court’s back-pay award, and argue that Akron has forfeited any challenge to the liability judgment because of this court’s opinion in Howe v. City of Akron (“Howe I”), 723 F.3d 651 (6th Cir.2013). Both parties seek — at the very least — a new trial on the issue of back pay and reassignment of the case to a different district judge. For the reasons expressed in this opinion, we AFFIRM the liability judgment. However, we REVERSE the back-pay award and REMAND the case for reassignment to a different district judge and a new trial on the issue of back pay. In addition, we MODIFY the district court’s order appointing a court monitor to limit the court monitor’s involvement to one promotional cycle. I. FACTS & PROCEDURAL HISTORY A. Akron’s 2004 Promotional Process The Plaintiffs are all members of the Akron Fire Department who took the 2004 promotion exam for either the rank of Lieutenant or Captain. Their claims arise out of the results of the Akron Fire Department’s 2004 promotional process. Akron hired E.B. Jacobs LLC to develop, administer, and score the December 2004 Lieutenant and Captain promotional exams for the Akron Fire Department. R. 277 at 7 (Findings of Fact and Conclusions of Law (“FFCL”) ¶¶ 70-71) (Page ID # 7742). Each examination included a 100-question multiple-choice component about technical job requirements. Id. (FFCL ¶ 72). In addition to the written component, candidates for the Lieutenant position had to complete “a written work sample exercise” and undergo two oral assessments, including “a subordinate conference and incident command.” Id. (FFCL ¶ 73). The Captain promotional examination had three oral exercises: “a subordinate conference, group exereise[,] and [an] incident command.” Id. at 8 (FFCL ¶ 74) (Page ID # 7743). After the examiners scored the exams, they converted the scores to a scale for which 100 was the highest score, and then created lists of eligible candidates for promotion. To be eligible for a promotion, the candidate had to achieve a final average test score of at least 70%. R. 80 at 10 (Def.’s Mot. for Summ. J.) (Page ID # 513). The test administrators combined the written and oral test scores and standardized those scores by converting them to a ninety-point scale. R. 196 at 84 (Trial Tr. Vol. 3) (Page ID # 4882); R. 211 at 141 (Trial Tr. Vol. 8) (Page ID # 5916). Next, the Fire Department awarded up to ten additional points based on seniority to the candidates’ final test scores, and then the candidates were ranked in order of the combination of their test score plus seniority. R. 196 at 83 (Trial Tr. Vol. 3) (Page ID # 4881); R. 211 at 141 (Trial Tr. Vol. 8) (Page ID # 5916). Candidates with the highest scores were at the top of the list; candidates with the lowest scores were at the bottom. See R. 212 at 127 (Trial Tr. Vol. 9) (Page ID # 6164). This final list was called the “eligibility list.” R. 99 at 11 (Pis.’ Resp. in Opp’n to Def.’s Mot. for Summ. J.) (Page ID # 2517). When there was a vacant Lieutenant or Captain position, the Personnel Director for the Fire Department submitted a certified list of candidates to the Mayor, which included. the names of those candidates with the three highest scores on the eligibility list — the so-called “Rule of Three.” R. 213 at 178 (Tr. Trial Vol. 7) (Page ID # 6502). Next, the Personnel Director interviewed the three candidates before submitting a recommendation about whom among the three candidates the Mayor should promote to the vacant position. Id.;' R. 212 at 128 (Tr. Trial Vol. 9) (Page ID # 6165). To fill the next available vacancy, the Personnel Director selected the top three names on the eligibility list, and the interview process began anew. R. 213 at 182-84 (Trial Tr. Vol. 7) (Page ID # 6506-08). If a candidate was interviewed and passed over three times, then his or her name would be removed from the list. R. 99 at 11 (Pis.’ Opp’n to Def.’s Mot. for Summ. J.) (Page ID #2517). Under this system, it is possible that a candidate with the top score might never receive a promotion. Id. On April 5, 2005, the Akron Civil Service Commission completed the eligibility list, which remained active for two years. R. 277 at 8 (FFCL ¶¶ 75-76) (Page ID # 7743). During that two-year period, twenty-eight candidates were promoted to the rank of Lieutenant and twelve to the rank of Captain. Id. (FFCL ¶¶ 78-79). Of the twenty-eight candidates who became Lieutenants only three were African Americans. Id. (FFCL ¶ 78). Of those twelve who became Captains seven were Caucasians. Id. (FFCL ¶ 79-80). The following Table represents the pass and promotion rates for each rank and protected group at issue: Rank Class Pass Rate Promotion Rate Over-40 76% (29/38) 24% (7/29) Lieutenant Under-40 87% (55/63) 38% (21/55) Caucasian 85% (69/81) 36% (25/69) African-American 75% (15/20) ' 20% (3/15) Captain Caucasian 81% (26/32) 27% (7/26) African-American 78% (7/9) 71% (5/7) Howe I, 723 F.3d at 656. B. The Claims On November 16, 2006, the Plaintiffs filed this lawsuit, alleging age and race discrimination in violation of federal statutory law. See R. 1 at 9-10 (Compl.Hf 30-37) (Page ID # 9-10). On October 19, 2007, the Plaintiffs amended their complaint to include claims of age and race discrimination in violation of Ohio law and violations of the Equal Protection Clause. R. 23 at 12-16 (1st Amend.Compl.1ff 49-68) (Page ID # 147-51). The Age-Discrimination Claims. Eleven plaintiffs, Mike Reed, Brenda Chapman, Michael Harvey, William Roy Wilkinson, Jeffrey Layne, James Farina, Jeff Schueller, Jerry Elie, Frank Poletta, Kerry Briggs, and Bruce Clough allege that the promotional process adversely impacted candidates for the rank of Lieutenant who were over the age of forty. See R. 277 at 1-5 (FFCL ¶¶ 1-47) (Page ID # 7736-40). In Counts I, III, and V, the Plaintiffs allege that the promotional exams had an adverse impact on twenty-three candidates for promotion to the ranks of Lieutenant and Captain because of their age in violation of the ADEA, 29 U.S.C. § 621 et seq., and Ohio Revised Code §§ 4112.02, .14, and .99. R. 23 at 11-13 (1st Amend.CompLIffl 45-46, 49-50, 53-54) (Page ID # 146-48). Counts II, IV, and VI allege that the candidates for promotion to the rank of Lieutenant and Captain were subjected to disparate treatment because of their age “in the administration and scoring of the promotional examinations” in violation of the ADEA, 29 U.S.C. §§ 621 et seq., and Ohio Revised Code §§ 4112.02, .14, and .99. Id. (1st Amend. Compl.lffl 47-48, 51-52, 55-56). The Race-Discrimination Claims. Three plaintiffs, Brenda Chapman, Michael Harvey, and Jerry Elie, allege that the promotional process for the rank of Lieutenant adversely impacted African-American candidates. See R. 23 at 14-15 (1st Amend.Compl.Hf 57-58, 61-62) (Page ID # 149-50). A group of twelve plaintiffs, William Howe, James Freeman, Leslie Geiser, John Triolo, Jeffrey Derenber-ger, David Hull, David O’Neil, Jerome Crawford, Bradley Robson, Michael Hausch, Bradley Carr, and Gregory Snyder allege that the promotional process adversely impacted Caucasian candidates for the rank of Captain. See id. at 14-15 (1st Amend.Compl.1ffl 59-60, 63-64) (Page ID # 149-50). Counts VII and IX alleged that