OPINION

Customs Fraud Investigations, LLC (CFI), the relator in this qui tarn action, appeals the District Court’s dismissal of its complaint with prejudice and the court’s denial of CFI’s subsequent motion' for leave to amend its complaint. We hold that the District Court erred in denying CFI’s motion to amend its complaint on futility grounds. Consequently, we will vacate that order and remand this case for further proceedings.

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Victaulic Co., the defendant ip the District Court and the appellee in this matter, is a Delaware corporation with its headquarters in Easton,- Pennsylvania. It is a global manufacturer and distributor of pipe fittings. CFI, a limited liability company based in Maryland, is made up of former insiders from the pipe fitting industry. According to CFI, although none'of its employees worked for Victaulic, CFI’s principals have worked on numerous trade investigations involving pipe and tube products and have provided direct support to senior officials at the U.S. International Trade Commission and the U.S. Department of Commerce on issues in the- industry.

To better understand CFI’s allegations, it is helpful to explain the regulatory environment in which Victaulic operates. Pipe fittings, such as those Victaulic manufactures, are the subject of specific, non-discretionary import regulations set forth in the Tariff Act of 1930.1 Pipe fittings must, with limited exceptions, be marked with the English name of the country of origin *246by means of one of five methods.2 Only if it is technically or commercially infeasible to mark an article by one of the five enumerated methods may a pipe fitting be marked in another manner. Under no circumstances may an article of foreign origin be completely unmarked.3 If an importer releases unmarked or improperly marked goods into the stream of commerce in the United States, the importer owes a duty of 10 per centum ad valorem on the improperly marked goods.4 This duty, known as a “marking duty,” is deemed to have accrued at the time of importation and must be paid in addition to any other duty imposed by law.5

This is not to say, however, that an importer may bring improperly marked goods into the United States merely by paying a marking duty. Instead, if improperly marked goods are imported and discovered by customs officials, an importer has three options: (1) re-export the goods, (2) destroy them, or (8) mark them appropriately so that they may be released from the custody of the United States for sale in the domestic market.6 Customs officials at United States ports of entry are unable to inspect every import; they rely primarily on the importers themselves to self-report any duties owed and any goods that are unmarked or improperly marked. In those instances where improperly marked goods enter the stream of commerce in the United States, the marking duty is due, retroactive to the time of importation.7 Imposition of the duty is non-discretionary since, by statute, such duties “shall not be remitted wholly or in part nor shall payment thereof be avoidable for any cause.”8 In setting forth this regulatory scheme, Congress specifically noted that marking duties “shall not be construed to be penal” and are to be considered similar to any other customs duty owed.9

The gravamen of CFTs allegations is that Victaulic has, over the past decade, imported millions of pounds of improperly marked pipe fittings without disclosing that the fittings are improperly marked. Since this improper marking was not discovered by customs officials, Victaulic avoided paying marking duties on these fittings. As support for its claims, CFI’s complaint alleged that Victaulic imported approximately 83 million pounds of fittings from overseas between 2008 and 2013 and a miniscule fraction of Victaulic’s pipe fittings for sale in the U.S. bear any indication of their foreign origin, with an even smaller percentage bearing country of origin markings compliant with the applicable statute. According to the complaint, “Vic-taulic is able to successfully (albeit unlawfully) import its unmarked pipe fittings into the United States by knowingly failing to pay or disclose to the CBP [Bureau of Customs and Border Protection] the marking duties the company owes ... by, among other things, falsifying its entry documents and otherwise concealing the foreign source of its pipe fittings such that CBP will not detect the company’s fraud.”

These actions, according to CFI, give rise to the present qui tam action under the so-called “reverse false claims” *247provision in the False Claims Act (FCA).10 Typically, a claim under the FCA alleges that a person or company submitted a bill to the government for work that was not performed or was performed improperly, resulting in an undeserved payment flowing to that person or company. The FCA was enacted as a reaction to rampant fraud and price gouging by merchants supplying the Union army during the Civil War.11 In this case, by contrast, the allegation is not that Victaulic is obtaining monies from the government to which it is not entitled, but rather that it is retaining money it should have paid the government in the form of marking duties. Wrongful retention cases such as these are known as “reverse false claims” actions.

CFI filed its initial complaint, under seal, on May 30, 2013, in the United States District Court for the Eastern . District of Pennsylvania. On August 7, the United States declined to intervene in the matter. After being served, Victaulic filed a motion to dismiss pursuant to Federal Rule of Civil Procedure -12(b)(1) and 12(b)(6). Vic-taulic contested the District Court’s jurisdiction by contending that CFI’s complaint violated the FCA’s ban on suits based primarily on publicly available information.12 Victaulic alleged, in the alternative, that the complaint failed to present a plausible claim because it was too conclusory. Discovery was stayed pending the District Court’s decision on the motion to dismiss.

When the District Court held a hearing on Victaulic’s motion, argument focused on Victaulic’s contentions that the FCA’s public disclosure bar was jurisdictional and that all of the information in CFI’s complaint was publicly available. In its subsequent opinion, the District Court rejected these arguments, holding that the FCA’s public disclosure bar was not jurisdictional and, in any event, CFI’s complaint was not based on publicly available information within the meaning of the FCA.

Then, turning to Victaulic’s alternative argument that the claim was conclusory, the District Court held that CFI’s complaint did not state a claim on which relief could be granted because it failed to cross the Twombly/Iqbal threshold from possible to plausible. In doing so, the District Court mentioned that it believed the FCA’s reverse false claims provision did not cover failure to pay marking duties, but declined to rule on those grounds because the complaint was based on legal conclusions unsupportable by the facts alleged. The District Court dismissed the complaint with prejudice, without any discussion of why CFI should not be afforded the opportunity to amend its complaint to solve any perceived deficiencies.

CFI promptly moved for relief from judgment and for leave to amend its complaint, including a proposed First Amended Complaint (FAC) that contained substantially more detailed factual allegations. While the contours of the claim remains the same in both complaints, the FAC includes details that address at least some of the concerns that the District Court had expressed in its opinion. Of particular import, the FAC details the rationale behind CFI’s investigation of Victaulic and discusses the methodology CFI used to develop its claims.

This investigation involved a multifaceted analysis before filing suit, consisting of two parts: (1) an analysis of shipping mani*248fest data purporting to show that Victaulic imports the majority of its pipe fittings from overseas and (2) a study of listings from the online auction site eBay for Vic-taulie products that CFI used as a proxy for the Victaulic product market. Out of the more than 200 listings for Victaulic pipe fittings CFI reviewed, there were virtually no products for sale that CFI considers properly marked. Based on its analysis, CFI concluded that systematic fraud must be occurring, since the majority of Victaulic’s products are imported but virtually no products for sale on the secondary market are properly marked with the foreign country of origin markings required by law.

CFI bolstered the FAC by attaching, an expert declaration stating that CFI’s analysis “provides ‘overwhelming evidence’ that Victaulic is not properly marking its pipe fittings,” and attached actual examples of the data on which CFI and its expert based their analyses. Moreover, the FAC included two allegations that did not appear in the original complaint: a statement from an unnamed witness who recalled a specific instance of obtaining improperly labeled Victaulic products, and a reference to a District Court hearing where, according to CFI, Victaulic showed a photograph of a pipe fitting to the court that CFI contends was a prime example of improper marking.

The District Court denied CFI’s motions on two grounds. First, it held that CFI unduly delayed its motion for leave to amend because it should have been on notice that the District Court was considering dismissing the complaint based on comments the court made at the motions hearing. Second, the District Court held that the FAC was futile, stating explicitly that failure to pay marking duties could not, as a matter of law, give rise to a reverse false claims action because the duties were too attenuated and contingent to qualify as the types of obligations to pay money to the government covered by the FCA. This appeal followed, in which the United States appears as amicus curiae, arguing that the District Court’s interpretation of the FCA’s reverse false claims provision is incorrect and that marking duty obligations are covered by the FCA.13

II.

