BRYSON, Circuit Judge.

This damages dispute is the last phase of litigation over a number of offshore oil and gas leases that the United States sold to oil companies in the 1980s. The litigation began in 2002, when the plaintiff oil companies filed breach of contract actions against the government in the Court of Federal Claims. After a trial, the court held that the government had breached its contracts with the oil companies by preventing them from drilling for oil in the offshore areas covered by the leases. This court affirmed the judgment of the Court of Federal Claims, and the restitution awards made to the plaintiffs totaled approximately $1 billion. Amber Res. Co. v. United States, 538 F.3d 1358 (Fed.Cir. 2008).

Not all of the plaintiffs in the Amber litigation accepted the restitutionary remedy, however. The one holdout was the appellant in this appeal, Nycal Offshore Development Corp., which held a 4.25 percent interest in two of the leases. Rather than accepting restitution as its remedy, Nycal waived its right to restitution and pursued a claim for lost profits. The Court of Federal Claims first held that it was permissible for Nycal to seek lost-profits damages even though the other owners of the leases in which Nycal held a partial share had accepted restitution. Nycal Offshore Dev. Corp. v. United States, 92 Fed.Cl. 209 (2010). The court then conducted a trial on Nycal's lost-profits claim, at the end of which the court concluded that Nycal had not proved its case for lost profits. Nycal Offshore Dev. Corp. v. United States, 106 Fed.Cl. 222 (2012). Nycal now appeals. We affirm the judgment of the Court of Federal Claims denying an award of lost profits to Nycal.

I

A

The factual background of this case is reviewed in detail in this court's opinion in Amber Resources Co. v. United States, and in the Court of Federal Claims opinion from which this appeal is taken. In brief summary, as part of its program of selling oil and gas leases to oil companies, the government in 1982 issued two leases for oil fields off the Southern California coast. Nycal ultimately obtained a 4.25 percent share of those leases. ARCO, the original owner of the leases, drilled an exploratory well on one of the leased properties, but that well produced only a small amount of oil flow. ARCO conducted no further exploration of either lease, but instead sold the leases to a group led by Samedan Oil Corporation. Samedan drilled another well, which produced a greater flow of oil, but the oil from that well was of low quality. Samedan subsequently made plans to drill another exploratory well, but before that well could be drilled, a federal district court ruled that the government's actions in extending the oil and gas leases were contrary to law in several respects. The Ninth Circuit affirmed the district court's ruling in 2002. The effect of that ruling was to terminate the ability of Samedan and the other lease owners to conduct drilling on the leased properties.

Samedan and other oil companies filed suit, contending that the government had breached its lease agreements with them. After the Court of Federal Claims held that the government had breached the lease agreements, all of the plaintiffs other than Nycal accepted restitution as a remedy. Nycal, however, sought a greater recovery by attempting to prove its right to an award of lost profits as part owner of the Samedan leases.

B

In a comprehensive opinion, the Court of Federal Claims addressed each of the arguments made by the parties as to whether Nycal had proved its right to lost-profits damages. The court began by noting that in a lost-profits case, the plaintiff must prove that the damages it seeks were foreseeable to the breaching party at the time of contract formation, were actually caused by the breach, and are reasonably certain. As to foreseeability, the court found that the government — the breaching party in this case — had reason to anticipate that the breach would cause the type of loss that Nycal incurred, but that it was not necessary for Nycal to show that the government could anticipate the amount of that loss. Although the government argued that the evidence did not show that it should have foreseen that the leases would ever be profitable, the court concluded that, given the terms of the lease agreements, the government assumed the risk that if it interfered with the oil companies' option to explore, "it was on the hook for whatever profits could be established with meaningful certainty." Nycal, 106 Fed.Cl. at 228. In this setting, the court ruled, it was "sufficient to establish foreseeability that there was a reasonable probability of recoverable reserves." Id.

