REENA RAGGI, Circuit Judge:

Quinnipiac University appeals pursuant to 28 U.S.C. § 1292(a)(1) from a permanent injunction ordered on July 22, 2010, by the United States District Court for the District of Connecticut (Stefan R. Underhill, Judge), after a bench trial at which Quinnipiac was found to have violated Title IX of the Education Amendments of 1972 ("Title IX") by failing to afford equal participation opportunities in varsity sports to female students. See Biediger v. Quinnipiac Univ., 728 F.Supp.2d 62 (D.Conn. 2010). Quinnipiac argues that the injunction, which prohibits any such future discrimination, should be vacated because it is based on a Title IX ruling infected by errors in counting the varsity athletic participation opportunities afforded Quinnipiac's female students in the 2009 — 10 school year. Specifically, Quinnipiac faults the district court for excluding from its count of the total athletic participation opportunities afforded female students: (1) 11 roster positions on the women's indoor and outdoor track and field teams, held by members of Quinnipiac's women's cross-country team who were required to join the track teams even though they were unable to compete in 2009 — 10 because they were injured or "red-shirted";1 and (2) all 30 roster positions on Quinnipiac's nascent women's competitive cheerleading team, based on a finding that the team did not afford the athletic participation opportunities of a varsity sport. Quinnipiac further contends that, even if these 41 roster positions should not count as varsity athletic participation opportunities for women, the district court erred in concluding that (3) the resulting 3.62% disparity between the percentage of all participation opportunities in varsity sports afforded female students (58.25%) and the percentage of enrolled female undergraduates (61.87%) established a Title IX violation warranting the challenged injunctive relief.

We identify no merit in these arguments, and we affirm the challenged injunction substantially for the reasons stated by the district court in its comprehensive and well reasoned opinion.

I. Background

A. Quinnipiac's Decision To Eliminate Women's Volleyball Prompts This Title IX Action

This lawsuit has its origins in Quinnipiac's March 2009 announcement that in the 2009 — 10 academic year, it would eliminate its varsity sports teams for women's volleyball, men's golf, and men's outdoor track and field, while simultaneously creating a new varsity sports team for women's competitive cheerleading. Plaintiffs, five Quinnipiac women's volleyball players and their coach, Robin Sparks, filed this action in April 2009, charging the university with violating Title IX by denying women equal varsity athletic participation opportunities, and seeking an injunction that, among other things, prevented Quinnipiac from eliminating its women's volleyball team. After a hearing, the district court preliminarily enjoined Quinnipiac from withdrawing support from its volleyball team, finding that Quinnipiac systematically and artificially increased women's teams' rosters and decreased men's teams' rosters to achieve the appearance of Title IX compliance. See Biediger v. Quinnipiac Univ., 616 F.Supp.2d 277 (D.Conn.2009). The district court subsequently certified a plaintiff class of all present and future female Quinnipiac students who had been or would be harmed by the alleged Title IX discrimination and sought injunctive relief. See Biediger v. Quinnipiac Univ., No. 3:09-cv-621 (SRU), 2010 WL 2017773 (D.Conn. May 20, 2010). In June 2010, the district court conducted a bench trial on plaintiffs' claim of disproportionate allocation of athletic participation opportunities and, finding in their favor, granted permanent injunctive relief.2

B. Statutory and Regulatory Background

To discuss the district court's challenged ruling further, we must briefly review certain controlling law and regulations.

Title IX provides, in relevant part, that "[n]o person in the United States shall, on the basis of sex, be excluded from participation in, be denied the benefits of, or be subjected to discrimination under any education program or activity receiving Federal financial assistance." 20 U.S.C. § 1681(a). Although the statutory language makes no mention of athletics programs, the former Department of Health, Education and Welfare ("HEW") and its successor agency, the Department of Education ("DOE"), have interpreted Title IX to require recipients of federal financial assistance operating or sponsoring "interscholastic, intercollegiate, club or intramural athletics" to "provide equal athletic opportunity for members of both sexes." 34 C.F.R. § 106.41(c).

Section 106.41(c) provides a non-exhaustive list of factors relevant to determining whether equal athletic opportunities are available:

Id. Title IX claims of sex discrimination in athletics fall into two categories based on the § 106.41(c) factors to which the claims are addressed: effective accommodation claims focus on § 106.41(c)(1), and equal treatment claims focus on § 106.41(c)(2)(10). See McCormick ex rel. McCormick v. Sch. Dist. of Mamaroneck, 370 F.3d 275, 291 (2d Cir.2004); accord Parker v. Franklin Cnty. Cmty. Sch. Corp., 667 F.3d 910, 919 (7th Cir.2012). At issue in this appeal is plaintiffs' effective accommodation claim.

In 1979, HEW published in the Federal Register a policy interpretation of § 106.41(c), which states that a school's compliance with the effective accommodation requirement will be assessed "in any one of the following ways":

1979 Policy Interpretation, 44 Fed.Reg. 71,413, 71,418 (Dec. 11, 1979). The 1979 Policy Interpretation thus affords a school three safe harbors in defending against an effective accommodation claim under § 106.41(c)(1).

In 1996, the DOE's Office of Civil Rights ("OCR"), which is responsible for enforcement of Title IX, see 20 U.S.C. § 3441(a)(3), clarified that the analysis for determining whether a university affords substantially proportionate participation opportunities to athletes of both sexes under the first prong of the three-part test — the prong relied on by Quinnipiac in defending against plaintiffs' Title IX effective accommodation claim — "begins with a determination of the number of participation opportunities afforded to male and female athletes in the intercollegiate athletic program." OCR, U.S. DOE, Clarification of Intercollegiate Athletics Policy Guidance: The Three-Part Test, at 2-3 (Jan. 15, 1996) ("1996 Clarification").3 OCR explained that, "[a]s a general rule, all athletes who are listed on a team's squad or eligibility list and are on the team as of the team's first competitive event are counted as participants." Id. at 3. Further, "an athlete who participates in more than one sport will be counted as a participant in each sport in which he or she participates." Id. It is not necessary for an athlete to meet minimum criteria of playing time or athletic ability to count as a participant. As OCR explained, "athletes who practice but may not compete" nevertheless "receive numerous benefits and services, such as training and practice time, coaching, tutoring services, locker room facilities, and equipment, as well as important non-tangible benefits derived from being a member of an intercollegiate athletic team." Id. Thus, "it is necessary to count all athletes who receive such benefits when determining the number of athletic opportunities provided to men and women." Id. In a letter accompanying the 1996 Clarification, however, OCR sounded a note of caution: for an athlete to be counted, he or she must be afforded a participation opportunity that is "real, not illusory," in that it offers the same benefits as would be provided to other bona fide athletes. See Letter from Norma V. Cantú, Assistant Sec'y for Civil Rights, OCR, U.S. DOE, to Colleagues, at 4 (Jan. 16, 1996) ("1996 OCR Letter").