The District Court had jurisdiction over this matter pursuant to 28 U.S.C. § 1331 and 31 U.S.C. § 3732, We have jurisdiction over the District Court’s orders dismissing the complaint, denying relief from judgment, and denying CFI’s motion for leave to amend pursuant to 28 U.S.C, § 1291. We review a District Court’s judgment of dismissal pursuant to Federal Rule of Civil Procedure 12(b)(6) de novo,14 We accept all factual allegations in the complaint as true and' “determine whether, under any reasonable reading of the complaint, the plaintiff may be entitled to relief.”15

We review a District Court’s denial of a Rule 59(e) motion for relief from judgment for abuse of discretion (except for questions of law, which are subject to plenary review).16 Similarly, we review a Rule 15 motion for leave to amend a complaint for abuse of discretion, and if “a *249timely motion to amend judgment is filed under Rule 59(e), the Rule 15 and 59 inquiries turn on the same factors.”17 Under such a review, we are cognizant of Rule 15’s admonition that leave to amend should be freely given “when justice so requires.”18 “A district court would necessarily abuse its discretion if it based its ruling on an erroneous view of the law....”19

III.

There are three instances when a court typically may exercise its discretion to deny a Rule 15(a) motion for leave to amend: when “(1)’ the moving party has demonstrated undue delay, bad faith or dilatory motives, (2) the amendment would be futile, or (3) the amendment would prejudice the other party.”20 The District Court relied on two of those grounds in denying CFI’s motion for leave to amend: undue delay and futility. We will explain why CFI’s delay was not undue before turning to the merits of the FAC.

A;

Generally, Rule 15 motions should be granted. In Foman v. Davis, the Supreme Court held that the fundamental purpose of Rule 15 is to allow a plaintiff “an opportunity to test his claim on the merits,” and although “the grant or denial of an opportunity to amend is within the discretion of the District Court,” that discretion is abused if it is exercised without giving the plaintiff sufficient opportunity to make her case.21

At oral argument before us, counsel for CFI admitted that CFI was “waiting to see what the court said” before filing its motion to amend its complaint because CFI had “thought the court was going to deny the motion to dismiss.” The District Court held that this tactic made CFI’s delay undue because CFI was “on notice of the defects in its complaint once Victaulic moved for dismissal,” and CFI was notified “that the Court was considering a dismissal with prejudice,” based on comments made from the bench during a hearing on Victaülic’s motion. The record, however, is not so clear.

First, the mere fact that a defendant -files a motion to dismiss is not necessarily sufficient to put a plaintiff on notice that the court will find his complaint to be deficient. One of the consequences of the Supreme Court’s decisions in Twombly and Iqbal22 is a general increase in the number of motions to dismiss filed against plaintiffs. As a result, plaintiffs are now twice as likely to face a motion to dismiss.23 It is highly unlikely that in the years since Twombly was decided, plaintiffs’ complaints are dramatically worse or *250less meritorious. Rather, defendants now have incentive “to challenge the sufficiency of the plaintiffs complaint more frequently.”24 More frequent motions to dismiss are not necessarily more meritorious motions to dismiss.

Second, in addition to arguing that CFI’s complaint did not pass muster under the applicable pleading standards, Victaulic argued that the public disclosure bar in the FCA deprived the District Court of jurisdiction over the case. Much of the hearing on Victaulic’s motion to dismiss dealt with the two relevant parts of that issue: whether the public disclosure bar was jurisdictional and whether the information on which CFI’s complaint is based was in the public domain within the meaning of the FCA. The District Court rejected Victaulic’s arguments, finding that the information on which CFI based its complaint was not in the public domain and holding that the public disclosure bar is not jurisdictional. Having disposed of these two substantial issues, the District Court then granted the motion to dismiss on the other ground raised by Victaulic: that the complaint was based on legal conclusions, not supported by fact.

CFI then moved to amend its complaint. In denying the motion, the District Court opined that, based on comments from the bench, the court itself had put CFI on notice that its complaint would be dismissed with prejudice. We disagree. As was pointed out at oral argument before us, judges at all levels make statements and ask questions during hearings that may not be a clear indication of the court’s views or how a case will eventually be decided. To expect the plaintiff to pick, from dozens of questions and statements over the course of a hearing, those questions that signal what the court will ultimately decide is to expect too much.

Moreover, even though at the hearing the District Court called the plaintiffs complaint “bare bones” and implied that the plaintiff might need to plead more facts, those statements were not a ruling, a holding, or an explanation of how the court intended to rule. We cannot see how, on this record, CFI could have reasonably been expected to understand from the District Court’s comments that CFI was in danger of having its entire suit dismissed with prejudice were it not to move to amend its complaint immediately after argument, instead of immediately after the decision came down.

This is not to say that a plaintiff will never be on notice of potential deficiencies based on a motion to dismiss or comments from the bench. Nevertheless, in the context of a typical Rule 12(b)(6) motion, a plaintiff is unlikely to know whether his complaint is actually deficient—and in need of revision—until after the District Court has ruled. Once CFI had actual notice of the perceived deficiencies in its complaint, it promptly moved to file its first amended complaint.

Third, we have rarely upheld a dismissal with prejudice of a complaint when the plaintiff has been given no opportunity to amend. Victaulic attempts to sidestep this fact by arguing that the FAC is a de facto second amended complaint because the District Court considered additional evidence outside the original complaint at the hearing on Victaulic’s motion. As a procedural matter, there is no basis for this contention. The record is clear that CFI’s motion for leave to amend was CFI’s first attempt to file an amended complaint.

Moreover, at the outset of the hearing on Victaulic’s motion to dismiss, *251the District Court noted that it had received “a lot of factual material from the plaintiff that goes beyond the allegations of the complaint.” Since Victaulic’s motion was filed pursuant to Rule 12(b)(1) as well as Rule 12(b)(6), consideration of this information was proper, to a point. When a Rule 12(b)(1) motion is evaluated as a “factual attack” on the Court’s subject matter jurisdiction, “the court may consider evidence outside the pleadings” in evaluating that attack.25 When a motion to dismiss implicates both Rule 12(b)(6) and Rule 12(b)(1), outside evidence may be considered for Rule 12(b)(1) purposes but not for Rule 12(b)(6) purposes.26

CFI’s counsel made this point at the hearing before the District Court, stating that CFI had submitted additional information only for purposes of the Rule 12(b)(1) motion and that that evidence should not be considered for the Rule 12(b)(6) motion. The District Court seems to have accepted the point, noting that it believed the additional evidence would help the court evaluate both parts of the motion, but acknowledging that the additional evidence was only submitted for the Rule 12(b)(1) motion. In its opinion, however, the District Court noted that it was not considering “these additional facts in assessing the sufficiency of the complaint itself,” but that it would consider the facts “in determining ... whether, having dismissed the original complaint, the Court should grant CFI leave to file an amended complaint containing these additional factual allegations.” The District Court did not refer to any legal basis for considering evidence outside the complaint in determining whether to dismiss a complaint with prejudice on a 12(b)(6) motion. Moreover, the District Court did not have a motion to amend pending before it when it issued its opinion, making any consideration of whether to grant such a motion hypothetical at best.