The court then turned to causation, which was the principal issue in dispute. Nycal's experts asserted that the leases would have proved highly profitable and that Nycal's share of those profits would have been approximately $72 million. The government's experts, on the other hand, testified that the amount of recoverable oil and gas in the two leases was not sufficient to make production more than marginally profitable. In addition, the government argued that even if there was enough oil and gas in the reservoir to cover the cost of production, Nycal could not establish causation, for three reasons: First, Nycal could not have obtained the financing to participate in development of the leases; second, Nycal failed to show the lease owners would have gone forward with production; and third, further exploration and development would have been barred by environmental permitting requirements unrelated to the breach. As to the first reason, the court found that the government had raised serious concerns, but the court determined that it did not have to resolve that issue because "environmental problems would have prevented development." Nycal, 106 Fed.Cl. at 229 n. 10.

The court began its causation analysis by addressing what it called "the principal factual dispute dividing the parties: the question of how much oil and gas could have been recovered." Nycal, 106 Fed.Cl. at 229. After a detailed analysis of the prelitigation and postlitigation estimates of the amount of recoverable oil and gas in the lease areas, the court found that the areas contained approximately 60 million barrels of recoverable oil. That amount, the court found, was sufficient to give rise to "a plausible scenario under which [Nycal] could have made a profit from its 4.25 percent interest in that quantity of oil and attendant natural gas." Id. at 240. The court therefore turned to the question whether, as the government contended, there were "independent shortcomings in plaintiff's proof of causation, namely, that plaintiff has not proved that the owners would have gone forward with production, and that the owners could not have overcome the environmental restrictions on development." Id.

Addressing the government's argument that the evidence was insufficient to establish with reasonable certainty that the owners would have proceeded to production on the leased properties, the court concluded that, at minimum, the owners were committed to drilling another exploratory well in an effort to determine whether there was sufficient oil and gas to warrant proceeding. Because the exploratory well was not drilled and the results of that well were not known, the court found that it was uncertain whether the owners would have gone forward. The court ruled that the uncertainty did not preclude Nycal from going forward with its claim, however, because the breach prevented drilling of the exploratory well. The court concluded that it would be "unfair to burden plaintiff with the obligation to prove it more likely than not that the owners would have gone forward with production when the reason we will never know the outcome was the government's breach." Nycal, 106 Fed.Cl. at 243. Therefore, the court concluded that under the circumstances of this case, Nycal had established as much as it needed to about the likelihood that the owners would have gone forward.

The court then turned to the question whether environmental and other obstacles would have prevented development of the leased fields. As to that issue, the court ruled that there were impediments unrelated to the breach that would have precluded development. Nycal, 106 Fed.Cl. at 243. First, the plaintiff "could not have obtained the necessary air pollution permits for the project from the Santa Barbara Air Pollution Control District" ("the District"), and second, the plaintiff "could not have obtained access to the facilities at Las Flores Canyon to process the oil, gas, and water produced at the oil rig." Id.

With respect to the environmental permits, the court explained that in Santa Barbara County, offshore activities are subject to a cap on certain kinds of emissions; if an activity exceeds that cap, the responsible party must offset all of its emissions. The court noted that the offshore drilling and production activity would generate substantial emissions. In addition, the court found that the lease owners would have had to build an onshore processing facility, which, according to the evidence, would be grouped with the offshore platform for purposes of calculating emissions.

The court analyzed the likely volume of emissions that would be created by the drilling and associated operations and found that the only option for the lease owners would be to purchase "emissions credits" from other sources. As to that issue, however, the court found that even accepting all of the favorable assumptions made by Nycal, "the owners would have been well short of the credits needed for rig operation and the ... drilling." Nycal, 106 Fed.Cl. at 246. Summing up its findings on that issue, the court concluded that Nycal "has not proven that the breach was the cause of its lost opportunity to explore and develop the leases. The owners' inability to obtain air pollution permits was an intervening cause of the lost opportunity to develop the lease." Id.

The court added that Nycal's answer that "time and money would eventually provide a solution to the permitting dilemma" did not overcome the problem, but created a new one: uncertainty as to damages. Conjecture that a solution would have been found, but without knowing when, or what it would have cost, "injects an intolerable level of uncertainty into calculating damages." Nycal, 106 Fed.Cl. at 247. The court found that the owners' costs would not be reasonably certain without a set timeline, and that it is unknown how much additional cost would have been incurred to create or obtain emissions credits.

In sum, the court found that the federal government's actions are "not the reason the owners ultimately would have been unable to proceed." Nycal, 106 Fed.Cl. at 247. "Plaintiff's inability to demonstrate that it is more likely than not that it would have obtained the necessary environmental permits is thus an independent basis for ruling that it cannot establish lost profits." Id.