In a 2008 letter, OCR explained that a genuine athletic participation opportunity must take place in the context of a "sport." Letter from Stephanie Monroe, Assistant Sec'y for Civil Rights, OCR, U.S. DOE, to Colleagues, at 1-2 (Sept. 17, 2008) ("2008 OCR Letter"). If a school is a member of a recognized intercollegiate athletic organization, such as the National Collegiate Athletic Association ("NCAA"), that subjects the activity at issue to its organizational requirements, OCR will "presume" that the activity is a sport and that participation can be counted under Title IX. Id. at 1-2. But if that presumption does not apply or has been rebutted, OCR will determine whether the activity qualifies as a sport by reference to several factors relating to "program structure and administration" and "team preparation and competition." Id. at 1-4.

Eight years earlier, in 2000, OCR had issued two letters stating that cheerleading, whether of the sideline or competitive variety, was presumptively not a sport, and that team members could not be counted as athletes under Title IX. See Letter from Mary Frances O'Shea, Nat'l Coordinator for Title IX Athletics, OCR, U.S. DOE, to David V. Stead, Exec. Dir., Minn. State High Sch. League, at 1-3 (Apr. 11, 2000) ("April 2000 OCR Letter"); accord Letter from Mary Frances O'Shea, Nat'l Coordinator for Title IX Athletics, OCR, U.S. DOE, to David V. Stead, Exec. Dir., Minn. State High Sch. League, at 1 (May 24, 2000) ("May 2000 OCR Letter"). While the letters indicated OCR's willingness to review particular cheerleading programs on a case-by-case basis, the parties stipulated in the district court that, since 2000, OCR has never recognized an intercollegiate varsity cheerleading program to be a sport for Title IX purposes. See Biediger v. Quinnipiac Univ., 728 F.Supp.2d at 92. Nor has Quinnipiac ever sought OCR recognition of its competitive cheerleading program as a sports activity. See id. at 85.

Once the numbers of real athletic participation opportunities afforded men and women have been determined in light of these principles, the next step of Title IX effective-accommodation analysis considers whether the numbers are substantially proportionate to each sex's enrollment. See 1996 Clarification at 4. OCR has not construed substantial proportionality to require exact proportionality. Rather, substantial proportionality is determined on a case-by-case basis in light of "the institution's specific circumstances and the size of its athletic program." Id. As a baseline, OCR will consider substantial proportionality achieved if the number of additional participants necessary required for exact proportionality "would not be sufficient to sustain a viable team." Id.

OCR affords schools considerable "flexibility and choice" in deciding how to provide substantially proportionate athletic opportunities to students of both sexes, including by eliminating teams, placing caps on its rosters, 1996 OCR Letter at 4, or "[e]xpanding ... athletic opportunities through new sports," 2008 OCR Letter at 4.

C. The District Court Ruling

At trial, Quinnipiac maintained that it offered athletic participation opportunities to male and female undergraduates substantially proportionate to their respective enrollments. In support, it pointed to evidence showing that, of the 5,686 students enrolled in Quinnipiac's undergraduate programs in the 2009 — 10 academic year, 3,518 were female and 2,168 were male. Varsity rosters for the first day of team competitions in 2009 — 10 listed 440 varsity athletes, of whom 274 were female and 166 were male. Thus, Quinnipiac maintained that women represented 61.87% of the total student body and 62.27% of all varsity athletes, while men represented 38.13% of the student body and 37.73% of all varsity athletes. See Biediger v. Quinnipiac Univ., 728 F.Supp.2d at 64-65.

Plaintiffs challenged Quinnipiac's count of its varsity athletes, arguing that (1) the university manipulated its team rosters to produce artificially undersized men's teams and artificially oversize women's teams; (2) counting the same women's membership on cross-country, indoor track, and outdoor track teams as three distinct athletic participation opportunities was unwarranted because Quinnipiac's indoor and outdoor track teams did not afford cross-country athletes genuine and distinct benefits; and (3) women who participated on the competitive cheerleading team should not be counted at all because the activity had not yet achieved the status of an intercollegiate varsity sport. See id. at 65.

After trial, the district court issued a detailed memorandum of decision in favor of plaintiffs. Therein, the district court rejected plaintiffs' contention that, in setting roster targets for each of its teams, Quinnipiac had manipulated the rosters so as to undercount male participants and overcount female participants, or to set artificially high targets for women's teams that denied women participants genuine athletic opportunities. See id. at 108-10. At the same time, the district court identified concerns about how Quinnipiac counted athletes participating on its women's cross-country, indoor track, and outdoor track teams, stating that it "recall[ed] roster manipulations similar to those" identified in its preliminary injunction opinion. Id. at 106. Nevertheless, in counting the genuine athletic participation opportunities, the district court declined to discount the 30-athlete rosters for either track team by 18 based on the number of positions held on each team by cross-country runners. Instead, it discounted the number of genuine participation opportunities in women's indoor track by five, for a total of 25, and in women's outdoor track by six, for a total of 24, because the numbers represented cross-country runners required to participate in track despite being injured and red-shirted. See id. at 78, 108. The district court also decided that none of the 30 roster positions assigned to women's competitive cheerleading should be counted because the activity did not yet afford genuine athletic participation opportunities in a varsity sport. See id. at 99-101.