In essence, by considering the evidence submitted on the Rule 12(b)(1) motion when deciding a Rule 12(b)(6) motion, the District Court converted Victaulie’s Rule 12(b)(6) motion into a motion for summary judgment. The court could have done so pursuant to Rule 12(d), under which consideration of evidence submitted outside the complaint would be proper. Rule 12(d) requires, however, that the parties “be given a reasonable opportunity to present all the material that is pertinent to the motion.” 27 The District Court did not notify the parties that it was converting Victaulic’s Rule 12(b)(6) motion to one for summary judgment under Rule 12(d), and CFI was not given a reasonable opportunity to present more information.

In addition to these procedural irregularities, the District Court abused its discretion in finding that CFI’s attempt to amend its complaint constituted undue delay. The District Court held that “CFI is imposing an unwarranted burden on the Court by requiring the Court to waste judicial resources revisiting issues that could have been addressed earlier,” and that “the FAC rests almost entirely on information that was already before the Court or that CFI could have presented to the Court prior to dismissal.”

The District Court relied on several cases28 to reach its conclusion. That reli-*252anee is, however, misplaced. It is true that in Jang v. Boston Scientific Scimed, Inc., we noted that we have “declined to reward a wait-and-see approach to pleading.”29 In context, however, that statement was of no practical import, since in Jang we reversed the District Court’s entry of judgment on the pleadings and remanded for further proceedings, explicitly noting that the plaintiff remained “free to file a new motion for leave to amend.”30

Similarly, in In re: Adams Golf, Inc. Securities Litigation, we reversed a District Court’s decision granting a Rule 12(b)(6) motion in part, but affirmed the denial of a motion for leave to amend based on futility and “undue delay.”31 In that case, the District Court had already allowed one Amended Complaint and found that the proposed Second Amended Complaint was futile since it did not contain new material allegations.32 Also, in California Public Employees’ Retirement System v. Chubb Corp. (CPERS), the case involved allegations of securities fraud subject to the Public Securities Litigation Reform Act. The court affirmed the denial of a motion for leave to amend after the district court had previously allowed two amended complaints, denied both and given extensive guidance to the plaintiff as to the deficiencies the district court saw with the amended complaints.33

Finally, the District Court relied upon Arthur v. Maersk, Inc.,34 as an example of our rejection of the “wait-and-see approach to pleading.” In Arthur, we held that a delay of less than a year from the filing of an initial complaint to the filing of an amended complaint is rarely, if ever, sufficient to become undue,35 Here, the elapsed time from filing of the initial complaint— which had to be filed under seal pursuant to the FCA and could not be served on the defendant—to the amended complaint was approximately sixteen months. Under the circumstances, the lapse of time is not “so excessive as to be presumptively unreasonable.” 36

In none of the cases the District Court relied upon did we uphold a dismissal with prejudice where the plaintiff had been given no opportunity to amend its complaint and would not be given an opportunity to amend in the future.

For the reasons stated above, we hold that the District Court’s denial of the CFI’s motion for leave to amend was error. Nevertheless, the District Court would have been justified in denying CFI’s motion if the FAC was itself futile, which was the alternative ground on which the District Court based its opinion. We turn to that rationale next.

B.

In rejecting CFI’s FAC as futile, the District Court held that, as a matter of law, failure to pay marking duties could not give rise to a reverse FCA claim and that CFI failed to meet the pleading requirements of Federal Rule of Civil Procedure 9(b). Both holdings were error. We *253will first .address why marking duties fall within the FCA’s reverse false claims provision before addressing the alleged deficiencies in CFI’s FAC.

1.

The reverse false claims provision oj: the FCA37 was revised as part of the Fraud Enforcement and Recovery Act of 2009 (FERA).38 Although many reforms were enacted as part of the FERA, Congress specifically enacted one portion in response to a perceived narrowing of the scope of the reverse false claims provision.

Prior to 2009, the reverse false claims provision provided for a civil penalty for one who “knowingly makes, uses, or causes to be" made or used, a false record or statement to conceal, avoid, or decrease an obligation to pay or transmit money or property to the Government.”39 The word “obligation” was not defined in the statute.40 The FERA made two substantial changes. First, it added to the reverse false claims provision the phrase “or knowingly conceals or knowingly and improperly avoids or decreases an obligation to pay or transmit money or property to the Government”.41 Second, it defined an ^obligation” as “an established duty, whether or not fixed, arising from an express or implied contractual, grantor-grantee, or li-censor-licensee ■ relationship, from a fee-based or similar relationship, from statute or regulation, or from the retention of any overpayment.”42 These two sections broadened the scope to which reverse false claims liability would attach.

The new definition was, in part, a reaction to the decision in American Textile Manufacturers Institute, Inc. v. The Limited, Inc. (ATMI), which held that the term “obligation” should be afforded “a different,, and more limited, meaning” than the meaning afforded the word “claim” in the FCA, and that reverse false claims liability should be viewed more narrowly than general false claims liability.43 Specifically, the ATMI court limited reverse false claims liability to those circumstances where “an obligation in the.nature of those that gave rise to actions of debt at common law for money or things owed” would have arisen.44 •

The Senate Report on the FERA states that the new definition of “obligation” was intended to address “confusion among courts that have developed conflicting definitions.” 45 The FERA rejected the reasoning in ATMI, with the Senate Report highlighting the definition’s express inclusion of “contingent, non-fixed obligations” that encompasses “the spectrum of possibilities from the fixed amount debt obligation,” typically at issue at. common law, “to the instance where there - is a relationship between the Government and a person that results in the duty to pay the Government money, whether or not the amount owed is yet fixed.”46 In effect, the FERA expressly rejected ATMI’s narrow interpretation of the FCA’s reverse false claims provision *254in favor of a more broadly inclusive definition.

Of particular importance here, the Senate Report discussed “customs duties for mismarking country of origin,” and how such duties would- be covered by the amended reverse false claims provision.47 The Report notes that an early version of the FERA named marking duties explicitly in the definition of “obligation” so as to leave no doubt about the abrogation of ATMI, but the Senate considered the language in the new definition so clear that “any such specific language would be unnecessary,” since “customs duties clearly fall within the new definition of the term ‘obligation.’”48 With this background in mind, we turn to the conduct at issue here.

At the outset, in reviewing the marking duty provision of the Tariff Act, the District Court held that “an importer does not owe marking duties upon importation of unmarked or mismarked merchandise.” While technically correct, this makes too fine a distinction between the time at which an importer must pay marking duties and the time at which such duties accrue. It is true, as Victaulic argues, that when mismarked or unmarked goods are in government custody the importer may not simply pay marking duties to obtain the release of such goods.49 By statute, such goods must be properly marked, reexported, or destroyed under government supervision.50 Yet, if such goods nevertheless escape detection and are released into the United States, the ten percent ad valo-rem duty is deemed to “have accrued at the time of importation” and is due and owing, without exception.51

This is precisely what CFI alleges Vic-taulic did in a systematic way for years. Victaulic, according to CFI, knew its goods were not marked properly and, therefore, knew that the imported pipe fittings should not have been released from government custody. Had Victaulic informed the government of this state of affairs, the goods would not have been allowed into the country. By staying silent, CFI alleges that Victaulic made a choice—to pay the ten percent marking duty owed on its goods, if its scheme was discovered, instead of paying to have the goods marked properly, re-exported, or destroyed. Hence, in CFI’s view, Victaulic knowingly concealed information from the government by not informing customs officials that the imported pipe fittings were not marked properly. According to CFI, once the pipe fittings cleared customs, Victaulic knew it owed marking duties that accrued on importation but did not pay them. This, in CFI’s view, gives rise to reverse false claims liability for the unpaid marking duties.

The plain text of the FCA’s reverse claims provision is clear: any individual who “knowingly conceals or knowingly and improperly avoids or decreases an obligation to pay or transmit money or property to the Government” may be subject to liability.52 As alleged by CFI in the amended complaint, Victaulic declined to notify the Bureau of Customs and Border Protection of its pipe fittings’ non-conforming status. This failure to notify resulted in the pipe fittings being released into the stream of commerce in the United States *255and, consequently, marking duties being owed and not paid.