The court then addressed what it referred to as "another major obstacle to the development" of the leased properties: the need to process the oil, gas, and water produced from the drilling platform. As to that issue, the court analyzed the available options in detail and found that the owners would not have been able to use existing capacity at Exxon's onshore processing site. In addition, the court found that building a new onshore facility "would simply have added to the virtual impossibility of obtaining the necessary permits." Nycal, 106 Fed.Cl. at 251. The court concluded that its finding that a new facility would not have been permitted "is sufficient to preclude the necessary finding that the breach caused damages." Id. at 253.

Summarizing its findings, the Court of Federal Claims stated that although Nycal had satisfied the requirement of showing that it would have been foreseeable to government officials that breach of the lease agreement could result in significant lost profits, Nycal had failed to prove that the breach was the proximate cause of any loss. Instead, the court concluded, the government proved "that an intervening cause, for which the United States was not responsible, would have precluded development of the [leased oil fields]: an inability on [the owners'] part to obtain the necessary air pollution permits" for the exploratory drilling, the permanent oil rig, and the associated onshore processing facility. Nycal, 106 Fed.Cl. at 253. Plaintiff, according to the court, "was unable to rebut this overwhelming evidence." Id.

II

Nycal's first argument on appeal is that the trial court improperly allocated the burden of proof with respect to whether the government's conduct caused Nycal's loss. In particular, Nycal argues that the court improperly imposed upon it the burden of proving that the lease owners would have been able to overcome the obstacles created by the need to obtain emissions credits from the District and the need to obtain access to an onshore production facility.1

The basic principles that apply to proof of causation in a lost-profits case are well settled. The showing of causation requires "comparison between the breach and non-breach worlds." Yankee Atomic Elec. Co. v. United States, 536 F.3d 1268, 1273 (Fed.Cir.2008). It is the plaintiff's burden to prove causation. See Rumsfeld v. Applied Cos., 325 F.3d 1328, 1336 (Fed. Cir.2003); Glendale Fed. Bank, FSB v. United States, 239 F.3d 1374, 1380 (Fed. Cir.2001); San Carlos Irrigation & Drainage Dist. v. United States, 111 F.3d 1557, 1563 (Fed.Cir.1997). To satisfy that burden, the plaintiff must show, by a preponderance of the evidence, that the plaintiff's alleged loss was "the proximate result of the breach." Energy Capital Corp. v. United States, 302 F.3d 1314, 1324-25 (Fed.Cir.2002); Cal. Fed. Bank, F.S.B. v. United States, 245 F.3d 1342, 1349 (Fed. Cir.2001).

Nycal does not take direct issue with those propositions, but instead argues that those propositions do not apply here because this case involves an "intervening cause." In the case of such an intervening cause, Nycal argues, the burden of proof shifts to the defendant to show that the intervening cause was the reason for the plaintiff's loss.

We reject that argument. The burden of proof on the issue of causation in a lost-profits case rests on the plaintiff without regard to the nature of the impediment that the plaintiff would have had to overcome in the nonbreach world to make a profit. In some instances the impediment will be obvious. For example, in a case such as this one, the plaintiff might fail to prove that there are enough oil reserves in the leased properties to make the lease agreement profitable. Or the plaintiff might fail to prove that it had the ability to extract and process enough oil to make a profit. Alternatively, there might be less obvious — but equally fatal — impediments to the plaintiff's ability to show that it would have been able to make a profit in the absence of a breach, such as that it lacked sufficient financing or technical expertise to complete the project. An inability to obtain the necessary permits to conduct drilling and processing activities is akin to those impediments, and they are treated the same as the more obvious ones.