Expanding Quinnipiac's reported roster positions for male athletes by one to reflect an additional participant on the men's ice hockey team revealed at trial, see id. at 71, 111, the district court counted a total of 400 varsity athletic participation opportunities, see id. at 111. Of these 400, it found that 233 — or 58.25% — were assigned to women and 167 — or 41.75% — were assigned to men. See id. The district court observed that "in strictly numerical terms," a 3.62% disparity between Quinnipiac's women's 58.25% varsity athletic participation and their 61.87% representation in the undergraduate population reflected only "a borderline case of disproportionate athletic opportunities for women." Id. Nevertheless, the district court concluded that the disparity was significant enough to support judgment in favor of plaintiffs because (1) the disparity was caused by Quinnipiac's own actions and not by natural fluctuations in enrollment; and (2) it was reasonable to expect Quinnipiac to close the gap because the 38 roster positions needed for that purpose would be enough to field a viable women's athletic team, and such a team already existed in the form of the women's volleyball team. See id. at 111-13.

Accordingly, the district court entered a declaratory judgment finding Quinnipiac to have violated Title IX and its implementing regulations by discriminating against women in failing to provide equal athletic participation opportunities to female students, and it permanently enjoined Quinnipiac from continuing to discriminate in this manner. The district court ordered Quinnipiac to submit a plan for complying with the injunction, which plan was to provide for continuation of the women's volleyball team during the 2010-11 athletic season. See id. at 114.

This timely appeal followed.

II. Discussion

A. Quinnipiac's Argument and the Standard of Review

Quinnipiac challenges the district court's award of permanent injunctive relief by attacking the finding of Title IX sex discrimination on which the relief is premised. Although the finding of sex discrimination is incorporated in a declaratory judgment that is not yet final and, therefore, not itself appealable, we nevertheless have jurisdiction to review the finding because it is "inextricably intertwined" with the challenged injunctive relief over which we do have interlocutory appellate jurisdiction pursuant to 28 U.S.C. § 1292(a)(1). Lamar Adver. of Penn, LLC v. Town of Orchard Park, 356 F.3d 365, 371-72 (2d Cir.2004).

Quinnipiac contends that the district court finding of sex discrimination is infected by three errors: (1) the exclusion of 11 positions on the women's indoor and outdoor track teams from its count of varsity athletic participation opportunities, (2) the exclusion of all 30 competitive cheerleading positions from its count of varsity athletic participation opportunities, and (3) the determination that an identified 3.62% disparity between women's representation in Quinnipiac's student body and on its varsity sports teams sufficed to show that women were not afforded substantially proportionate varsity athletic participation opportunities.

We review the award of permanent injunctive relief for abuse of discretion, see City of New York v. Mickalis Pawn Shop, LLC, 645 F.3d 114, 142 (2d Cir.2011), but where, as here, appellant does not challenge the scope of such relief but its basis in law and fact, we review the district court's factual findings only for clear error and its conclusions of law de novo, see City of New York v. Golden Feather Smoke Shop, Inc., 597 F.3d 115, 120 (2d Cir.2010); accord Bessemer Trust Co., N.A. v. Branin, 618 F.3d 76, 85 (2d Cir.2010) (noting "strong presumption" in favor of trial court's findings of fact, which appellate court will not upset absent "definite and firm conviction that a mistake has been committed" (internal quotation marks omitted)); see also Fed.R.Civ.P. 52(a)(6) (providing that findings of fact made by district court in nonjury trial must not be set aside by reviewing court "unless clearly erroneous").

B. Deference to Agency Interpretation of Title IX's Implementing Regulations

In addressing Quinnipiac's arguments, we note at the outset that no party challenges the district court's reliance on agency policy statements and letters interpreting 34 C.F.R. § 106.41(c)(1). This court has already ruled that the 1979 Policy Interpretation of § 106.41(c) is entitled to a "particularly high" degree of judicial deference under Chevron U.S.A. Inc. v. Natural Resources Defense Council, Inc., 467 U.S. 837, 104 S.Ct. 2778, 81 L.Ed.2d 694 (1984), because Congress explicitly delegated to the administering agency "the task of prescribing standards for athletic programs under Title IX." McCormick ex rel. McCormick v. Sch. Dist. of Mamaroneck, 370 F.3d at 288 (internal quotation marks omitted).4 We here conclude that the 1996 Clarification, the accompanying 1996 OCR Letter, and the 2000 and 2008 OCR Letters are likewise entitled to substantial deference under Auer v. Robbins, 519 U.S. 452, 461, 117 S.Ct. 905, 137 L.Ed.2d 79 (1997), because they reflect reasonable agency interpretations of ambiguities in its own regulation, and there is no reason to think that the agency's interpretations do not reflect its "fair and considered judgment on the matter in question." Mullins v. City of New York, 653 F.3d 104, 113-14 (2d Cir.2011) (internal quotation marks omitted); see Mansourian v. Regents of Univ. of Cal., 602 F.3d 957, 965 n. 9 (9th Cir.2010) (collecting cases deferring to 1979 Policy Interpretation and 1996 Clarification). Indeed, even if the agency interpretations of § 106.41(c)(1) reflected in the 1996 Clarification and subsequent letters were not entitled to Auer deference, they would be entitled to substantial deference under United States v. Mead Corp., 533 U.S. 218, 121 S.Ct. 2164, 150 L.Ed.2d 292 (2001), because their logical consistency with the agency's earlier 1979 Policy Interpretation amplifies their "`power to persuade.'" Christopher v. SmithKline Beecham Corp., ___ U.S. ___, 132 S.Ct. 2156, 2169, 183 L.Ed.2d 153 (2012) (quoting Mead Corp., 533 U.S. at 228, 121 S.Ct. 2164) (according agency interpretation of own regulation "deference proportional to" its persuasiveness under Mead, where interpretation not entitled to controlling deference under Auer).