the promotional examinations for the rank of Lieutenant had a disparate impact on African-American candidates in violation of Title VII, 42 U.S.C. § 2000e et seq., and Ohio Revised Code § 4112.02(A). Id. at 14-15 (1st Amend.Compl.W 57-58, 61-62) (Page ID # 149-50). Counts VIII and X alleged that the promotional exam adversely impacted Caucasian candidates for the rank of Captain. Id. at 14-15 (1st Amend.Compl.lffl 59-60, 63-64) (Page ID # 149-50). Counts XI and XII alleged that the administration of the promotional examinations violated the Equal Protection Clause of the Fourteenth Amendment. Id. at 15-16 (1st Amend. CompLIffl 65-68) (Page ID # 150-51). On December 1, 2008, the district court entered summary judgment in favor of Akron for Counts XI and XII, the equal-protection claims. R. 176 at 1 (Order on Mot. for Recons.) (Page ID # 4196). A jury trial regarding the remaining claims commenced on December 3, 2008. During the trial, the plaintiffs dismissed their disparate-treatment claims (Counts II, IV, and VI) and the Captain candidates’ dispa- „ rate-impact, age-discrimination claims (Counts I, III, and V), which related to the plaintiffs who were candidates for the rank of Captain. R. 216 at 1 (Pis.’ Notice of Stipulation of Dismissal) (Page ID # 6585); R. 218 at 1 (Order Dismissing Disparate Treatment Claims) (Page ID # 6590); R. 309 at 2 (Tr. Trial Vol. 13) (Page ID # 16338). The jury’s task was to determine whether Akron’s promotional process had a disparate impact on African-American or over-forty candidates for the rank of Lieutenant and Caucasian candidates for the rank of Captain. R. 309 at 2 (Tr. Trial Vol. 13) (Page ID # 16338). C. The Trial The Plaintiffs and Akron presented evidence about the statistical significance of the disparities between the promotion of each protected group and argued about whether the statistical tests were appropriate tools to evaluate the disparate-impact claims. The Plaintiffs also offered expert opinion testimony that the examinations and the promotion processes were not job related. Akron’s experts offered opinion testimony to the contrary — that the promotional process was justified by business necessity. On December 23, 2008, the jury returned a unanimous verdict in favor of all of the Plaintiffs and specifically found that business necessity did not justify the promotion process. See R. 237 at 1-44 (Jury Verdict) (Page ID # 7312-55). The jury awarded each candidate for the rank of Lieutenant $9,000 in compensatory damages and $72,000 in front pay. See id. at 10-20 (Page ID # 7321-31). The jury awarded each candidate for the rank of Captain $10,000 of compensatory damages and $80,000 in front pay. Id. at 21-32 (Page ID # 7332-43). On October 2, 2009, the district court filed its findings of fact and conclusions of law, noting that it was “bound by the jury’s factual findings to the extent that the jury and non-jury claims overlapped.” R. 277 at 10 (FFCL ¶92) (Page ID # 7745) (citing Gutzwiller v. Fenik, 860 F.2d 1317, 1332-33 (6th Cir.1988); Lewis v. Sears, Roebuck & Co. (In re Lewis), 845 F.2d 624, 628-29 (6th Cir.1988)). The district court concluded that the Plaintiffs had “established a prima facie case of disparate impact on both their [ADEA] age and [Title VII] race claims.” Id. at 11 (FFCL ¶ 99) (Page ID # 7746). In addition, the district court concluded ■ that “[b]ased upon the jury’s findings ... Akron failed to prove that its employment practices in making selections for promotions to Lieutenant in 2004 were based on reasonable factors other than age or race.” Id. (FFCL ¶ 101). Thus, the district court found that Akron’s “2004 promotional process for promotion to Lieutenant” and Captain discriminated against the Plaintiffs on the basis of race in violation of 42 U.S.C. § 2000e-2(k)(l)(A)(i) and the Ohio Revised Code §§ 4112.02(A) and .99. Id. at 11-12 (FFCL ¶¶ 102-03) (Page ID # 7746-47). The district court awarded the Plaintiffs “front pay as determined by the jury,” as well as attorney fees and costs and further relief to be addressed after full briefing. Id. at 12 (FFCL ¶¶ 104-05) (Page ID # 7747). D. The Post-Verdict Motions On October 19, 2009, the Plaintiffs and Akron filed post-judgment motions. The Plaintiffs filed a motion pursuant to Federal Rule of Civil Procedure 59(e) to alter or amend the judgment, requesting additional relief: (1) back pay calculated through the date of judgment or promotion; (2) “grossing up” for tax liability on the wages paid in a lump sum; (3) prejudgment interest; (4) permanent injunctive relief in the form of a promotion for any prevailing plaintiff electing to be promoted; (5) pension adjustments; (6) post-judgment interest from the date of judgment until payment; (7) a posthumous promotion .and adjustment for Crawford; (8) permanent injunc-tive relief in the form of a new equitable, valid promotional process; appointment of a receiver to oversee the development of a new promotional process; (9) court monitoring until all issues related to the case are fully resolved; and (10) “any other relief as set forth in Plaintiffs’ motions for equitable relief.” R. 280 at 1-2 (Pis.’ Rule 59(e) Mot. to Amend. J.) (Page ID # 7756-57). Akron filed two motions: A renewed motion for judgment as a matter of law, new trial, or remittitur pursuant to Federal Rules of Civil Procedure 50(b) and 59; and a Rule 59(e) motion to alter or amend the judgment, new trial, or remittitur. See R. 282 (Def.’s Renewed Mot. for J. as a Matter of Law “JMOL” or Mot. for a New Trial, or- Remittitur) (Page ID # 7761-69); R. 283 (Def.’s Rule 59(e) Mot. to Amend J. or Mot. for New Trial, or Remittitur on Pis.’ Title VII Claims) (Page ID # 7771-74). Akron argued, inter alia, that the evidence of adverse impact was insufficient. To this end, Akron argued four theories. First, Akron argued that the disparities between the various groups who went through the promotion process were hot statistically significant. Second, Akron asserted that pass rates were the appropriate measure of adverse impact— not promotion rates — and the evidence did not support a finding that there was a-four-fifths-rule violation when the experts compared the different pass rates of each group. R. 285 at 11-14 (Def.’s Mem. in Support of JMOL) (Page ID # 7788-91). Third, Akron also faulted the Plaintiffs for failing to introduce statistical evidence other than a violation of the four-fifths rule and argued that evidence of a violation of the four-fifths rule was insufficient because the sample size was small. Id. at 16-19, 22-24 (Page ID # 7793-96, 7800-01). Finally, Akron complained that the Plaintiffs had not established that Akron was an “unusual employer,” i.e., an employer who discriminates against the majority. See id. at 14-16 (Page ID # 7791-93). Alternatively, Akron asserted that it was entitled to a new trial because the jury’s verdict was against the manifest weight of the evidence and the district court made legal errors and admitted certain evidence in error. R. 282 at 7-8 (Def.’s Renewed Mot. for JMOL, New Trial, or Remittitur) (Page ID # 7767-68); R. 283 at 3 (Def.’s Rule 59(e) Mot. to Alter or Amend J., New Trial, or Remittitur) (Page ID # 7773). Akron also sought a new