The District Court held that this conduct is immaterial and cannot give rise to a reverse false claims liability. To reach this conclusion, the court followed the reasoning in ATMI, but, as previously discussed, that reasoning has been called -into doubt, if not entirely abrogated, by the FERA. Prior to the FERA, the “knowingly and improperly avoids or decreases an obligation” language was absent from the FCA.53 In the pre-FERA FCA, a false statement or record was a necessary element for reverse FCA liability to attach-.54 A false statement is no longer a required element, since the post-FERA FCA specifies that mere knowledge and avoidance of an obligation is sufficient, without the submission of a false record, to give rise to liability.55 Consequently, the District Court’s reliance on ATMI and ATMI’s focus on the submission of a false record is misplaced.

Indeed, the District Court’s lengthy discussion of whether Victaulie filled out its customs forms in a proper manner is ultimately of no import since, under the post-FERA FCA, Victaulie need not have made any express statement to the government to give rise to reverse false claims liability. The statute, 19 U.S.C. § 1484(a)(1), requires an importer to provide “such information as is necessary to enable [CBP] to determine whether [its] merchandise -may be released from the custody of [CBP]” and to “enable [CBP] to properly assess duties on [imported] merchandise.” If Vic-taulic knowingly failed to disclose to CBP the fact that its goods were unmarked or improperly marked despite its affirmative obligation to do so under § 1484(a)(1) and if such goods nevertheless escaped detection and were released into the United States, Victaulie would be liable under the FCA. Thus, CFI need only prove that Victaulie • knew its pipe fittings were improperly marked and did not notify the Bureau of Customs and Border Protection, since to do so is to conceal information customs officials needed to know in order to determine whether to release Victaulic’s goods from its custody.56

From a policy perspective, the possibility of reverse false claims liability in such circumstances makes sense in the context of the larger import/export regulatory scheme created by Congress. Because of the government’s inability to inspect every shipment entering the United States, an importer may have an incentive to decline to mention that its goods are mismarked on the assumption that the mismarMng will not be discovered. In doing so, an importer avoids its obligation under 19 U.S.C. § 1484 to provide the government with such information as is necessary to enable the Bureau of Customs and Border Protection to determine whether the merchandise may be released, from government custody or whether it must be properly marked, re-exported or destroyed pursuant to 19 U.S.C. § 1304(i). Moreover, if the importer believes the value of bringing unmarked or improperly marked goods into the country exceeds the risk that the deception will be discovered and the ten percent ad valorem duty will be owed, an *256importer may decline to mention that its goods are mismarked, since the chance that some goods will be discovered as mis-marked and that marking duties will be owed would still result in a net gain to the company. Reverse false claims liability changes that value proposition because a finding of deception carries the possibility of treble damages.

The statutory text, legislative history, and policy rationale underlying the regulatory scheme all lead to one conclusion: reverse false claims liability may attach as a result of avoiding marking duties. Consequently, the District Court erred in holding otherwise.

2.

The District Court’s determination that CFI’s FAC failed to meet the pleading requirements of Federal Rules of Civil Procedure 8(a)57 and 9(b)58 is also in error. At the motion to dismiss stage, a court must “accept as true all of the allegations contained in a complaint,” make all reasonable inferences in favor of the plaintiff, and refrain from engaging in any credibility determinations.59 In the FAC, CFI lays out in great detail each shipment of pipe-fittings Victaulic imported during the requisite time period, as well as the methodology pursuant to which CFI concluded that these shipments consisted of improperly marked or unmarked goods for which the marking duties were not paid. Given the operation of customs marking duties, CFI’s discovery of what it believes to be unmarked or improperly marked goods in the stream of commerce in the United States plausibly shows liability under the FCA.

This “discovery” by CFI must of course be based on a reliable methodology. The FAC details the process by which CFI came to its conclusions. After determining that a “significant majority”60 of Victaulic’s pipe fittings were imported from China and Poland, CFI reasoned that “one would expect to see Victaulic pipe fittings sold in the United States and manufactured in recent years bearing ‘Made in China’ or ‘Made in Poland’ country-of-origin markings.”61 In the FAC, CFI then describes how it “executed a unique study of the secondary market for Victaulic pipe fittings (CFI’s ‘product study*), with the goal of objectively determining what percentage of Victaulic pipe fittings for sale in the United States have foreign country-of-origin markings.”62

CFI attached to the FAC a report by its expert, Abraham J. Wyner, Ph.D,, a professor of Statistics at the University of Pennsylvania’s Wharton School of Business. Professor Wyner explained that because CFI did not “have access to direct evidence that traces and tracks imported Victaulic pipe fittings in the U.S, supply chain,” “statistical methods can be used to establish indirect evidence.” Professor Wyner then “opines that the process chosen by CFI to survey the secondary market for Victaulic products ‘is standard practice’ in this regard.”63

*257As set forth in the FAC, in setting up its survey, CFI determined that Victaulic sold pipe fittings through distributors and directly to end-users64 and that a review of such sales is only possible through a review of after-market sales.65 Victaulic products are sold on secondary markets in the United States, including on eBay which CFI determined “is an active' and diverse secondary sales outlet for Victaulic products.” 66 CFI then noted that a review of secondary sales outlets provided a much wider spectrum of total Victaulic sales in the country than a review of the sales of a particular distributor. A secondary market sales review included “different channels of distribution, as well as a wider range of dates in which sales might have been made.”67

Professor Wyner concluded that “CFI’s findings are so stark that the only conclusion one can possibly reach is that Victaulic is not properly marking its imports,”68 At the motion to dismiss stage, without the benefit of any discovery, taking all facts as true, and making all reasonable inferences in favor of the plaintiff, we conclude that that showing is enough to allow this matter to proceed.

It is this study, however, that the dissent describes as “unsupported assumptions” and “numerical guesswork.” The dissent criticizes the numbers arrived at by CFI, for instance that statistically less than 2% of the Victaulic pipe fittings in the secondary market bore foreign country of origin markings.69 That finding of less than 2% is not, however, necessary to demonstrate the plausibility that, since Victaulic is importing a “significant majority” of its pipefittings, some approximation of that number of Victaulic pipefittings with foreign country-of-origin markings would show up in the secondary market.70 71

The District Court was skeptical of the validity of CFI’s methods of determining whether Victaulic had imported unmarked goods. We, too, are skeptical. There is little evidence to show that CFI’s unusual procedure of reviewing eBay listings is an accurate proxy for the universe of Victaulic’s products available for sale in the United States. Yet, such skepticism is misplaced at the Rule 12(b)(6) stage. For the reasons stated above, we conclude that the variable being measured here, the existence of country of origin markings on Victaulic pipefittings, could support the results of CFI’s product study only if Vic-taulic was not properly marking its imported pipefittings.

*258Turning then to Rule 9(b), we conclude that the FAC adequately meets the particularity requirements for alleging fraud. In the FCA context, a plaintiff “must provide ‘particular details of a scheme to submit false claims [or avoid obligations] paired with reliable indicia that lead to a strong inference that claims were actually submitted [or obligations avoided].’ ”72 The FAC refers to voluminous records detailing the shipments at issue, when they entered the country, the alleged problems with those shipments, and, by operation of law, when liability would have attached.