In contrast to the parties, amicus curiae Eagle Forum Education & Legal Defense Fund argues that continued judicial deference to the agency's 1979 Policy Interpretation of 34 C.F.R. § 106.41(c), see McCormick ex rel. McCormick v. Sch. Dist. of Mamaroneck, 370 F.3d at 288, is unwarranted after Alexander v. Sandoval, 532 U.S. 275, 282-83 & n. 2, 121 S.Ct. 1511, 149 L.Ed.2d 517 (2001) (holding private cause of action for disparate impact unavailable under 42 U.S.C. § 2000d, which prohibits discrimination "on the ground of race, color, or national origin"), because the test imposes a disparate impact standard for liability exceeding the statutory prohibition of intentional discrimination. Assuming that we would consider an amicus argument not joined in by any party, see United States v. Ionia Mgmt. S.A., 555 F.3d 303, 310 (2d Cir.2009) (noting appellate court not obligated to consider arguments presented only by amicus), and assuming further that a challenge to our McCormick precedent would not require en banc review, see Shipping Corp. of India Ltd. v. Jaldhi Overseas Pte Ltd., 585 F.3d 58, 67 (2d Cir.2009) (recognizing that panel bound by prior decisions "until such time as they are overruled either by an en banc panel of our Court or by the Supreme Court" (internal quotation marks omitted)), we would not be persuaded in any event. The argument rests on a mistaken assumption: that plaintiffs claim disparate impact. In fact, their complaint is disparate treatment. It is useful to clarify this point.

Title IX has been construed to prohibit the intentional exclusion of students from collegiate athletics programs on the basis of sex. See 20 U.S.C. § 1681(a); 34 C.F.R. § 106.41(a). A school's decision to provide students with athletic participation opportunities through separate sports programs for each sex thus necessarily raises a disparate treatment rather than disparate impact claim in that the school decides which athletic opportunities are available to particular students "on the basis of sex."5 20 U.S.C. § 1681(a); cf. Ricci v. DeStefano, 557 U.S. 557, 579, 129 S.Ct. 2658, 174 L.Ed.2d 490 (2009) (holding that city engaged in disparate treatment on basis of race in discarding results of firefighter promotional exam because higher scoring candidates were white, despite city's proffered objective to avoid disparate impact of test on black candidates). The critical question in this case is thus not whether Quinnipiac's disparate treatment of varsity athletes was based on their sex, but whether the treatment constituted unlawful discrimination under Title IX.

As OCR has interpreted § 1681(a), not every decision to maintain separate sports programs for male and female students constitutes proscribed discrimination. See 34 C.F.R. § 106.41(b). A choice to allocate specific athletic opportunities on the basis of sex will not violate Title IX provided that, in general, the participation opportunities afforded the two sexes are "equal." Id. § 106.41(c). Plaintiffs here alleged that Quinnipiac did not treat men and women equally in allocating athletic participation opportunities because the opportunities afforded women (1) were not substantially proportionate to women's undergraduate enrollment, and (2) did not fully and effectively accommodate women's athletic interests and abilities. See Cohen v. Brown Univ., 101 F.3d 155, 175 (1st Cir.1996). The three-part test did not reduce plaintiffs' burden to prove these elements of their disparate treatment claim. Rather, it afforded Quinnipiac three distinct opportunities to demonstrate that its sex-based treatment of athletes was not unlawful. See Boucher v. Syracuse Univ., 164 F.3d 113, 117 (2d Cir.1999) (recognizing three-part test to provide school with "three safe harbor defenses," each independently sufficient to defeat claim of unlawful disparate treatment in accommodating athletic interests of both male and female students); cf. Ricci v. DeStefano, 557 U.S. at 580, 129 S.Ct. 2658 ("The question is not whether that conduct was discriminatory but whether the City had a lawful justification for its race-based action.").

Here, Quinnipiac elected to defend against plaintiffs' discrimination claim only by reference to the first safe harbor created by the three-part test, arguing that its athletics program provided "substantially proportionate" athletic participation opportunities to women. For reasons we discuss infra at 99-108, the district court reasonably found to the contrary, thus simultaneously rejecting Quinnipiac's defense and finding for plaintiffs on the first element of their disparate treatment claim. To the extent that plaintiffs further offered evidence that Quinnipiac's disproportionate provision of athletic participation opportunities failed fully and effectively to accommodate the athletic interests and abilities of its female undergraduates insofar as it eliminated the women's volleyball team, Quinnipiac did not dispute the point.6 Nor did it attempt to argue that the school has a history of expanding women's athletic participation opportunities.

In sum, as a matter of Quinnipiac's litigation strategy, resolution of this case effectively turned on whether Quinnipiac's sex based treatment of varsity athletes provided its female students with genuine athletic participation opportunities substantially proportionate to their enrollment. Because the district court found that it did not, plaintiffs carried their burden to prove unlawful disparate treatment. In these circumstances, amicus curiae's challenge to the judicial deference accorded the agency's 1979 Policy Interpretation generally, or its articulated three-part test specifically, is unpersuasive.

C. Athletic Participation Opportunities for Women Runners: Discounting the Reported Numbers for Indoor and Outdoor Track

During the 2009 — 10 academic year, the roster for Quinnipiac's women's cross-country team listed 18 athletes; the roster for its women's indoor track team listed 30 athletes; and the roster for its women's outdoor track team listed 30 athletes. Quinnipiac faults the district court for concluding that this represented 67 rather than 78 genuine athletic participation opportunities for women runners. We identify no error of law or fact in the district court's carefully reasoned resolution of this issue.

Before the district court, plaintiffs argued that Quinnipiac should not be allowed to count as 54 athletic participation opportunities the cross-country, indoor track, and outdoor track roster positions held by the same 18 women. As the district court recognized, the issue admitted no easy resolution. The 1996 Clarification plainly states that "an athlete who participates in more than one sport will be counted as a participant in each sport in which ... she participates." 1996 Clarification at 3. But the trial evidence reflected circumstances not addressed in the 1996 Clarification: Quinnipiac's women cross-country runners were not afforded a choice as to whether to participate in more than one sport; they were required to do so. Specifically, their participation on the cross-country team was conditioned on their membership on the indoor and outdoor track teams. See Biediger v. Quinnipiac Univ., 728 F.Supp.2d at 78. No other Quinnipiac athletes were required to join multiple sports teams. See id. Notably, male cross-country runners were not required to join men's indoor and outdoor track teams, as Quinnipiac had no such teams in 2009 — 10. See id. Indeed, male cross-country runners were prohibited from representing Quinnipiac as individual entrants in indoor and outdoor track events. See id. at 75, 78, 105. As the district court recognized, these circumstances raise questions as to whether simultaneous participation on the women's cross-country, indoor track, and outdoor track teams at Quinnipiac represented three genuine athletic opportunities, or whether cross-country runners' mandated participation on the indoor and outdoor track teams was simply a form of alternative off-season training for the cross-country runners, one that allowed Quinnipiac to inflate the rosters of its women's indoor and outdoor track teams.