trial on the issue of damages for two reasons. First, Akron argued that the lock-step damages award for each class of plaintiff was inconsistent with the Plaintiffs’ testimony about their individual damages. R. 285 at 27 (Def.’s Br. in Support of JMOL or Mot. for New Trial) (Page ID # 7804). Second, Akron asserted that the jury had not considered that not all of the Plaintiffs would have been promoted had the process been fair. Id. (citing Biondo v. City of Chi., 382 F.3d 680, 688-89 (7th Cir.2004)). On December 30, 2010, the district court filed a memorandum opinion granting in part and denying in part the Plaintiffs’ and Akron’s Rule 59(e) motions to amend the judgment, denying Akron’s motion for judgment as a matter of law, and granting in part Akron’s motion for a new trial on the issue of damages alone. See R. 311 at 1-2 (D.Ct.Mem.Op.) (Page ID # 16399-16400). First, the district court concluded that Akron had waived its argument that promotion rates were not an appropriate metric to use because Akron had not advanced this argument in its pre-verdict motion for judgment as a matter of law. Id. at 16-17 (Page ID # 16414-15). In the alternative, however, the district court held that promotion rates were appropriate criteria for application of the four-fifths rule in a case challenging promotion policies. Id. at 18 (Page ID # 16416) (citing Phillips v. Cohen, 400 F.3d 388, 399 (6th Cir.2005)). Second, the district court found that Akron had “waived” the argument that the Plaintiffs had to prove that Akron is the unusual employer that engages in “reverse discrimination.” Id. at 20-21 (Page ID # 16418-19). Although Akron had requested a jury instruction requiring a showing of “background circumstances” that a facially neutral policy adversely impacted the majority, the district court found waiver because Akron had not furthered its argument for the proposed instruction during the charging conference. Id. at 20-21 (Page ID # 16418-19) (citing R. 138 at 30 (Proposed Joint Jury Instrs.) (Page ID # 3967); R. 148 at 14 (Def.’s Proposed Jury Instrs.) (Page ID #4036); R. 309 at 4-44 (Tr. Trial Yol. 13) (Page ID # 16340-80)). Third, the district court rejected Akron’s argument that even if there were violations of the four-fifths rule, the disparities were not statistically significant because of the small size of the sample. Id. at 21-24 (Page ID # 16419-22). When the district court turned to Akron’s motion for a new trial, it rejected the bulk of Akron’s arguments, see id. at 29-34 (Page ID # 16427-32), but agreed with Akron that “the jury recognized, but failed to follow, their duty to award damages based on the testimony of the individual Plaintiffs” because the jury had awarded the individual Plaintiffs the same amounts in compensatory damages and front pay, id. at 29 (Page ID # 16427) (internal quotation marks omitted). The evidence at trial established that some of the Plaintiffs spent more time preparing for the examinations than other Plaintiffs, and some Plaintiffs failed multiple examinations. Id. at 29-30 (Page ID # 16427-28). Accordingly, the district court granted Akron’s motion for a new trial “solely on damages.” Id. at 34 (Page ID # 16432). The district court did not address the Plaintiffs’ Rule 59(e) motion to alter or amend the judgment. Soon thereafter, Akron filed a motion to alter or amend the judgment to include a statement seeking certification of an interlocutory appeal pursuant to 28 U.S.C. § 1292(b) for one legal question: “Does ‘selection’ refer to pass rates or promotion rates in adverse impact promotional testing cases?” R. 314 at 1 (Def.’s Mot. to Amend J.) (Page ID # 8076). The district court denied the motion, in part because it doubted that Akron had preserved the issue, but also because Akron had not satisfied the § 1292(b) standard for certification. See R. 324 at 1-4 (D. Ct. Order Re § 1292(b) Certification) (Page ID # 8168-71). E. Plaintiffs’ Motion for Promotion On February 9, 2009, soon after the district court entered the liability judgment, the Plaintiffs filed a motion for a permanent injunction. The Plaintiffs requested “a permanent injunction prohibiting ... Akron from utilizing or otherwise acting upon any promotional process, including but not limited to the process developed and administered in December, 2004, for filling the ranks of Lieutenant and Captain.” R. 256 at 1 (Pis.’ Mot. for Permanent Inj.) (Page ID # 7528). The Plaintiffs also requested an injunction requiring] the development of a job-related non-discriminatory promotion process, under the supervision and guidance of a receiver appointed by this Court, that selects qualified candidates without adverse impact because of race or age and complies with Title VII of the Civil Rights Act of 1964, as amended, 42 U.S.C. § 2000e et seq., the ADEA, 29 U.S.C. § 621, et seq., and the Uniform Guidelines on Employee Selection, 29 C.F.R. § 1607, et seq. Id. In the interim, the Plaintiffs sought “the promotion of each Plaintiff to the rank of Lieutenant and Captain,” and for the fire department to appoint “all acting officers for the ranks of Lieutenant and Captain, until the actual promotion of the Plaintiffs, exclusively from the pool of Plaintiffs, rotated on a seniority basis, with the incremental base pay set at the full-step in-grade level pending the development of the new promotion process.” Id. at 2 (Page ID # 7529). On September 29, 2009, the district court denied without prejudice the Plaintiffs’ motion for a permanent injunction because the relief sought related to the Title VII claim for which the district court had not yet entered its findings of fact and conclusions of law. R. 276 at 1 (D. Ct. Order Re Permanent Inj.) (Page ID # 7734). E. Renewed Damages Discovery The parties disagreed about how the new trial on the issue of damages should proceed, so the district court ordered the parties to provide briefing about whether they would need additional discovery. R. 315 at 1 (D. Ct. Order Re Damages Disc.) (Page ID # 8081). On April 5, 2011, the district court set the jury trial for July 18, 2011, and reopened discovery to be completed by June 17, 2011. R. 326 at 1 (Pretrial Order) (Page ID #8173). The renewed discovery period was intended to provide Akron with an opportunity to explore issues related to the Plaintiffs’ calculation of damages. R. 322 at 4-5 (Def.’s Position Statement Re: New Trial on Damages) (Page ID # 8159-60). On June 23, 2011, the district court ordered the Plaintiffs.to disclose “their damage calculation and how they arrive at those numbers.” R. 357 at 24-25 (Tr. Telephone Conference) (Page ID #8298-99). Plaintiffs’ counsel assured the court that the formula involved “basically multiplication, division, addition and subtraction and that’s all it is.” Id. at 24 (Page ID # 8298). Akron had not provided the Plaintiffs with the payroll documents needed to perform the necessary calculations, however, and so the district court ordered Akron to produce those documents. Id. at 27-28 (Page ID # 8301-02). Akron redeposed all twenty-three Plaintiffs, who revealed that they had calculated their back pay using a formula created by Plaintiff Gregory Snyder, who had been the employee-benefits officer in the Akron Fire Department. Snyder used the average salaries of officers promoted in 2005 beginning with the date of the first promotions from the eligibility lists to produce back-pay calculations for each plaintiff. R. 370-2 at 16-17, 40-44 (Snyder Dep. at 15-16, 39-43) (Page ID # 8902-03, 8926-30). During these depositions, the Plaintiffs claim that they became aware of some errors in their computations of back pay and notified the district court and Akron’s attorneys that they intended to adjust the calculations. Specifically, Plaintiff Carr reviewed Snyder’s calculations to determine whether the issues that Akron raised during the depositions warranted adjustments. R. 469 at 60 (Tr. Carr Testimony) (Page ID # 12852). On June 16, 2011, one day before the close of discovery, Akron disclosed the identity of its witness who would testify about the Plaintiffs’ back pay. Pis.’ Br. at 5 n. 3. After that disclosure, Carr recalculated the back pay based on the Plaintiffs’ real pay. R. 469 at 60 (Tr. Trial Vol. 3 at 383) (Page ID #12852). The Plaintiffs produced Carr’s new calculations on June 17, 2011, which was the final day of discovery. Pis.’ Br. at 6. G. The District Court Sets a Start Date for Back Pay and Promotes the Plaintiffs On July 7, 2011, approximately one week before the retrial, the district court entered an order holding that the Plaintiffs had forfeited the right to a trial by jury on the issue of back pay. R. 403 at 1 (D. Ct. Order Re Bench Trial and Mot. for Promotion) (Page ID # 10937). The district court further held that the promotions ordered by July 18, 2011, made the question of front pay no longer one for the jury. Id. The district court based the decision about the start date for calculating back pay on the Plaintiffs’ failure to request a jury instruction on the issue of back pay during the first trial, id. at 2 (Page ID # 10938), and because the Plaintiffs had not timely requested a jury trial in accordance with Federal Rule of Civil Procedure Rule 38, id. at 4 (Page ID # 10940). Moreover, the district court found that the Plaintiffs “ha[d] treated the calculation of back pay damages as a matter to be decided by” the district court because they had filed motions to alter or amend the judgment in which they had asked the court to add the back pay calculations to the total award of damages. Id. at 3 (Page ID # 10939). The court further noted that it had similarly prohibited Akron from arguing lost opportunities during the retrial for the same reason. Id. at 4 (Page ID # 10940). In addition, the district court “revisited” the Plaintiffs’ earlier motion for promotion and ordered that Akron promote all of the Plaintiffs no later than July 18, 2011, the date on which the trial would commence. Id. at 1 (Page ID # 10937). The district court cited drastic changes to Akron’s fire department as one of the motivating reasons for the injunction promoting the Plaintiffs and noted that there “are over 25 vacancies in the lieutenant position and five vacancies at the captain position.” R. 416 at 2 (D. Ct. Order Re Mot. for Promotion) (Page ID # 11105). The court noted that “[o]ver half of the Plaintiffs have retired or are no longer seeking promotion” or are “currently acting in the capacities for which they seek promotion.” Id. Although the district court’s opinion addressed the Plaintiffs’ motion for a permanent injunction, the district court did not mention whether the promotions were intended to be temporary or permanent. See id. at 1-3 (Page ID # 11104-06). On July 14, 2011, Akron filed a notice of appeal of the district court’s July 7 oral order and July 13 supplemental order to promote the Plaintiffs effective July 18, 2011. R. 419 at 1 (Page ID # 11115). The Sixth Circuit issued a temporary stay to allow time for the Plaintiffs to respond to the motion for an emergency stay. In the meantime, Akron moved to suspend the promotions pending the appeal of the injunction. R. 423 at 1 (Def.’s Mot. to Suspend Inj.) (Page ID # 11187). The district court granted a continuance of the retrial, R. 434 (Marginal Order) (Page ID # 11342), and denied Akron’s request for a stay, finding that Akron was not likely to succeed in showing that the district court abused its discretion to promote the Plaintiffs after they had obtained a judgment in their favor, R. 435 at 1-11 (D. Ct. Order Re Stay) (Page ID # 11343-53). On July 21, 2011, the Sixth Circuit dissolved the temporary stay and denied Akron’s motion to stay the promotions pending the resolution of the interlocutory appeal. R. 443 at 2-3 (6th Cir.Order). During the status conference before the retrial, the district court altered the injunction to make the Plaintiffs’ promotions effective July 22, 2011. R. 444 at 1 (D. Ct. Order Re .Alteration of Inj.) (Page ID # 11415). Akron had requested to treat the promotions as “provisional” promotions. Id. at 1-2 (Page ID # 11415-16). The district court initially granted that request, noting that if the “ ‘provisional’ promotion process somehow provides less than the relief ordered,” then the district court reserved the ability-to “take any other steps necessary to ensure compliance with its prior orders.” Id. at 2. The Plaintiffs objected to provisional promotions to the extent that they were not permanent promotions. R. 446 at 2 (Pis.’ Objection as to “Provisional” Appointments and Supplemental to Pis.’ Mot. to Enforce) (Page ID # 11466). The district court acknowledged that the “provisional promotions” would rely upon informal agreements and therefore were not the type of promotion the court had envisioned. R. 454 at 3 (D. Ct. Order Re Objection to “Provisional” Appointment) (Page ID # 11523). Despite Akron’s assertions that “provisional promotions” were necessary to ensure that it would not have to “demote” the Plaintiffs in the event that the Sixth Circuit reversed judgment or the injunction, the district court sustained the Plaintiffs’ objections and ordered Akron to “FORMALLY PROMOTE each Plaintiff to the appropriate rank” permanently. Id. at 3-4 (Page ID # 11523-24). H. The District Court’s Order Regarding Back-Pay Start Dates On July 13, 2011, after the district court had ordered Akron to promote all of the Plaintiffs, the district court issued an order stating that the back-pay calculations would commence on April 5, 2007, the date the eligibility list expired and the Plaintiffs could no longer be promoted based on the 2004 promotional exam. R. 416 at 3 (D. Ct. Order Re Back Pay Start Date) (Page ID # 11106). The district court noted that the Plaintiffs had previously argued that the statute of limitations did not bar their claims because the claims did not accrue until “the completion of the ‘total selection process.’ ” Id. (quoting R. 290 at 23 (Pis.’ Mem. in Opp’n to Mot. for JMOL) (Page ID # 7965)). Accordingly, the district court found that “[t]he promotional process was not completed until the expiration of the list generated by the test,” and therefore the Plaintiffs were not harmed until the list expired. Id. at 4 (Page ID # 11107). The Plaintiffs filed a motion for reconsideration regarding the dates for back pay. R. 441 at 1-7 (Mot. for Recons.) (Page ID # 11399-494). The district court summarily denied the motion for reconsideration. R. 449 at 1 (D.Ct.Order) (Page ID # 11486). I. The Discovery Sanctions On July 15, 2011, the Plaintiffs filed supplemental trial exhibits, including Exhibit 208, which was a document prepared by Carr reflecting his calculations of the Plaintiffs’ back pay losses with a differential starting April 4, 2007. R. 429 .at 3 (Pis.’ Amend. Ex. List Rerial) (Page ID # 11284). That same day, Akron disclosed its final back-pay calculations. R. 457-2 at 3 (Elfin Decl. ¶ 17) (Page ID #11673). The difference between Akron’s and the Plaintiffs’ computation of back pay was approximately $14,000. R. 467 at 4 (Tr. Retrial Vol. 1) (Page ID # 12473). The retrial commenced on July 25, 2011, and the district court addressed Akron’s concern that the Plaintiffs had disclosed their back-pay calculations late. See id. at 37-38 (Page ID # 12506-07). The Plaintiffs’ original calculation of back pay required taking the average salary of all Lieutenants or Captains promoted using the 2004 examination and resulting eligibility list. R. 448 at 1 (D. Ct. Order Re Supplemental Deps.) (Page ID # 11482). The Plaintiffs who were candidates for the rank of Lieutenant would compare their actual salary with that of a promoted candidate for each year after the promotion. Id. Those Plaintiffs who were candidates for the rank of Captain would compare their actual salaries with the average salary of a promoted Captain. See id. Carr’s new formulation took a different approach: each Plaintiff used the paycheck he or she personally received and “incorporate[d] step increases into each paycheck” to reflect the pay increase they would have received had they been promoted. Id. at 1-2 (Page ID # 11482-83). Thus, in the first year after the promotion, a Plaintiff would receive a percentage pay increase of her actual salary, and then in subsequent years receive additional percentage increases. Carr indicated that he preferred his method of calculating back pay, but he abandoned his calculations because the other Plaintiffs intended to use Snyder’s method. See R. 469 at 60-63 (Tr. Retrial Vol. 3) (Page ID # 12852-55). The Plaintiffs claimed that they had to change their calculations because the district court had promoted them and thus they could no longer compare their paychecks to promoted firefighters who had already received step increases. R. 448 at 3 (D. Ct. Order Re Supplemental Deps.) (Page ID # 11484); see also R. 467 at 42-43 (Tr. Retrial Vol. 1) (Page ID # 12511-12). Nevertheless, the district court found that Carr’s formula had existed prior to the court’s order promoting the Plaintiffs, but Akron had not deposed Carr about how he had made his calculations because it had been clear that the Plaintiffs intended to use Snyder’s method. R. 448 at 3-4 (D. Ct. Order Re Supplemental Deps.) (Page ID # 11484-85). In order to permit Akron to inquire into the Plaintiffs’ new method for calculating back pay, the district court reopened the depositions of Carr and Snyder. Id. 'at 4 (Page ID # 11485). After the depositions and before the retrial resumed, the district court conducted a voir dire examination of Carr to determine why the Plaintiffs had changed their back-pay calculations. The district court asked Carr, “[W]hat if anything at all did the Court’s order of promotion have to do with the change in methodology by the plaintiffs?” R. 469 at 74 (Tr. Retrial Vol. 3) (Page ID # 12866). Carr answered: Front pay got taken out of play. And there was a question of whether the start day. If the start date changed, then we couldn’t use Mr. Snyder’s calculations because it would have inflated the numbers if we would have kept it that way, because we would have only had one person to compare to, and that would have been a highly — one of the highest paid captains, Captain Willough-by. Id. at 74-75 (Page ID # 12866-67). The district court clarified: “So, in essence, the methodology didn’t change. Just simply the fact-the dates in essence changed, correct?” Id. at 75 (Page ID # 12867). Carr replied, “Yes, sir.” Id. On July 28, 2011, at the close of the Plaintiffs’ case, the district court entered an order excluding Carr’s calculations from evidence. The district court found that the Plaintiffs had “engaged in a classic bait-and-switch maneuver,” allowing Akron to conduct discovery on the Snyder method without indicating that the Plaintiffs might use the Carr method for their final calculations. R. 484 at 7 (D. Ct. Order Excluding Ex. 208) (Page ID # 13413). In addition, the district court rejected the Plaintiffs’ contention that the court’s promotion order had caused them to change course because Carr had computed back pay using his method before the promotion order went into effect. Id. The district court concluded that the late disclosure of Carr’s calculations had prejudiced Akron because, at their depositions, all the Plaintiffs stated that they had relied on Snyder’s calculation of back pay, but at trial, they stated that they had recalculated their back pay to verify Carr’s calculations. Akron had not been able to depose Plaintiffs other than Carr about their individual calculations based on this new information. Id. at 8 (Page ID # 13414). And the district court decided that it was highly suspicious that the Plaintiffs had calculated their own back pay only after the district court had expressed doubt that the Plaintiffs could rely on Carr’s methodology. Id. Finally, the district court found that the “Plaintiffs’ damages ha[d] been a moving target,” id. at 9 (Page ID # 13415), concluding that “[w]hether this [was] a strategic choice or simply poor trial preparation, it is improper and prejudicial,” id. at 10 (Page ID # 13416). Therefore, the district court excluded Carr’s back-pay calculations, Exhibit 208, as a sanction pursuant to Federal Rule of Civil Procedure 37(b)(2). Id. at 11-12 (Page ID # 13417-18). As an additional sanction, the district court indicated that it would likely award attorney fees for the costs of litigating the motion to exclude Carr’s testimony. Id. at 12 (Page ID # 13418). J. The Retrial After excluding Exhibit 208, the district court suspended the retrial. Akron filed a motion for judgment on partial findings pursuant to Federal Rule of Civil Procedure 52(c), arguing that the Plaintiffs had not presented competent evidence to substantiate back pay, among other issues. See R. 499 at 1-30 (Def.’s Mem. in Supp. of Mot. for J. on Partial Findings) (Page ID # 14626-55). On September 24, 2012, the district court denied Akron’s Rule 52(c) motion, concluding that the Plaintiffs had presented evidence from which the court could determine back pay for each Plaintiff. R. 531 at 3 (D. Ct. Order Re Mot. for J. on Partial Findings) (Page ID # 15372). On November 28, 2012, nearly four years after the first trial and fifteen months after the retrial first began, the trial resumed. Akron moved to admit exhibits into evidence, rested, and renewed its motion for a directed verdict pursuant to Federal Rule of Civil Procedure 52. R. 565 at 4-7 (Tr. Retrial Vol. 5) (Page ID # 15881-84). Akron argued that the only evidence in the record was the testimony of Mark McLeod, Akron’s witness, who had not performed back-pay