Although CFI has not, as the dissent points out, alleged “which shipments, during which time periods, at which ports, were supposedly unlawful,” in Foglia, we held that the facts were sufficient to meet Rule 9(b)’s heightened pleading standard where the plaintiff alleged that a dialysis center was not actually using all of the medicine for which it was getting reimbursed by Medicare. “Accepting the factual assertions made by Foglia as time,” we reasoned, we had “patient logs that show that less [medicine] was used than would be required if it were used in the single use fashion”; Medicare’s reimbursement scheme presented “an opportunity for the sort of fraud alleged”; and only the defendant “ha[d] access to the documents that could easily prove the claim one way or another.”73 Likewise, here, we accept CFI’s allegations, as we must at this stage, that far. more Victaulic pipe fittings on the secondary market should have country-of-origin markings, that the way marking duties are assessed provides an opportunity for fraud, and that only Victaulic has access to the documents that could prove or disprove CFI’s well-pled allegations.

We conclude that, at this pleading stage, nothing more is required to give Victaulic adequate notice of the claims raised against it.

In sum, failure to pay marking duties may give rise to reverse false claims liability. CFI’s FAC contains just enough reference to hard facts, combined with other allegations and an expert’s declaration, to allege a plausible course of conduct by Victaulic to which liability would attach. Thus, since CFI did not unduly delay its motion for leave to amend and the proposed amended pleading is not futile, the District Court abused its discretion in denying CFI’s motion. We will therefore reverse and remand for further proceedings.

C.

Although we hold that CFI has done just enough to allow this matter to proceed, we are aware of the great expense and difficulty that may accompany False Claims Act discovery and the burden on defendants and their shareholders and investors of having unresolved allegations of fraudulent conduct in pending proceedings. Because of our awareness, we have looked to the recent amendments to the Federal Rules of Civil Procedure; those rules provide some guidance as to how excessive expense and difficulty may be avoided and how discovery should proceed.

In December 2015, a series of amendments to the Federal Rules were enacted to improve a system of civil litigation that “in many cases ... has become too expensive, time-consuming, and contentious, inhibiting effective access to the courts.”74 *259To counter these problems, the 2015 amendments placed a greater emphasis on judicial involvement in discovery and case management and cooperation among litigants’ counsel.75

Rule 26, which governs discovery, was among the rules amended. Rule 26(b)(1) now includes a discussion of proportionality, stating

Parties may obtain discovery regarding any nonprivileged matter that is relevant to any party’s claim or defense and proportional to the needs of the case, considering the importance of the issues at stake in the action, the amount in controversy, the parties’ relative access to relevant information, the parties’ resources, the importance of the discovery in resolving the issues, and whether the burden or expense of the proposed discovery outweighs its likely benefit.

As Chief Justice Roberts wrote of these amendments, “[t]he key here is careful and realistic assessment of actual need” that may “require the active involvement of a neutral arbiter—the federal judge—to guide decisions respecting the scope of discovery.”76 The instant matter is a prime example of the need for such controlled discovery.

CFI alleges a massive, systematic effort by Victaulic to avoid paying marking duties on any of its imports. Since Victaulic’s motion to dismiss was granted, there has been no answer from the defendant as to whether any of CFI’s allegations are true. An answer could shed some light on these allegations. Similarly, while CFI has identified millions of pounds of imported pipe fittings that it alleges were mis-marked, proportional discovery would counsel in favor of limiting the scope of early discovery. It will be up to the District Court and counsel to determine an appropriately limited discovery plan, perhaps reviewing the documents and duties paid on a representative sample of the shipments identified by CFI.

In any event, Chief Justice Roberts noted that “[jjudges must be willing to take on a stewardship role, managing their cases from the outset rather than allowing parties alone to dictate the scope of discovery and the pace of litigation.”77 The instant matter will require the active involvement of the District Court, in conjunction with counsel and their clients, to limit the expense and burden of discovery while still providing enough information to allow CFI to test its claims on the merits.

IV.

For the foregoing reasons, we will vacate the order of the District Court denying CFI’s motions for relief from judgment and for leave to amend its complaint. We will remand this matter for further proceedings consistent with this opinion.

concurring in part, dissenting in part, and dissenting from the judgment.

Customs Fraud Investigations, LLC (“CFI”) brings this action under the False Claims Act, alleging a ten-year scheme to defraud the government on the basis of statistical evidence alone.1 That evidence *260consists almost entirely of non-random observations gleaned from product advertisements- on the website of the online retailer eBay. Whereas Twombly and Iqbal require plausible allegations of wrongdoing, CFI gives us unsupported assumptions and numerical guesswork. Whereas Rule 9(b) requires that fraud be alleged with particularity, CFI gives us ten years of raw import data and insists there is evidence of fraud in there, somewhere, while completely failing to identify which shipments, during which time periods, at which ports were illegal. The mere suggestion of fraud, which is all CFI has alleged, is not enough to state a plausible claim or to satisfy the heightened pleading standards of Rule 9(b).

Faced with obvious deficiencies in CFI’s allegations, the District Court granted the defendant’s motion to dismiss the complaint—with prejudice—and then denied CFI’s motion to reopen the judgment so that it could file an amended complaint. I disagree with the majority’s decision to vacate the District Court’s dismissal and reinstate this case. When asserting a violation of the False Claims Act, a plaintiff must state a plausible claim and allege fraud with particularity. CFI has failed in both respects. I therefore partially dissent.2

I. The Proposed Amended Complaint Fails to Allege a Plausible Claim

CFI’s eight-page, 35-paragraph complaint alleges that Victaulic, a manufacturer of iron and steel pipe fittings, has engaged in a decade-long scheme to defraud the government by mismarking its imported products. The District Court dismissed that complaint for failure to allege a plausible claim within the meaning of Twombly and Iqbal.3 When CFI moved to reopen the judgment, the District Court denied that motion too—this time, not on plausibility grounds, but for reasons that included undue delay and CFI’s failure to satisfy Rule 9(b)’s heightened standard for pleading fraud in its proposed amended complaint.4

Because this is an appeal from the District Court’s final order, we would ordinarily limit our review to issues arising from CFI’s motion to reopen the judgment—ie., undue delay and the proper application of Rule 9(b). But the real problems with the proposed amended complaint run deeper. Since “[w]e exercise plenary review over a decision granting a motion to dismiss!,] ... ‘[w]e may affirm the district court on any ground supported by the record.’”5 I therefore think it’s worth exploring whether the proposed amended complaint even raises a plausible allegation under the False Claims Act, *261much less whether it makes those allegations with the requisite particularity.

CFI says that before suing Victaulic it conducted a “complex, and multifaceted analysis.”6 I am not willing to credit this characterization. In my view, CFI’s investigation into Victaulic’s imports is incapable of supporting the kinds of statistical inferences that CFI wants us to draw. To explain why, I begin by summarizing some basic principles of valid survey design. I then apply those principles, to assess the plausibility of the allegations in CFI’s proposed amended complaint.

A. The Fundamentals of Statistical Sampling

A valid statistical survey essentially has three steps: (i) identify a population of interest, (ii) take a random sample from that population, and (iii) use the observations in the sample to draw inferences about the population as a whole.7 We see examples of this process every day in opinion polls. A survey firm will identify a population to study, draw a random sample from that population, and then, based on its observations, make inferences about that population to a greater or lesser degree of confidence based on the sample size. These principles apply to all probabilistic surveys, including the kind of survey that CFI conducted—or, at least, attempted to conduct—in this case.

There are a few critical.features that are necessary for such a survey to be valid. First, it is important for the sample to be drawn from the correct population of interest. When a survey makes an error relating to “the specification of the population to be sampled ... any estimates made on the basis of the sample data will be biased.”8 This makes sense. If there are differences between the population being studied and the population actually sampled, the survey’s results will necessarily be unreliable.