In this respect, the district court carefully reviewed evidence that we only summarize: Quinnipiac had a highly competitive women's cross-country team, which, by the 2009 — 10 school year, had won the last five New England Conference championships, see id. at 77; cross-country runners' mandated participation on the indoor and outdoor track teams afforded these runners more training time (albeit for a different type of running) during the cross-country off-season than NCAA rules would otherwise have allowed, see id. at 102; Quinnipiac expanded its indoor and outdoor track teams' rosters to accommodate mandated participation by cross-country runners, see id. at 86; despite the resulting large rosters, Quinnipiac's indoor and outdoor track teams participated in only the minimum number of track and field tournaments required by the NCAA and were never competitive for team awards as no Quinnipiac athletes entered field events, see id. at 102-03; and Quinnipiac offered scholarship money only to those members of the indoor and outdoor track teams who also ran cross-country, see id. at 76. The totality of these circumstances suggested that the 60 positions on Quinnipiac's indoor and outdoor track team rosters were not reflective of genuine participation opportunities in these sports, but were inflated to afford mandated year-round training for the 18 members of the women's cross-country team.

While identifying such a roster-manipulation concern, the district court nevertheless proceeded cautiously in drawing conclusions as to any Title IX violation. Notably, it decided that the evidence did not "justify discounting all of the cross-country runners' participation on the [women's] indoor and outdoor track teams." Id. at 108 (emphasis added). Such a ruling would have reduced by 36 the number of athletic participation opportunities that Quinnipiac claimed to afford female students. In explaining its decision, the district court observed that 13 of the 18 women cross-country runners had competed for Quinnipiac in four or more indoor track meets, accounting for 54.4% of the team's races. See id. at 107. Meanwhile, 12 of the 18 women cross-country runners had competed for Quinnipiac in three or more outdoor track meets, accounting for 50.0% of the team's races. See id. Finding that this reflected "a substantial contribution" by cross-country runners to Quinnipiac's indoor and outdoor track teams, the district court concluded that the school's "Title IX calculation should account for it," regardless of whether cross-country runners' participation in indoor and outdoor track was mandated. Id. Thus, it rejected plaintiffs' argument that these cross-country runners should not also be viewed as having been afforded further athletic participation opportunities as members of the indoor and outdoor track teams.

At the same time, however, the district court persuasively explained why a smaller number of cross-county runners, required to join Quinnipiac's track teams but participating in no competitions — or in one case, only one competition — could not be viewed as having been afforded multiple genuine athletic participation opportunities. Specifically, five positions on the indoor track team and six positions on the outdoor track team were held by cross-country runners who did not — and effectively could not — avail themselves of distinct participation opportunities on the track teams because they were injured or red-shirted. See id. at 78. Not only did these injured or red-shirted runners not compete in indoor or outdoor track events, they received no benefits from membership on these teams beyond those that they were already receiving as injured or red-shirted members of the cross-country team during that sport's off-season. See id. at 106.7 Thus, the district court concluded that for injured and red-shirted cross-country runners, the athletic participation opportunities afforded by mandated membership on the indoor and outdoor track teams were "truly illusory." Id. at 107 n. 26.

What was not illusory, however, was Quinnipiac's ability to "pad[] its rosters" with female athletes who had "no hope of competing or otherwise participating meaningfully during the indoor and outdoor track seasons." Id. As the district court aptly observed, it would be "unacceptable for Quinnipiac to pump up its women's track team rosters" by requiring every injured field hockey, soccer, and volleyball player to join these teams even though they "would never actually compete in the indoor and outdoor track seasons and, for that matter, would never want to enter a race." Id. But, the district court found, "that is essentially what Quinnipiac is doing with its injured cross-country runners." Id. Thus, the district court discounted Quinnipiac's claimed 30 athletic participation opportunities in indoor track by five, and its claimed 30 athletic participation opportunities in outdoor track by six. See id. at 108. We conclude that this reduction in the total number of athletic participation opportunities for women runners in cross-country, indoor track, and outdoor track from Quinnipiac's claimed 78 to an actual 67 is fully supported by the record evidence and by the applicable law.

In challenging this action, Quinnipiac complains that it was denied due process by lack of notice that the question of whether injured and red-shirted cross-country runners were afforded genuine athletic participation opportunities in indoor and outdoor track was at issue. We are not convinced. As Quinnipiac concedes, it certainly had notice that plaintiffs were challenging Quinnipiac's practice of counting cross-country runners who were listed as members of the indoor and outdoor track teams as each having been afforded three distinct athletic participation opportunities. We consider this sufficient to have alerted Quinnipiac that the practice was at issue and that Quinnipiac should prepare to defend it, both generally and specifically as applied to cross-country runners who were incapable of competing in any indoor or outdoor track events. The fact that Quinnipiac had notice of the issue in dispute and the opportunity to defend its challenged actions distinguishes this case from Doubleday & Co., Inc. v. Curtis, 763 F.2d 495, 502-03 (2d Cir.1985), in which this court invoked due process to reverse the dismissal of a plaintiff's claim on the basis of an affirmative defense not pleaded or raised by the defendant in a bench trial, as well as from Greene v. Town of Blooming Grove, 935 F.2d 507, 511 (2d Cir.1991), in which this court reversed a judgment entered after trial on a pendant state claim that was not pleaded by plaintiff with its federal claim, and that defendant had not been afforded an opportunity to defend against.