calculations, but had reduced the Plaintiffs’ lost earnings calculations to reflect a loss of chance. Id. at 8-11 (Page ID # 15885-88). K. Howe I: Appeal of the Injunction Ordering Promotions While the parties were relitigating the issue of damages in the district court, this court was considering whether the district court had abused its discretion by issuing the injunction that permanently promoted the Plaintiffs. See Howe I, 723 F.3d 651. In Howe I, Akron advanced two arguments: (1) that the Plaintiffs had failed to present a prima facie case of disparate impact liability; and (2) that “the district court abused its discretion in issuing the injunction.” Id. at 657. On July 22, 2013, following briefing and argument, we held that “the district court did not abuse its discretion in issuing the preliminary injunction requiring [Akron] to promote certain Plaintiffs.” Id. at 663-64. In order to reach that conclusion, we held “that all of the promoted Plaintiffs had demonstrated substantial likelihood of success on the merits with regard to the adverse effect element of their disparate impact claims.” Id. at 661. L. The Back-Pay Award On August 30, 2013, the district court entered its findings of fact and conclusions of law with respect to the Plaintiffs’ back pay. The district court used McLeod’s calculations to compute the Plaintiffs’ back pay, see R. 588 at 2-6 (Findings of Fact ¶¶ 9-23) (Page ID # 16480-84), noting that the “computations involved simple mathematical functions and were not expert calculations,” id. at 8 (Conclusions of Law ¶ 12) (Page ID # 16486). The back-pay calculations began on April 4, 2007, and continued until July 17, 2011, the day before the Plaintiffs’ promotions went into effect. Id. at 3-4 (Findings of Fact ¶ 21-22) (Page ID # 16481-82). Accordingly, the district court found that there was sufficient evidence to award the Plaintiffs a total of $616,217.75 in back pay. Id. at 9 (Conclusions of Law ¶ 14) (Page ID # 16487). The district court calculated each Plaintiffs individual back-pay award. See id. at 9-12 (FFCL ¶¶ 14A-U) (Page ID # 16487-90). To the extent that the district court’s calculations may include some front pay, the court noted that it would still award that amount. Id. at 8 (Conclusions of Law ¶ 11) (Page ID # 16486). In addition, the district court dismissed Plaintiff Michael Harvey’s claim to back pay because he never testified and the record did not support a back-pay award. Id. at 12 (Conclusions of Law ¶ 15) (Page ID # 16490). Finally, the district court found no just reason for delay pursuant to Federal Rule of Civil Procedure 54(b). Id. (Conclusions of Law ¶ 16). On September 3, 2013, the district court denied Akron’s renewed motion for judgment under Rule 52(c). R. 589 at 1 (D. Ct. Order Re Def.’s Renewed Mot. for J. on Partial Findings) (Page ID # 16491). The district court found that Akron had waived its legal theory that the Plaintiffs’ back pay had to be reduced based on the probability that they would not be promoted because Akron had not presented that testimony or argument during the first trial. Id. at 2 (Page ID # 16492). Moreover, the court concluded that the Plaintiffs had not opened the door to that theory 'during their cross-examination of McLeod. Id. On September 27, 2013, Akron filed a Notice of Appeal of (1) “the Findings of Fact and Conclusions of Law entered in this action on the 30th day of August, 2013 (Doc. 588), that awards Plaintiffs $616,217.75 and includes ‘no just reason for delay’ (2) the Order (“Doc.589”) denying Akron’s renewed Rule 52(c) motion;' and (3) “interlocutory orders that issued prior to August 30, 2013 and are merged into the August 30, 2013 Findings of Fact and Conclusions of Law.” R. 590 at 1 (Notice of Appeal Case No. 13-4172) (Page ID # 16494). On October 10, 2013, the Plaintiffs filed their cross-appeal for Case No. 13-4172 regarding back pay. On February 19, 2014, the Plaintiffs filed a motion for prejudgment and post-judgment interest. R. 613 at 1-9 (Pis.’ Mot. for Pre & PosNJ. Interest) (Page ID # 16646-54). Akron opposed the motion. R. 638 at 1-14 (Def.’s Opp’n to Mot for Pre & Post-J. Interest) (Page ID # 17301-14). To date, the district court has not yet ruled on the Plaintiffs’ motion. M. The Permanent Injunction and Appointment of a Court Monitor On December 28, 2012, after the retrial ended, the Plaintiffs filed a renewed motion for a permanent injunction after they learned that the Akron Fire Department planned to promote firefighters to the ranks of Lieutenant and Captain. R. 573 at 1 (Pis.’ Renewed Mot. for Permanent Inj. and Appointment of a Receiver) (Page ID # 16065). They asked the ' district court to enter an order barring Akron “from utilizing or otherwise acting upon any promotional process, including but not limited to the process developed and administered in December, 2004, for filling the ranks of Lieutenant and Captain.” Id. at 1-2 (Page ID # 16065-66). In addition, the Plaintiffs requested that the district court mandate that Akron “develop[] a job-related nondiscriminatory promotion process, under the supervision and guidance of a receiver appointed by [the district court].” Id. at 2 (Page ID # 16066). Akron opposed the Plaintiffs’ motion. See R. 577 at 1-11 (Def.’s Br. in Opp’n to Pis.’ Renewed Mot. for Permanent Inj.) (Page ID # 16083-93). On March 27, 2014, the district court entered a permanent injunction and appointed David R. Cohen to serve as the Court Monitor. The district court found that the promotions and back-pay award did not make the Plaintiffs whole because they had been “deprived of a fair process and a fair opportunity to be promoted at the outset of the creation of the eligibility list.” R. 643 at 6 (D. Ct. Order Re Permanent Inj.) (Page ID # 17331). The district court specially noted that, although the promotions addressed some of the harm they suffered, there remained questions about how the denial of the fair process at the outset would impact the Plaintiffs’ access to fair promotions in the future. See id. The permanent injunction forbade Akron to do the following: (1) to use the 2004 examination or promotion process or hire any of the entities involved in the creation of the examination or promotion process; (2) to use “any promotional examination process” that “results in disparate impact upon any protected group of applicants and is not job related for the promotional position”; (3) to “take any step” in the promotion process for any firefighters, or use any promotional examination without the approval of the Court Monitor; (4) to retaliate against any employee who has complained of discrimination “on the basis of their race or age in the promotional process, or has participated in the investigation or litigation of any claim or allegation of such discrimination, or has sought or obtained relief from the court in this case”; (5) to discriminate on the basis of race or age “in the development or implementation of its promotional process.” Id. at 7 (Page ID # 17332). The permanent injunction required “[t]he Parties” to “timely comply with the orders of the Court Monitor.” Id. The district court also required the appointed Court Monitor to do the following: (1) “adopt a