Second, a valid statistical sample must be drawn randomly. Surveys rely on random sampling because “[t]he statistics derived from observations or measurements of random samples permit one to estimate the parameters of the population.”9 Indeed, “random selection is the only selection mechanism ... that automatically guarantees the absence of selection bias. That is because when we use random sampling we are, by definition, assuring the absence of any association that may exist between selection rules and the variables in our study.”10 In a nonrandom sample, by contrast, the selection rule “may inadvertently ... introduce bias.”11

It is frequently the case that a random sample is either not available or difficult to obtain. Survey methodologists and statisti*262cians have developed numerous tools to address this problem. What a researcher cannot do, however, is draw a nonrandom “convenience sample” simply because the data is close at hand and then assume away all the statistical problems that such a technique creates.12 Unfortunately, this is precisely what CFI did. In the words of Charles Seife, we are about to be “Fooled by the Numbers.”13

B. Step One: The Review of Victaulic Import Data

CFI claims that its president “personally spenft] at least 700 hours” on its investigation,14 a figure that is fairly extraordinary on its own and only becomes more so once it becomes clear what CFI actually did—and, more to the point, did not do.

CFI’s first step was to estimate the proportion of Victaulic products imported from overseas in recent years. To do so, it reviewed figures from a subscription service, Zepol, that aggregates data from ships carrying imports into the United States.15 CFI tells us that Zepol is an “expensive fee-based subscription service” with an annual cost of $5,995.16 It also says that the information in Zepol’s database is so unwieldy as to be comprehensible only by persons who have “worked with customs import data over many years ... [who can] understand what conclusions can properly be drawn” from such data.17

CFI queried the database for the word “Victaulic” for the nine-year period between 2003 and 2012.18 Its president then “personally reviewed the narrative description for every import entry and culled through line by line to eliminate items that were not iron or steel pipe fittings.”19 We are told that “[o]nly upon completing the above multi-step process was CFI able to obtain a usable database from which Vie-taulic’s imports could then be segregated and tabulated by country and from which CFI could draw reliable conclusions.”20 In an era when Microsoft Excel or, indeed, any data management software can filter data based on complex queries, it is completely unclear why this kind of line-byline effort was even necessary.

At this point, CFI had constructed a dataset purporting to show all of Victaulic’s imports of pipe fittings into the United States. According to these figures, over the period from 2003 through 2012 Victaulic imported 83 million pounds of pipe fittings from China and Poland (an average of about 9.2 million pounds per year).21 Between 2010 and 2012, this annual average climbed to 15.2 million pounds per year.22

Of course, that figure is not helpful without some baseline. Knowing this, CFI *263sought to convert Victaulic’s raw imports into a dollar figure, and then to compare that dollar figure against Victaulic’s total revenue. Unfortunately, the Zepol database aggregates information about Victaulic’s imports across several, differently-priced product lines. CFI’s approach to solving this problem was, at best, extremely problematic.

CFI started by using Victaulic’s 2011 price list to compile “a total of 147 separate price observations for 49 different products with three sizes each to arrive at an estimated per pound price of $36.40.”23 CFI admits that this figure may not be reliable, however, because “[discounts off price lists ... are very common in the pipe fittings industry.”24 CFI therefore “assume[s] conservatively” that Victaulic’s imported pipe fittings were sold “at deeply discounted prices” averaging between $10 and $15 per pound.25 Using these figures, CFI estimates that, during the period from 2010 through 2012, Victaulic’s annual sales deriving from Chinese and Polish imports were somewhere between $152 million and $228 million per year.26

Next, CFI cites unnamed “[a]uthorita-tive independent sources” for the proposition that ‘Victaulic’s annual revenue is in the approximate range of $250-280 million.”27 It then uses these numbers to claim that pipe fittings imported from China and Poland accounted for between 54% and 91% of Victaulic’s annual sales between 2010 and 2012.28

Drawing all inferences in CFI’s favor, I accept—at least for the sake of argument—that foreign-made pipe fittings accounted for between 54% and 91% of Vic-taulic’s annual sales during the period from 2010 through 2012.29 Notice, however, that nothing in the proposed amended complaint so far supports the plausible inference that Victaulic defrauded the government, much less that it did so over ten years. To support that allegation, CFI relies on its so-called “eBay investigation.” And that is where CFI’s claims ultimately fail.

C. Step Two: The “eBay Investigation” and Its Obvious Deficiencies

At this point in our narrative, CFI (i) believes that Victaulic is importing large quantities of foreign-made pipe fittings into the United States, and (ii) suspects that Victaulic is not properly marking those pipe fittings to reflect their countries-of-origin. But how to prove those sus*264picions? CFI’s answer was to survey the online retailer eBay in an attempt to draw inferences about the broader U.S. market.

To that end, CFI’s president personally spent between one and five hours per day over a period of six months compiling eBay postings for Victaulic pipe fittings.30 CFI then examined these postings to determine whether they contained photographs of Victaulic products with visible country-of-origin marks.

What was the goal of this investigation? Well, recall that CFI estimates that between 54% to 91% of Victaulic’s pipe fittings were imported from China and Poland between 2010 and 2012, According to CFI, we should therefore expect to see “Made in China” or “Made in Poland” markings on somewhere between 54% and 91% of all Victaulic pipe fittings for sale in the United States—and, by corollary, for sale on eBay.31 „

That hypothesis, however, assumes, with no basis in alleged fact, that secondhand postings on eBay are representative of all Victaulic products for sale in the United States. It also assumes, again with no basis in alleged fact, that photographs in eBay postings (i) depict the very items being sold rather than stock images or photographs of other inventory, and (ii) depict those items in such a way that foreign country-of-origin markings would be clearly visible. Both of these assumptions are questionable. First, Victaulic claims that “[its] full product line is not available on eBay,” meaning that “[r]esellers on eBay would only have access to small quantities of overstock and/or older, used, salvaged, stolen, or counterfeit products.”32 Second, CFI’s complaint alleges that U.S.-made products tend to command a higher price than foreign-made products.33 Resellers on eBay therefore may have a strong incentive to obscure foreign country-of-origin markings. We, of course, cannot credit a defendant’s factual assertions at the motion to dismiss stage—but doing so is different from recognizing that the plausibility of CFI’s allegations depends on multiple unsupported assumptions about how eBay actually functions.

What is fairly clear to this point is that CFI did not actually base its conclusions on a comprehensive analysis of Victaulic pipe fittings for sale on eBay. What CFI did instead was to construct a subsample of a subsample of a subsample. For example:

• CFI began by searching eBay for “Victaulic” in the “new” subset of the “fittings” product category. These searches “typically resulted in about 600 active eBay listings daily.”34

• In some postings, the word “Victaulic” appeared in the title, but it was clear that the posting was not actually for a Victaulic pipe fitting. These postings were excluded.35

• Some postings were for “old stock.” These were excluded because CFI’s analysis “was intended to examine products of relatively recent manufacture (e.g., from 2005 to the present).” That 2005 number is surprising because CFI’s earlier calculations focus on import figures for the period from 2010 to 2012— to say nothing of the fact that CFI actually alleges a fraudulent scheme going back to 2003.

*265• At this point, 20% of postings “did not include actual photos of the products for sale.”36 These, too, were excluded. Eliminating listings without photos, of course, is the same thing as assuming that 100% of the pipe fittings advertised in those listings lacked foreign country-of-origin marks—an assumption that is itself deeply problematic.