There is no ready way to distinguish, in a lost-profits case, between proof of causation in general and what Nycal refers to as "intervening" causes. As a colloquial matter, it may be appropriate to refer to certain prospective impediments to profit as "intervening," but for burden-of-proof purposes the use of that term does not justify treating certain factors bearing on causation differently from others. For example, there is no reason to distinguish between a failure of proof of causation based on factors such as the high expense of production, unavailability of capital, and low oil prices, on the one hand, and a failure of proof based on factors such as the inability to comply with safety or environmental regulations, on the other. All may bear, to a greater or lesser extent, on the ultimate issue of causation. And once they are identified as significant factors in the analysis, there is no reason that the plaintiff should bear the burden of proof as to some of them but not as to others.2

To be sure, some potential impediments — perhaps including whether the plaintiff could have obtained the necessary permitting — might not be immediately obvious to a plaintiff who is trying to prove causation. In a similar instance involving a potential offset to a claim of lost profits, we have required the defendant to point out the potential offset and have required the plaintiff to then show that the potential offset would not have prevented the plaintiff from earning the profits it claims. See, e.g., Energy Nw. v. United States, 641 F.3d 1300, 1308 n. 5 (Fed.Cir.2011) ("While the burden of proof for causation remains squarely with the plaintiff, a defendant seeking an offset has an obligation to move forward by pointing out the costs it believes the plaintiff avoided because of the breach' ...."); S. Nuclear Operating Co. v. United States, 637 F.3d 1297, 1304 (Fed. Cir.2011) (same); see also Boston Edison Co. v. United States, 658 F.3d 1361, 1369 (Fed.Cir.2011). In this case, the government focused the attention of the parties and the court on the emissions-permits problem, so that issue was clearly in dispute as part of the causation analysis. As such, the plaintiff was properly required to prove, as part of its showing on causation, that it would have been able to conduct drilling and processing operations without running afoul of the District's antipollution restrictions.

Nycal's argument to the contrary is based on case authority dealing with distinctly different issues. Nycal relies heavily on the Supreme Court's decision in Bigelow v. RKO Radio Pictures, 327 U.S. 251, 66 S.Ct. 574, 90 L.Ed. 652 (1946). The question before the Supreme Court in that case was whether the evidence of damages in an antitrust case was sufficient to support the jury's verdict. In the course of its opinion, the Court discussed the principle that the defendant should not be heard to argue that the evidence of damages was insufficiently precise "where the defendant by his own wrong has prevented a more precise computation." Id. at 264, 66 S.Ct. 574. "Any other rule would enable the wrongdoer to profit by his wrongdoing at the expense of his victim." Id.

Bigelow does not stand for the proposition that the defendant in a lost-profits case bears the burden of proof on causation, or any factor bearing on causation. The Court recognized that a "wrongdoer may not object to the plaintiff's reasonable estimate of the cause of injury and of its amount, supported by the evidence, because [the estimate is] not based on more accurate data which the wrongdoer's misconduct has rendered unavailable." Bigelow, 327 U.S. at 265, 66 S.Ct. 574. That observation, however, goes to the degree of precision demanded of the plaintiff, not to the question whether the plaintiff bears the burden of proof.

Nycal relies on several other cases as well, none of which are helpful to it. Some are based on statutes that dictate a shift in the burden of proof in prescribed circumstances. See Walther v. Sec'y of Health & Human Servs., 485 F.3d 1146 (Fed.Cir. 2007) (under Vaccine Act, after petitioner has made prima facie showing of causation, government bears burden to show cause of injury other than vaccine); Edwards-Warren Tire Co. v. J.J. Blazer Constr. Co., 565 F.2d 401 (6th Cir.1977) (under Ohio statute, after proof that accepted goods did not conform to manufacturer's warranty, burden shifts to defendant to show product misuse or other cause). Others involve tort causes of action in which courts imposed on the defendant the burden of proving that the plaintiff's injury was the result of a superseding cause, i.e., an independent act by someone other than the defendant that has the legal effect of negating the defendant's liability. See BCS Servs., Inc. v. Heartwood 88, LLC, 637 F.3d 750, 757 (7th Cir.2011); Roberts v. Printup, 595 F.3d 1181, 1189-90 (10th Cir.2010); Gathercrest, Ltd. State Bank of Ind. v. First Am. Bank & Trust, 805 F.2d 995, 997 (11th Cir.1986).