Quinnipiac further complains that it was not given notice that the district court would draw a negative inference about the genuineness of the indoor and outdoor track participation opportunities afforded female cross-country runners from the fact that the runners were required to join the track team. A factfinder's ability to draw reasonable inferences from the evidence is well established, see, e.g., Diesel Props. S.r.l. v. Greystone Bus. Credit II LLC, 631 F.3d 42, 52 (2d Cir. 2011) (recognizing court's obligation as "trier of fact ... to determine which of the witnesses it finds credible, which of the permissible competing inferences it will draw, and whether the party having the burden of proof has persuaded it as factfinder that the requisite facts are proven" (internal quotation marks omitted)), and Quinnipiac points us to no precedent holding that a factfinder must notify parties in advance of the particular inferences it is inclined to draw from record evidence. Indeed, we here reject that argument. Quinnipiac is entitled to challenge the sufficiency of the evidence to support the inference drawn by the district court, but in the absence of a sufficiency concern, if Quinnipiac failed to appreciate the possible adverse significance of a mandate that cross-country runners join the school's indoor and outdoor track teams, the fault was its own, not the district court's.

Insofar as Quinnipiac questions the sufficiency of the trial evidence to establish a track participation requirement, the argument borders on the frivolous. When Carolyn Martin, who coached all Quinnipiac's running teams, was asked at her deposition about women cross-country runners also running track, she stated, "I require them to." Martin Dep. at 184:25. Further, the thrust of Coach Martin's testimony was that women cross-country runners' indoor and outdoor track participation was a given. This was sufficient to permit the district court to find that Quinnipiac required cross-country runners to join the indoor and outdoor track teams. Indeed, the conclusion was reinforced by evidence that each of Quinnipiac's 18 cross-country runners was listed on the indoor and outdoor track team rosters, including those cross-country runners who were injured or red-shirted. Insofar as Quinnipiac points to its expert testimony that "cross-country runners almost always compete on the track teams," to undermine the district court's mandate finding, Expert Report of Samuel Seemes at 8, we note that a factfinder is not required to accept expert opinion, see Pope v. Cnty. of Albany, 687 F.3d 565, 581 (2d Cir.2012). In any event, the record shows that the district court carefully reviewed the totality of the evidence and concluded therefrom that cross-country runners who were required to join and who actually competed on the indoor and outdoor track teams did obtain additional genuine athletic participation opportunities. It found only that the same conclusion did not obtain for cross-country runners subjected to the same mandate even though they could not, and did not, participate in track competitions because they were injured or red-shirted. In such circumstances, women runners received no more athletic benefits from mandated membership on Quinnipiac's indoor and outdoor track teams than they were already receiving as members of the cross-country team.

Accordingly, we identify no error in the district court's decision to discount Quinnipiac's reported athletic participation opportunities for women on its cross-country, indoor track, and outdoor track teams from 78 to 67.

D. Athletic Participation Opportunities for Women in Competitive Cheerleading: The Determination That the Activity Does Not Yet Qualify as a "Sport"

Competitive cheerleading, which Quinnipiac decided to create as a new women's varsity sport team for 2009 — 10, is a late twentieth-century outgrowth of traditional sideline cheerleading. Whereas sideline cheerleaders generally strive to entertain audiences or solicit crowd reaction at sport or school functions, a competitive cheerleading team seeks to pit its skills against other teams for the purpose of winning. See Biediger v. Quinnipiac Univ., 728 F.Supp.2d at 78. Thus, to distinguish the two activities, competitive cheerleaders

Id. (observing that competitive cheerleading is an "athletic endeavor" that might be described as "group floor gymnastics" (internal quotation marks omitted)).

The district court nevertheless concluded that the 30 roster positions that Quinnipiac assigned competitive cheerleading for 2009 — 10 could not be counted under Title IX because the activity did not yet afford the participation opportunities of a varsity "sport." See id. at 101.

Preliminary to reaching this conclusion, the district court observed that competitive cheerleading is not yet recognized as a "sport," or even an "emerging sport," by the NCAA,8 action that would have triggered a presumption in favor of counting its participants under Title IX. See id. at 93-94 (citing 2008 OCR Letter). Nor has DOE recognized competitive cheerleading as a sport; to the contrary, in two letters in 2000, OCR indicated competitive cheerleading is presumptively not a sport, while leaving open the possibility for a different conclusion with respect to a particular cheerleading program. See April 2000 OCR Letter at 3; May 2000 OCR Letter at 1. There is, however, no record evidence of any competitive cheerleading program being recognized by DOE as a sport. See Biediger v. Quinnipiac Univ., 728 F.Supp.2d at 92.

Mindful of these circumstances, the district court proceeded carefully to review the structure, administration, team preparation, and competition of Quinnipiac's competitive cheerleading program to determine whether it nevertheless qualified as a sport whose athletic participation opportunities should be counted for purposes of Title IX. See 2008 OCR Letter at 2-4 (listing factors relevant to identifying activity as sport). Again, we only briefly summarize the district court's detailed findings, which find ample support in the record evidence. The district court found that in terms of the team's operating budget, benefits, services, and coaching staff, competitive cheerleading was generally structured and administered by Quinnipiac's athletics department in a manner consistent with the school's other varsity teams. See Biediger v. Quinnipiac Univ., 728 F.Supp.2d at 95. The district court noted two "minor" exceptions to this conclusion: Quinnipiac did not afford its competitive cheerleading team locker space; and because the NCAA did not recognize competitive cheerleading as a sport, the team did not receive NCAA catastrophic injury insurance and had to obtain it from a separate provider. Id. at 99; see id. at 95. With respect to factors relating to the team's preparation and competition, the district court found that the competitive cheerleading team's practice time, regimen, and venue were consistent with other varsity sports. See id. at 96. Further, as with other varsity sports, the length of the competitive cheerleading season and the minimum number of competitions in which a team would participate were pre-determined by a governing athletic organization, the recently formed National Competitive Stunt and Tumbling Association, of which Quinnipiac was a founding member. See id. at 82-83, 96-97. Finally, the purpose of the team — to compete athletically at the intercollegiate varsity level — was akin to that of other varsity sports. See id. at 99.