schedule which requires [Akron] to notify the [Court] Monitor and the Parties before commencing any step in creating a new promotional process”; (2) to develop a process, “which allows Plaintiffs to review [Akron’s] proposals, provide objections or input where appropriate, and be compensated for that review,” and which “specifies] any and all limitations placed on Plaintiffs with regard to both content and compensation”; and (3) to prepare a Document Retention Order. Id. at 8. The district court gave the Court Monitor the discretion to require Akron “to disclose any information relating to any step in its proposed new promotional process before allowing [Akron] to proceed to any step in the process,” or “to establish that it has satisfied conditions specified by the [Court] Monitor, or to obtain the [Court] Monitor’s explicit approval before commencing any step in the proposed new promotional process.” Id. Failure to comply with any provision of the permanent injunction could “be punished by court-ordered sanction if another party moves for such sanction,” which may include contempt proceedings. Id. at 9. The district court gave the parties ten days to file objections to the permanent injunction. Id. at 12. Because neither party objected to Cohen’s appointment as the Court Monitor, the district court entered the Order of Appointment on April 8, 2014. R. 653 at 1 (Order of Appointment) (Page ID # 17373). Three days later, on April 11, 2014, Akron filed a notice of appeal of the permanent injunction and order of appointment. R. 654 at 1 (Notice of Appeal Case No. 14-3352) (Page ID # 17383). After filing the notice of appeal, Akron sought a stay of the permanent injunction from the district court, which was denied. R. 666 at 1 (D. Ct. Order Re Stay of Permanent Inj.) (Page ID # 17440). The ■ district court rejected the request for a stay because Akron had not made “even a meager showing of likelihood of success on the merits.” Id. at 5 (Page ID # 17444). Tellingly, the district court reiterated that it “found that [a permanent injunction] was necessary for complete relief,” that the “Plaintiffs will never know with any certainty whether they could have been promoted much sooner,” and that “obstacles remain for them for future testing, such as lacking the proper amount of time in grade to qualify for that future testing.” Id. at 4 (Page ID # 17443). Moreover, the district court emphasized that Akron’s conduct— “even post-verdict conduct” — had caused the court to believe that it should oversee the promotion process, citing Akron’s “attempt ] to segregate Plaintiffs from all others in their rank by attaching a ‘provisional’ term to their title.” Id. In response to Akron’s argument that the court lacked the authority to enter a permanent injunction absent a showing of intentional discrimination, the district court noted that the Plaintiffs had “presented a strong argument that the evidence of disparate impact was so overwhelming that one could infer intentional discrimination,” but declined to make that specific finding. Id. at 5 (Page ID # 17444). The district court also emphasized that Akron had “offer[ed] no argument of any kind to suggest how the relief could be narrowed to more fully respect the principles of federalism or comity,” and “[i]nstead, ... [Akron] stubbornly adheres to its pre-verdict belief that no relief of any kind should be afforded these Plaintiffs.” Id. Akron has never asked this court to issue a stay of the permanent injunction. See 6th Cir. Docket, Case No. 14-3352. The Court Monitor continues to work with the parties and file status reports with the district court. See, e.g., R. 676 at 1-3 (Special Master Quarterly Report No. 1) (Page ID # 17706-08). N. Appeals No. 13-4172 and No. 14-3352 This is a consolidated appeal. Case No. 13-4172 involves the appeal of a liability judgment in favor of the Plaintiffs with respect to their disparate-impact age- and race-discrimination claims and the award of back pay. Akron challenges the liability judgments on three grounds. First, Akron challenges the sufficiency of the evidence of disparate impact. In particular, Akron argues that the district court erroneously relied up on the EEOC’s so-called four-fifths rule, which provides that “[a] selection rate for any race, sex, or ethnic group which is less than four-fifths (4/5) (or eighty percent) of the rate for the group with the highest rate will generally be regarded ... as evidence of adverse impact....” 29 C.F.R. § 1607.4(D). Akron challenges the four-fifths rule in this context because it believes that the dataset in this case is too small. Akron Br. at 32-38. Second, Akron contends that it is entitled to judgment as a matter of law with respect to the twelve Caucasian Plaintiffs who applied for the rank of Captain because the “Plaintiffs offered no evidence of background circumstances suggesting [Akron] is the unusual employer who discriminates against the majority (Caucasians).” Id. at 38. Akron also requests a new trial on the issue of liability because the district court issued an erroneous jury instruction and because the verdict was against the manifest weight of the evidence. See id. at 44-48. Akron also challenges the district court’s award of back pay. See id. at 49-52. The Plaintiffs filed a cross-appeal in Case No. 13-4172, challenging the back-pay award on the basis that the district court utilized an incorrect date to begin calculating back pay and failed to calculate step increases. See Pis.’ Br. at 60-64. In addition, the Plaintiffs argue that the district court abused its discretion by excluding their back-pay calculations as a sanction for alleged discovery violations during the retrial. Id. at 64-71. Finally, the Plaintiffs contend that the district court made various errors when calculating back-pay awards for Plaintiffs Snyder, Harvey, and Sehueller. Id. at 71-72. In Case No. 14-3352, Akron appeals the district court’s order entering a permanent injunction and appointing a Court Monitor because it contends that the injunction'is not narrowly tailored to address the harm to the Plaintiffs or sufficiently limited in scope or duration. Akron Br. at 52-60. II. THE LIABILITY JUDGMENTS A. The Impact of Howe I: Law of the Case The Plaintiffs contend that we should not review Akron’s challenges to the liability judgment either because we have already decided the issues in Howe I, or because Akron could have raised the arguments in its appeal of the promotion order, but did not. See Pis.’ Br. at 31-41. We agree. In Howe I, we noted that the district court had not yet entered a final judgment and “may yet revisit its decision regarding promotions,” and so “we reviewed] only the question of whether the district court abused its discretion in issuing the injunction and reaeh[ed] the merits of the case only as necessary to do so.” Howe I, 723 F.3d at 657-58. We therefore analyzed Akron’s challenges to the liability judgments to determine whether Akron was “ ‘likely to prevail on the merits.’ ” Id. at 658 (quoting Samuel v. Herrick Mem’l Hosp., 201 F.3d 830, 833 (6th Cir.2000) (listing the four factors we consider when reviewing the propriety of a preliminary injunction)). Using this framework in Howe I, we examined Akron’s three challenges to the validity of the liability judgments. First, Akron argued that the Plaintiffs had not identified a specific employment practice that caused a disparate impact. Howe I, 723 F.3d at 658-59 (citing Grant v. Metro. Gov’t of Nashville & Davidson Cnty., 446 Fed.Appx. 737 (6th Cir.2011)). We held that the “Plaintiffs sufficiently identified a specific employment practice.” Id. at 659. Second, Akron contended “that the district court erred as a matter of law in permitting Plaintiffs to demonstrate adverse ef.fect by applying the ‘four-fifths rule’ to promotion rates instead of exam pass rates.” Id. at 659. Akron did not contest the validity of the four-fifths rule. See id. at 659-60. We held that the Plaintiffs could use the four-fifths rule with respect to promotion rates, and therefore the Plaintiffs had demonstrated that the promotion process had an adverse effect on African-American and over-forty candidates for the rank of Lieutenant. Id. at 660. Third, Akron challenged the liability judgment in favor of the Caucasian candidates for Captain because the “Plaintiffs failed to show that [Akron] is that unusual employer who discriminates against the majority.” Id. (internal quotation marks omitted). We held that Akron had waived that argument, but we also concluded that “[e]ven if the argument had not been waived, it is far from clear that the unusual-employer requirement” is applicable in the case of a disparate-impact—rather than disparate-treatment—claim. Id. at 661. Akron argues that our holding that Akron had waived its argument that the Plaintiffs were required to prove that Akron is the “unusual employer who discriminates against the majority” was “clear error and should not be followed.” Akron Br. at 38. Akron also urges us to consider all of their challenges to the liability judgments because Howe I was a review of a preliminary injunction, and therefore was not a full review of the liability judgment. Akron Reply Br. at 8. We will not address either issue, however, because the doctrine of law of the case counsels against reconsideration of issues that have already been decided. The doctrine of law of the case provides that the courts should not “reconsider a matter once resolved in a continuing proceeding.” 18B Chaeles Alan Wright, Arthur R. Miller, and Edward H. Cooper, Federal PRACTICE And Prooedure: JurisdictioN And Related Matters § 4478 (4th ed.2015). “The purpose of the law-of-the-case doctrine is to ensure that ‘the same issue presented a second time in the same case in the same court should lead to the same result.’ ” Sherley v. Sebelius, 689 F.3d 776, 780 (D.C.Cir.2012) (quoting LaShawn A. v. Barry, 87 F.3d 1389, 1393 (D.C.Cir.1996)). For a prior decision to control, the prior tribunal must have actually decided the issue. Weight et al„ supra, § 4478. “A position that has been assumed without decision for purposes of resolving another issue is not the law of the case.” Id. “An alternate holding, however, does establish the law of the case.” Id. Unlike claim preclusion, the law of the case does not apply to issues that a party could have raised, but did not. Id. The law-of-the-case doctrine is a prudential practice; a court may revisit earlier issues, but should decline to do so to encourage efficient litigation and deter “indefatigable diehards.” Id. Whether a panel should treat a pri- or panel’s ruling on a preliminary injunction as the law of the case is tricky, however. Rulings on preliminary injunctions are generally “‘tentative deeision[s] on the merits,’ ” which “change[ ] the ‘incentives’ of the parties that inform their litigation strategies.” Gooch v. Life Investors Ins. Co. of Am., 672 F.3d 402, 433 (6th Cir.2012) (quoting Bieneman v. City of Chi., 838 F.2d 962, 964 (7th Cir.1988)). But when the appellate panel considering the preliminary injunction has issued “[a] fully considered appellate ruling on an issue of law,” then that opinion becomes the law of the case. Wright et al., supra, § 4478.5. This case presents an unusual circumstance because we considered the issues presented in Howe I with a completely developed record; we had transcripts from a completed jury trial available for review. “[W]here the earlier ruling, though on preliminary-injunction review, was established in a definitive, fully considered legal decision based on a fully developed factual record and a decisionmaking process that included full briefing and argument without unusual -time constraints,” then the law-of-the-case doctrine applies. Sherley, 689 F.3d at 782. In Sherley, the D.C. Circuit vacated a preliminary injunction in favor of the plaintiffs and remanded the case to the district court for further proceedings, after which the district court entered summary judgment in favor of the defendants. Id. at 779. The plaintiffs appealed the entry of summary judgment and offered “precisely the same argument” that the prior panel had rejected, arguing that the preliminary nature of a review of a denial of a preliminary injunction made the law-of-the-case doctrine inapplicable. Id. at 781. The D.C. Circuit held that the doctrine of law of the case prevented reconsideration of that prior holding because “[t]he time constraints and limited record” that usually make the law-of-the-case doctrine inappropriate in most cases involving preliminary injunctions were “not present.” Id. at 788. The D.C. Circuit’s conclusion is not novel; other circuits facing similar procedural issues have reached the same conclusion. See id. at 782-83 (citing Naser Jewelers, Inc. v. City of Concord, 538 F.3d 17, 20 (1st Cir.2008) (“[T]he [law-of-the-case] doctrine applies when [the] court has previously ruled on a motion for preliminary injunction and the record before the prior panel was sufficiently developed and the facts necessary to shape the prior legal matrix were sufficiently clear.”) (internal quotation marks omitted); This That & The Other Gift & Tobacco, Inc. v. Cobb Cnty., 439 F.3d 1275, 1284-85 (11th Cir.2006) (same); Entergy, Ark., Inc. v. Nebraska, 241 F.3d 979, 987 (8th Cir.2001) (same); Royal Ins. Co. of Am. v. Quinn-L Capital Corp., 3 F.3d 877, 880-81 (5th Cir.1993) (same)). We therefore join the other circuits and hold that, when a court reviewing the propriety of a preliminary injunction issues a fully considered ruling on an issue of law with the benefit of a fully developed record, then the conclusions with respect to the likelihood of success on the merits are the law of the case in any subsequent appeal. In Howe I, Akron appealed the promotion of all of the Plaintiffs with the benefit of a complete record that “was sufficiently developed and the facts necessary to shape the proper legal matrix were sufficiently clear.” Naser Jewelers, 538 F.3d at 20 (internal quotation marks and bracket omitted). We “carefully considered” each argument that Akron raised as to why the Plaintiffs’ liability judgment would not be upheld on appeal and issued a reasoned judgment. Entergy, 241 F.3d at 987. We therefore conclude that the holdings of Howe I are the law of the case. That means that unless Akron provides compelling reasons to revisit those holdings, we will not address Akron’s