Nycal also relies on cases standing for the proposition that if a plaintiff in a patent case succeeds in establishing a reasonable probability that sales made by the infringing defendant would have been made by the patentee (as, for example, in a two-supplier market), the burden then shifts to the defendant to show that, absent infringement, not all of the infringer's sales would have gone to the plaintiff. See Kaufman Co. v. Lantech, Inc., 926 F.2d 1136, 1141-42 (Fed.Cir.1991); see also Rite-Hite Corp. v. Kelley Co., 56 F.3d 1538, 1545 (Fed.Cir.1995) (en banc). That line of cases does not support Nycal's position. In patent lost-profits cases, the burden to prove causation is clearly on the plaintiff; it is only after the plaintiff has shown a reasonable probability that the infringer's sales were made at the expense of the patentee that the burden shifts to the defendant to show that the claimed damages are not as great as the plaintiff's initial showing might suggest.3

Finally, Nycal cites cases involving the contract defense of frustration of purpose, in which the burden of proof falls on the defendant to show that it is excused from performance because the purpose of the contract was no longer served by mutual performance. See, e.g., Seaboard Lumber Co. v. United States, 308 F.3d 1283, 1296 (Fed.Cir.2002). As explained above, however, causation is not a defense to a claim of lost profits, but is an element of the plaintiff's proof of damages. The defense of frustration of purpose is given a narrow construction because it defeats the explicit terms of the parties' agreement. Proof of the elements of lost profits, by contrast, is essential to ensuring that the plaintiff is compensated for the breach, but not overcompensated by receiving a recovery exceeding the benefits it would have obtained if the contract had been performed.

In sum, none of the cases cited by Nycal deal with the issue in this case, which is whether the plaintiff must bear the burden of proof as to causation in a lost-profits case.4 As to that issue, this court's decisions are uniform and clear: the burden of proof is imposed on the plaintiff, as the trial court correctly held in this case. We therefore reject Nycal's argument that the trial court misallocated the burden of proof on the issue of causation.

III

Nycal contends that even if it bore the burden of proof as to causation, it satisfied that burden.

A

First, Nycal takes issue with the trial court's finding that the District would not have granted the lease owners the necessary permits, because denying those permits would have effected a regulatory taking of the owners' property under the Fifth Amendment. In substance, Nycal's argument is that the lease owners' takings claim would have been so strong, and the threat of litigation a matter of such concern to the District, that the District would have found a way to allow the drilling and production process to go forward.

There are several flaws in this argument. To begin with, it was waived below, as the trial court noted. Nycal, 106 Fed. Cl. at 247 n. 40. There is only the barest hint of the "takings" argument in the record below, and that hint came too late in any event. The trial court correctly noted that the takings argument was not made in the complaint or at trial. Nycal, however, points to one sentence in its post-trial brief stating that a decision by the District not to issue a permit "would raise issues of regulatory taking that duplicate the lost profits calculation here at issue." But that sentence does not suggest Nycal's current argument: that the District would have capitulated to Nycal because of the force of Nycal's takings argument.5 The trial court therefore did not abuse its discretion in concluding that the "takings" argument was waived.

Waiver aside, Nycal introduced no evidence on the takings issue at trial. The trial court therefore had no basis from which to assess the strength of the takings claim. Nor did the court have any evidence from which to judge the likelihood that Samedan would have raised the takings issue with the District, or the likelihood that the District would have given in to Samedan if it had. Because the takings argument has no evidentiary support, it must be rejected.

B

Nycal next directly challenges four of the trial court's factual findings as "deeply flawed." We review the court's factual findings under the "clear error" standard.

First, Nycal disputes the trial court's finding that the emissions resulting from drilling an exploratory well would have exceeded the District's emissions cap. The court based that conclusion on its finding that the District would have aggregated all the emissions from the wells drilled by Samedan's mobile drilling rig, including wells on properties outside the leases at issue in this case. In making that finding, the trial court noted that the District had made a similar decision with respect to a previous offshore oil drilling project known as SWARS. Nycal contends that Samedan's project was very different from the SWARS project and that it cannot be inferred from the treatment of the SWARS project that the District would have handled Samedan's project in the same manner.

Nycal's argument runs up against trial testimony to the contrary. Two knowledgeable witnesses testified at trial that the District intended to treat the multiple wells as a single project, as had been done in the case of the SWARS project. That evidence is sufficient to support the trial court's finding on that issue.

Second, Nycal argues that the trial court was wrong to find that Samedan would not have been able to purchase credits to offset the emissions from its exploratory well and permanent platform. Nycal argues that it could have obtained those credits by making a payment to a "new technology fund" established by the District that provides grants to projects that reduce emissions. Nycal points out that the SWARS project was allowed to proceed after the operator of that project made a $750,000 payment to the fund.