At the same time, however, the district court identified a number of circumstances that sufficiently distinguished Quinnipiac's competitive cheerleading program from traditional varsity sports as to "compel[] the decision that, for the 2009 — 10 season," the program could not "be counted as a varsity sport for purposes of Title IX." Id. First, Quinnipiac did not — and, in 2009 — 10, could not — conduct any off-campus recruitment for its competitive cheerleading team, in marked contrast not only to the school's other varsity sports teams but also to a typical NCAA Division I sports program. See id. at 95-96, 99. The district court explained the significance of this circumstance: "Although the women on the Quinnipiac competitive cheer team were athletically able, they would have been all the more talented had [Coach] Powers been able to seek out the best competitive cheerleaders around the country, as any other varsity coach would have been able to do." Id. at 99.

More important, no uniform set of rules applied to competitive cheerleading competition throughout the 2009 — 10 season. Indeed, in the ten competitions in which the Quinnipiac team participated during the regular season, it was judged according to five different scoring systems. See id. at 97. Further, in these competitions, Quinnipiac did not face only varsity intercollegiate competitive cheerleading teams. Rather, it was challenged by "a motley assortment of competitors," id. at 98, including collegiate club opponents who did not receive varsity benefits, collegiate sideline cheerleading teams, and all-star opponents unaffiliated with a particular academic institution, some of whom may still have been high-school age, see id. at 97-98. As the district court observed, "application of a uniform set of rules for competition and the restriction of competition to contests against other varsity opponents" are the "touchstones" of a varsity sports program. Id. at 99-100. "Those features ensure that play is fair in each game, that teams' performances can be compared across a season, and that teams can be distinguished in terms of quality." Id. at 100.

The concerns raised by these irregularities in season competition were only aggravated by aspects of post-season play. Notably, competitive cheerleading offered no progressive playoff system leading to a championship game. See id. at 98. Rather, it provided an open invitational, which neither excluded any team on the basis of its regular season performance nor ranked or seeded participating teams on that basis. See id. Instead, all entrants competed in a single championship round in which the team with the highest score won. See id. That round, moreover, was subject to a new rule of competition that had not applied to Quinnipiac in any of its regular season competitions: a mandatory 45-60 second "spirit" segment in which a team was judged by the intensity of the response it elicited from the crowd and the number of the sponsoring brand's props that it employed, features that Quinnipiac's coach confirmed were more characteristic of sideline rather than competitive cheerleading. See id. at 98-99. Viewing the totality of these circumstances, the district court concluded that the competitive cheerleading team's post-season competition did not conform to expectations for a varsity sport.

Id. at 100.9

Based on these findings, as well as those pertaining to regular season play, the district court concluded that Quinnipiac's competitive cheerleading team did not compete in circumstances indicative of varsity sports. Thus, it ruled that Quinnipiac's 30 roster positions for competitive cheerleading could not be counted for Title IX purposes because the activity did not yet afford women genuine participation opportunities in a varsity sport. See id. at 100-01.

In challenging this conclusion, Quinnipiac questions the weight the district court assigned the various factors it identified as supporting or undermining recognition of competitive cheerleading as a genuine varsity sport. Quinnipiac argues that this court should decide the question de novo. We generally accord considerable discretion to a factfinder in deciding what weight to assign competing evidence pointing toward different conclusions. See Diesel Props. S.r.l. v. Greystone Bus. Credit II LLC, 631 F.3d at 52 ("`Where there are two permissible views of the evidence, the factfinder's choice between them cannot be clearly erroneous.'") (quoting Anderson v. Bessemer City, 470 U.S. 564, 574, 105 S.Ct. 1504, 84 L.Ed.2d 518 (1985)). But the point merits little discussion here because, even assuming that de novo review were warranted, we conclude for the same reasons stated in detail by the district court and summarized in this opinion that, although there are facts on both sides of the argument, in the end, the balance tips decidedly against finding competitive cheerleading presently to be a "sport" whose participation opportunities should be counted for purposes of Title IX. Like the district court, we acknowledge record evidence showing that competitive cheerleading can be physically challenging, requiring competitors to possess "strength, agility, and grace." Biediger v. Quinnipiac Univ., 728 F.Supp.2d at 101. Similarly, we do not foreclose the possibility that the activity, with better organization and defined rules, might some day warrant recognition as a varsity sport. But, like the district court, we conclude that the record evidence shows that "that time has not yet arrived." Id.

Accordingly, we conclude that the district court was correct not to count the 30 roster positions assigned to competitive cheerleading in determining the number of genuine varsity athletic participation opportunities that Quinnipiac afforded female students.

E. Finding a Title IX Violation Based on a 3.62% Disparity

Having reduced Quinnipiac's claimed athletic participation opportunities for women by 41 — representing 30 competitive cheerleaders and 11 cross-country runners required to join the indoor and outdoor track teams but unable to compete on those teams because of their injuries or red-shirt status — the district court correctly found that the school had a total of 400 varsity athletic participation opportunities, of which 233, or 58.25%, were assigned to women. See id. at 111. Because enrollment data established that 61.87% of Quinnipiac's undergraduate population were women, this indicated a 3.62% disparity in the athletic opportunities that Quinnipiac afforded women. See id. The district court concluded that this disparity was sufficient to support a finding that Quinnipiac had failed to afford female students varsity athletic participation opportunities substantially proportionate to their enrollment. See id. at 113.

Quinnipiac argues that a 3.62% disparity is too small to support such a finding. In any event, it submits that the district court erred in holding Quinnipiac responsible for the disparity in light of fluctuations in enrollment and Quinnipiac's good faith reliance on the district court's statement at the time of the preliminary injunction decision that it would likely count all women members of the cross-country, indoor track, outdoor track, and competitive cheerleading teams as athletic participants for purposes of Title IX. Further, Quinnipiac contends that the district court erroneously accorded dispositive weight to the fact that the number of additional female roster spots needed to achieve exact proportionality — 38 — would have been sufficient for Quinnipiac to field an additional varsity team.