After filtering the data this way, CFI identified 221 postings for Victaulic pipe fittings that contained photographs. Of those 221 postings, 29 contained photographs of products marked as being made in the United States; three contained photographs of products with foreign country-of-origin marks; and 189 contained photographs where no country-of-origin marks were apparent.37 Of the 189 postings in the third group, “there were approximately 40 listings that had limited or unclear photographs, such that it would have been difficult to see country-of-origin markings.”38

CFI decided that it wanted more information about the 40 listings with indeterminate photographs. Rather than purchase products from all 40 of them, however, CFI purchased just ten to examine in person. CFI never says whether these products were randomly chosen. Of these, it turned out that one was not a Victaulic product at all, four had no country-of-origin markings, four had U.S. country-of-origin markings, and one item “was packed with a U.S. origin label, but did not appear to have a permanent origin marking.”39

If we assume (again, with no basis in alleged fact) that the ten-product sample is representative of all products in the group of 40 postings with indeterminate photographs, then the results of the eBay study looks like this:

Table 1: Results of CFI’s eBay Investigation

*266[[Image here]]

This is the extent of the evidence of a decade-long scheme to defraud the government. CFI points to the extrapolated “fact” that 169 of the Victaulic products in its 221-item sample—about 75% of the total—lack country-of-origin markings.40 Recall, too, that CFI asserts that at least 54% of Victaulic products for sale on eBay should be stamped “made in China” or “made in Poland.” CFI therefore contends that “[t]he only reasonable conclusion that can be drawn from [its] analysis is that Victaulic has unlawfully imported huge quantities of unmarked pipe fittings from its foreign manufacturing plants and has then sold those unmarked fittings in the U.S.”41

Based on the record before us, here is the entire logical chain supporting CFI’s allegations:

• Step one: Based on import data and information from unnamed sources, 54% to 91% of Victaulic’s annual sales between 2010 and 2012 derived from imports of pipe fittings from China and Poland.

• Step two: We should therefore expect that, in any representative sample of Victaulic’s products for sale in the U.S. market, 54% to 91% of items should bear country-of-origin markings from China and Poland.

• Step three: Assume that Victaulic products available on eBay constitute a perfectly representative sample of Victaulic products for sale in the United States.

• Step four: Assume that photographs on eBay are not stock images but *267rather accurate depictions of the physical items being sold.

• Step five: Assume that a nonrandom sample of 221 of Victaulic items for sale on eBay is also perfectly representative of Victaulic products sold in the United States.

• Step six: While 40 items out of this 221-item - sample contain unclear photographs, assume that we can rectify that problem with a nonrandom sample of ten items, examined in person.

• Step seven: Extrapolating from these two nonrandom samples, we can conclude that over 75% of Vic-taulie products for sale on eBay, lack country-of-origin marks.

• Step eight: Because we have assumed that eBay is perfectly representative of the U.S. market, we can conclude that 75% of all Victaulic products sold in the United States must lack country-of-origin marks as well.

• Step nine: Therefore, Victaulic has been defrauding the United States government of accrued marking duties since at least 2003.

This chain of inferences simply does not support a plausible allegation of fraud.

I turn first to the relevant legal standard. As we recently explained in Finkelman v. National Football League,42 the essence of the Supreme Court’s plausibility test under Twombly and Iqbal is that allegations merely consistent with liability are not enough to survive a motion to dismiss.43 When assessing whether a complaint raises sufficiently plausible allegations, the Supreme Court has instructed us to “draw on [our] judicial experience and common sense.”44

My common sense tells me that a plaintiff cannot plausibly allege a ten-year scheme to defraud the government .on the basis of 221 eBay postings. At most, the eBay study provides evidence consistent with fraud.45 It does not provide any evidence more plausibly suggesting that fraud actually occurred.

The first problem is that CFI surveyed the wrong population. It would have been perfectly acceptable for CFI to draw a random sample from eBay if it was trying to draw inferences about the larger universe of Victaulic products actually sold on eBay. The problem is that CFI wants to use eBay as a proxy for the entire U.S. market for Victaulic pipe fittings. Unfortunately, CFI never sampled that larger population. CFI could have rectified this problem by making factual allegations sufficient to support the plausible inference that eBay serves as an appropriate proxy for the entire U.S. market, but the only allegations to that effect in the complaint *268are entirely conclusory.46 This is unsurprising, since there is no reason to believe that eBay—-an e-commerce platform that sells everything from clothing to electronics to collectible coins, sometimes via auction and sometimes via direct person-to-person transactions—looks or functions anything like the broader market for iron and steel pipe fittings.

This brings us to the second problem with the eBay study—the fact that CFI did not take a random sample at all. Thus, even if we were to treat eBay as a viable stand-in for the U.S. market, the eBay study is still fatally flawed because CFI did not take a random sample of Victaulie products for sale on eBay. Instead, it spent weeks building its own curated subset of 221 postings, all the while applying any number of criteria (including the requirement that postings contain photographs) likely to skew its results. This is to say nothing of the fact that CFI’s actual conclusions involve additional extrapolations based on the ten Victaulie products that CFI examined in person. CFI constructed a convenience sample, not a random one, and such a sample “provides no rigorous assurance that the sample will represent the population of interest.”47

The District Court raised these very objections when it dismissed CFI’s first complaint.48 In an effort to respond to these concerns, CFI hired Dr. Abraham J. Wyner, Director of the Undergraduate Program in Statistics at the University of Pennsylvania’s Wharton School, to write a declaration that it attached as an exhibit to the proposed amended complaint. Unfortunately, Dr. Wyner fails to articulate any independent justifications for CFI’s methodology. Instead, his declaration rests entirely on CFI’s own conclusory assumptions about eBay. Here is the key language:

My analysis is based on ... very reasonable and quite conservative assumptions .... I will assume that the slice of the secondary market for Victaulie pipe fittings represented by eBay contains a proportion of imported products at least approximately similar to the proportion of imported products among all U.S. sales and that any significant deviation is caused only by chance.49

The sleight of hand here is to assert, •without any basis in alleged fact, that it is “very reasonable” to assume that the universe of products being sold on eBay somehow mirrors the entire U.S. market. Indeed, the entire rhetorical gambit of the Wyner declaration is to repeat CFI’s con-clusory allegations back to the reader in *269more, technical-sounding terms. A few examples illustrate the point.

First, Dr* Wyner recognizes that the findings from the eBay investigation “could be skewed” if eBay were not representative of the U.S. market, but he says that these fears are “contrary to [CFI’s] actual observations of eBay as a diverse sales outlet with a representative national cross-section of Victaulic pipe fittings, including geographically and by supplier and product variety.”50 This conclusory language is lifted directly from the proposed amended complaint.51

Second, Dr. Wyner acknowledges that the validity of the eBay study depends on the accuracy of photographs in eBay postings, but he downplays that concern because “[a]ccording to [CFI] ... the vast majority of relevant listings had pictures and the vast majority of these pictures provided views of the Victaulic product such that a country-of-origin marking would have been visible had it existed.”52 In other words: the eBay study is accurate because CFI says it is.

. Third, while Victaulic warns that “eBay sellers may have concealed import markings,” Dr. Wyner tells us that “[t]his is inconsistent with the evidence provided, by [CFI] that only 40 of the 221 items had incomplete or unclear images.”53 This mode of reasoning is exactly backwards. If the results of a survey are biased, those same results cannot support the reliability of the survey design in the first instance.

Accordingly, Dr. Wyner’s conclusion— that “assuming the validity of [his assumptions], [he] would be more than 99.9% confident that Victaulic is improperly marking a significant portion of its imports”—is profoundly misleading.54 If I were to assume that the judges of the Third Circuit comprise an accurate cross-section of the U.S. population,' I would then be able to conclude that a startlingly high proportion of the general public has a law degree. But of course, 'it would be frivolous to make that assumption in the first instance. Understood in context, Dr. Wyner’s declaration is little more than a reflecticin of CFI’s own unsupported assumptions about eBay, only dressed up in more persuasive-sounding statistical jargon. For this reason, his declaration completely fails to nudge CFI’s allegations across the plausibility threshold.