Based on evidence at trial, the trial court found that there were not enough offset credits available to offset the emissions that Samedan's project would create. Nycal's witness conceded that the available offsets were "extremely limited," and the government's permitting expert testified that "offsets in Santa Barbara are very limited, or non-existent." Moreover, Nycal did not introduce evidence of any projects that could be funded through the new-technology fund and result in significant emissions offsets.6 The trial court's finding on the unavailability of offsets is therefore not clearly erroneous.

Third, Nycal argues that the court erroneously found that Samedan would not have been able to construct an onshore processing facility for the oil, gas, and water produced on the leased properties because the emissions from that facility would have been aggregated with Samedan's offshore activities. Nycal's answer is that it could have secured the necessary credits, whether by paying into the District's new-technology fund or otherwise. Again, however, the court's finding that the possibilities of obtaining credits by contributing to the new-technology fund were very limited or nonexistent is supported by evidence and must be sustained.

Fourth, Nycal contends that, even if the trial court was correct in finding that Samedan could not have constructed a new onshore facility, Samedan could have obtained access to Exxon's existing onshore processing facility at Las Flores Canyon. When Exxon was permitted to construct that facility, it was required to promise to provide "equitable access" to other companies. Nycal argues that Exxon's obligation would have required it to offer its excess capacity to Samedan.

Although the trial court found that Exxon had some obligation, which was not fully explored at trial, to allow the use of its existing facilities or the unused land at the Las Flores Canyon site for construction of a new facility, the court found that Exxon planned to use any excess capacity at its Las Flores processing facility for its own purposes, and that Exxon had denied two previous requests to use its facilities. Moreover, the court found that Exxon lacked the capacity to process the natural gas and water that would have been produced from the leased properties. Beyond that, although Exxon had agreed to provide "equitable access" to its facilities, the court did not find that Exxon's agreement required it to process oil, gas, and water from other producers regardless of its own needs. Those findings are not clearly erroneous and support the trial court's conclusion that Samedan would not have been able to use Exxon's facility for its processing needs.

C

In its final argument, Nycal addresses the alternative ground for decision by the trial court: that even if Samedan had obtained the required emissions permits by paying into the new-technology fund and been able to construct a processing facility, Nycal's claim would still fail because it was unknown how much such efforts would cost, and thus the amount of damages would be fatally uncertain. Nycal's response is, in essence, that if drilling had been permitted to proceed, the profits from the oil and gas produced from the leased properties would have been so great that any costs incurred in obtaining the requisite emission permits and constructing a processing facility would have been inconsequential. In making that argument, Nycal relies on this court's cases holding that imprecision in the calculation of lost profits is not fatal to a damages award.

The government responds that the uncertainties as to cost were not questions of "absolute exactness or mathematical precision," Bluebonnet Sav. Bank v. United States, 266 F.3d 1348, 1355 (Fed.Cir.2001), but were of sufficient magnitude that they left the court unable to calculate damages with any degree of certainty.

The trial court agreed with the government's characterization. The court observed that "[c]onjecture that, `we would have come up with a solution, although we don't know when, or what it would have cost' injects an intolerable level of uncertainty into calculating damages." Nycal, 106 Fed.Cl. at 247. The court added that, even "[a]ccepting on faith that, given enough money and time, the owners could have eventually obtained the necessary permits means we cannot rely on plaintiff's schedule of development, nor would we know how much it would have cost to build and operate the various facilities" or to create or obtain emissions credits. Id.

We acknowledge that there is force to the trial court's conclusion that the evidence is not sufficient to permit the court to make "a fair and reasonable approximation of the damages." Energy Capital Corp. v. United States, 302 F.3d 1314, 1329 (Fed.Cir.2002), quoting Locke v. United States, 151 Ct.Cl. 262, 283 F.2d 521, 524 (1960). However, in light of our disposition of the causation issue, it is unnecessary for us to reach the trial court's alternative ground of decision, and we decline to do so. Accordingly, we uphold the trial court's ruling that Nycal failed to meet its burden of proving causation and thus has not established its right to a lost-profits award.

AFFIRMED.