Quinnipiac's arguments fail to persuade. First, its emphasis on the relatively small percentage of disparity is unwarranted. The district court itself recognized that "in strictly numerical terms," a 3.62% disparity presents "a borderline case of disproportionate athletic opportunities." Id. at 111. But as the 1996 Clarification makes clear, substantial proportionality is not determined by any bright-line statistical test. See 1996 Clarification at 4; see also Equity In Athletics, Inc. v. DOE, 639 F.3d 91, 110 (4th Cir.2011) ("DOE has not specified a magic number at which substantial proportionality is achieved."). While a district court outside this circuit reports finding no case in which a disparity of two percentage points or less has been held to manifest a lack of substantial proportionality, see Equity in Athletics, Inc. v. DOE, 675 F.Supp.2d 660, 682-83 (W.D.Va.2009), aff'd, 639 F.3d 91 (4th Cir.2011), we do not pursue the issue because the disparity in this case is greater than 2%, and we do not, in any event, understand the 1996 Clarification to create a statistical safe harbor at this or any other percentage. Instead, the Clarification instructs that substantial proportionality is properly determined on a "case-by-case basis" after a careful assessment of the school's "specific circumstances," including the causes of the disparity and the reasonableness of requiring the school to add additional athletic opportunities to eliminate the disparity. 1996 Clarification at 4; see also Amicus Br. of U.S. 23-25.10 The district court's challenged ruling was based on precisely this analysis.

Specifically, the district court pointed to record evidence showing that the 3.62% identified disparity was almost entirely attributable to Quinnipiac's own careful control of its athletic rosters. See Biediger v. Quinnipiac Univ., 728 F.Supp.2d at 111-12. Although Quinnipiac claims that, but for a 0.27% increase in female enrollment in 2009 — 10 beyond its control, the disparity would have been only 3.35%, the difference is not one that undermines the district court's conclusion that Quinnipiac's voluntary actions largely caused the disparity.

While Quinnipiac professes to have relied on the district court's observation at the time of the preliminary injunction ruling that it would likely count all women members of the cross-country, indoor track, outdoor track, and competitive cheerleading teams as athletic participants for purposes of Title IX, Quinnipiac — or certainly its able counsel — surely knew the risks of such reliance. "A decision on a preliminary injunction is, in effect, only a prediction about the merits of the case," Morris v. Hoffa, 361 F.3d 177, 189 (3d Cir.2004) (internal quotation marks and brackets omitted); thus, "findings of fact and conclusions of law made by a court granting a preliminary injunction are not binding," University of Tex. v. Camenisch, 451 U.S. 390, 395, 101 S.Ct. 1830, 68 L.Ed.2d 175 (1981), and "do not preclude reexamination of the merits at a subsequent trial," Irish Lesbian & Gay Org. v. Giuliani, 143 F.3d 638, 644 (2d Cir.1998); see also Gooch v. Life Investors Ins. Co. of Am., 672 F.3d 402, 433 (6th Cir.2012) (observing that "a preliminary injunction makes a prediction about the merits ruling and is not itself a merits ruling"). In any event, the 1996 Clarification indicates only that a school will not be held responsible under Title IX for disparities caused by matters outside its control. See 1996 Clarification at 4. Nowhere does it indicate that a school can avoid responsibility for future remediation of Title IX disparities caused by its own choices if it can show that those choices were made in good faith.

Finally, we do not understand the district court to have ruled, as Quinnipiac suggests, that no matter how small a disparity, if it can be closed by the creation of a new sports team, a school will be found not to have afforded substantially proportionate athletic opportunities. Rather, we understand the court to have discussed the possible creation of a new sports team only to explain why it was reasonable to expect Quinnipiac to add additional athletic opportunities for women to close the identified 3.62% disparity. In so concluding, the district court noted that, insofar as the gap reflected 38 positions, each of Quinnipiac's women's varsity teams had 30 or fewer roster spots, making it "certain that an independent sports team could be created from the shortfall of participation opportunities." Biediger v. Quinnipiac Univ., 728 F.Supp.2d at 112 & n. 27. Moreover, the district court observed that little effort was required for Quinnipiac to afford the additional participation opportunities of an independent sports team: "That independent sports team would be the eliminated women's volleyball squad, a team that, based on Quinnipiac's 2010-11 roster target, requires a mere 14 players to compete." Id. at 112. Of course, the district court did not suggest that Quinnipiac's compliance with Title IX was dependent on it forever fielding a women's volleyball team. See id. at 113-14. But the ease with which Quinnipiac could afford these particular additional varsity athletic opportunities was a "specific circumstance[]" that, pursuant to the 1996 Clarification, supported the conclusion that a 3.62% disparity in this case demonstrated that Quinnipiac was not affording substantially proportionate varsity athletic participation opportunities to its female students. 1996 Clarification at 4.

Accordingly, we reject Quinnipiac's challenge to the district court's finding that the school engaged in sex discrimination in violation of Title IX, and we affirm the order enjoining Quinnipiac from continuing such discrimination.

III. Conclusion

To summarize, we conclude as follows:

1. For purposes of determining the number of genuine varsity athletic participation opportunities that Quinnipiac afforded women students, the district court correctly declined to count:

a. five roster positions on the women's indoor track team and six roster positions on the women's outdoor track team because these were held by cross-country runners who (i) were required to join the indoor and outdoor track teams even though they could not compete on those teams because they were injured or red-shirted and (ii) did not receive any additional benefits from membership on the track teams beyond those received as injured or red-shirted off-season members of the cross-country team;

b. any of the 30 roster positions for women's competitive cheerleading because that activity was not yet sufficiently organized or its rules sufficiently defined to afford women genuine participation opportunities in a varsity sport.

2. Where the 3.62% disparity between the percentage of women students enrolled at Quinnipiac and the percentage of women listed on varsity sports teams was largely caused by Quinnipiac's voluntary decisions with respect to its athletics programs and reasonably remedied by the addition of more athletic opportunities for women, the district court correctly concluded that the disparity demonstrated a failure to provide substantially proportionate athletic participation opportunities as required by Title IX.

Accordingly, the district court's order enjoining Quinnipiac from continuing to discriminate against female students by failing to provide them with equal athletic participation opportunities is AFFIRMED.