Stepping away from the specifics of CFI’s investigation, the significant issue in this case concerns how we think about the plausibility standard when a complaint rests entirely on statistical evidence. In the mine, run of cases, of course, Daubert and the Federal Rules of Evidence will filter out unreliable statistical evidence in due course.55 But to my mind, ,we act contrary to Twombly and Iqbal when we refuse to ask whether statistical evidence actually supports a plausible inference of wrongdo*270ing at all, particularly when a complaint rests on statistical evidence alone. In the words of one observer, “[statistical studies are neither magic nor snake oil, and the experts neither sorcerers nor (generally speaking) charlatans. Rather, what legal actors need to do is treat statistical studies critically.”56 Just so—even at the motion to dismiss stage.

A recent case from the Second Circuit illustrates this point. In Burgis v. New York City Department of Sanitation,57 the plaintiffs alleged that officials had “discriminated against them and others similarly situated on the basis of their race and/or national origin in the [Department of Sanitation’s] promotional practices.”58 In support of their Equal Protection claim, they relied exclusively on statistical evidence. The Second Circuit held for the first time that, in a case alleging employment discrimination, “statistics alone may be sufficient” to get past the motion to dismiss stage.59

But the Second Circuit also stated that, “to show discriminatory intent ... based on statistics alone, the statistics must not only be statistically significant in the mathematical sense, but they must also be of a level that makes other plausible non-discriminatory explanations very unlikely.”60 The plaintiffs in Burgis “failed to allege statistics that me[t] the standards articulated above,” in part because their evidence “show[ed] only the raw percentages of White, Black, and Hispanic individuals at each employment level, without providing any detail as to the number of individuals at each level, the qualifications of individuals in the applicant pool and of those hired for each position, or the number of openings at each level.”61 In the Second Circuit’s view, this was not enough to allege a viable claim.

Burgis demonstrates that numbers alone are not enough to get a litigant past the motion to dismiss stage. Rather, a litigant’s statistical evidence must be reliable enough to raise a plausible inference of wrongdoing. Here, I believe that a basic facility with statistical concepts demonstrate that the plaintiffs eBay study supports no plausible inference at all—let alone one that surpasses the high bar to allege fraud.62

The ultimate lesson of Twombly and Iqbal is that a federal lawsuit is not a mechanism to confirm a vague suspicion that fraudulent conduct occurred. Sturdier factual allegations are necessary. The Twom-bly plaintiffs, observing parallel conduct in the marketspace, were awfully concerned about an antitrust conspiracy. Finkelman himself observed higher prices in the resale market for Super Bowl tickets and had “a strong suspicion that [his] ticketfs] would have been cheaper if more tickets had been available for purchase by members of the general public.”63 CFI browses postings on eBay and has a powerful inkling that Victaulic has been mismarking its products. In all these instances, what is lacking is either some first-person account *271indicating that unlawful conduct has actually occurred, or at the very least, some other generalized allegation that raises a plausible inference of wrongdoing.

To be fair, there is one moment in the Proposed Amended Complaint when CFI tries to offer a first-person account of fraudulent conduct. Here it is:

One witness, who has worked for many years in the pipe and tube industry, recalls a customer procuring Victaulic pipe fittings that the company represented were 100% U.S. manufactured. This witness observed that at the bottom of one box of Victaulic inventory, a packing list indicated that the products had originated from Poland. None of the Victaulic pipe fittings were marked with any foreign country name, however.64

This is CFI’s best evidence: one unnamed witness in an unknown location who,, one time, saw one box of Victaulic pipe fittings that appeared to be mismarked. That single anecdote simply cannot be enough to support plausible allegations of a ten-year scheme to defraud the government. Accordingly, I would affirm the District Court’s denial of CFI’s motion to reopen the judgment on this alternative ground.

II. The Proposed Amended Complaint Also Fails to Satisfy Rule 9(b)

I would also conclude that the proposed amended complaint fails to comply with Rule 9(b). CFI’s pleadings contain “voluminous records detailing the shipments at issue, when they entered the country, the alleged problems with those shipments, and, by operation of law, when liability would have attached.”65 In the majority’s view, “nothing more is required to give Victaulic adequate notice of the claims raised against it.”66 I respectfully disagree.

We start with the applicable law. Rule 9(b) requires that “a party must state with particularity the circumstances constituting fraud or mistake.”67 In Foglia v. Renal Ventures Management, LLC,68 we explained that two approaches had emerged in the Courts of Appeals regarding how to comply with Rule 9(b) in a False Claims Act suit. Under one approach, “a plaintiff must show ‘representative samples’ of the alleged fraudulent conduct, specifying the time, place, and content of the acts and the identity of the actors.”69 We adopted a second, more lenient approach, holding that “it is sufficient for a plaintiff to allege ‘particular details of a scheme to submit false claims paired with reliable indicia that lead to a strong inference that claims were actually submitted.’ ”70 We rejected the stricter alternative because, in our view, it would have required qui tam rela-tors to offer a level of “detail at the pleading stage [that] would be ‘one small step shy of requiring production of actual documentation with the complaint, a level of proof not demanded to win at trial and significantly more than any federal pleading rule contemplates.’ ”71

Foglia itself was a “close case as to meeting the requirements of Rule 9(b).”72 Still, we concluded that the plaintiffs alle*272gations were satisfactory because (i) they “suffice[d] to give [the defendant] notice of the charges against it, as is required by Rule 9(b),” and (ii) “only [the defendant] ha[d] access to the documents that could easily prove the claim one way or another—the full billing records from the time under consideration.”73

Our only precedential opinion to have applied Foglia in a subsequent False Claims Act case, United States ex rel. Moore & Co., P.A. v. Majestic Blue Fisheries, LLC,74 made it clear that Rule 9(b) still has sharper teeth than Rule 8. We said there that, under Rule 9(b), “[a] plaintiff alleging fraud [under the False Claims Act] must ... support its allegations ‘with all of the essential factual background that would accompany the first paragraph of any newspaper story—that is, the who, what, when, where and how of the events at issue.’ ”75 This is a greater level of detail than that associated with mere notice pleading.

The proposed amended complaint does not satisfy these standards. While it may be true that CFI’s complaint includes “voluminous records detailing the shipments at issue,”76 it is important to keep in mind that these records detail all of Victaulic’s imports from China and Poland over the period from 2003 through 2012.77 Based on its flawed eBay study, CFI insists that some unknown portion of those shipments must involve mismarked goods. But CFI fails entirely to tell us which shipments, during which time periods, at which ports, were supposedly unlawful. To suggest that there must be fraud there—somewhere— cannot possibly be enough to satisfy Rule 9(b). Such an approach neither provides us “with reliable indicia that lead to a strong inference that [false] claims were actually submitted,”78 nor tells us anything specific about “‘the who, what, when, where and how of the events at issue.’”79 It is, instead, a data dump camouflaged as a set of particularized allegations.80

I would therefore affirm the District Court’s termination of this case on this ground as well.

III. Conclusion

The desirability of increasing or decreasing anti-fraud efforts through the mechanism of the False Claims Act is a topic of heated debate.81 By highlighting *273the deficiencies in CFI’s allegations, I express no opinion on these matters, whose resolution lies more properly with the executive and legislative branches.

Even so, it is certainly within our province to enforce legal standards as they presently exist. In my view, CFI cannot overcome the plausibility bar of Iqbal and Twombly because its flawed eBay study completely fails to raise a well-supported inference of fraud. CFI cannot satisfy Rule 9(b) because it has failed to allege fraud with particularity. What’s more, I also believe that the District Court was correct to deny CFI’s motion to reopen the judgment on the ground of undue delay.82

I therefore respectfully dissent,