BARRON, Circuit Judge.

This case turns on the standards for showing that a class action has an amount in controversy of more than $5 million, which is the threshold for enabling a case to be removed to federal court under the Class Action Fairness Act of 2005 ("CAFA"). Because we conclude that the defendants did not meet their burden of showing that the amount in controversy in this class action exceeds that threshold — at least at this stage in the litigation — we agree with the plaintiffs that removal was improper. We thus do not reach the other issues that the District Court resolved in dismissing this suit, and we remand with instructions to the District Court to remand the case to state court for lack of jurisdiction.

I.

The defendants are business entities that organize physically challenging obstacle course events in various locations in the United States. The four named plaintiffs registered to participate in one of those events — the "Mudderella" event — scheduled to take place on September 6, 2014, in Haverhill, Massachusetts.

This suit began in Massachusetts Superior Court. The plaintiffs' complaint alleged that, on August 22, 2014, the defendants notified the plaintiffs that the event had been moved approximately twelve miles from Haverhill, to Amesbury, Massachusetts.1 The complaint also alleged that, on August 29, 2014, just a week before the event, the defendants again notified the plaintiffs that the event had been moved, this time to Westbrook, Maine, which is 79 miles from Haverhill. The complaint alleged that, as a result of that second — and final — change in location, the four named plaintiffs were unable to participate in the event, and that the defendants refused to refund the plaintiffs their registration fees.

The complaint asserts various claims under Massachusetts law. Those claims are breach of contract, breach of the covenant of good faith and fair dealing, unjust enrichment, and violation of the Massachusetts Consumer Protection Act, Mass. Gen. Laws ch. 93A.

Of particular significance to this appeal is what the complaint pleads with respect to relief. The complaint states that those seeking relief are, pursuant to Rule 23 of the Massachusetts Rules of Civil Procedure, not just the four named plaintiffs but also:

The complaint further states that the class seeks, in addition to damages "in amounts to be determined at trial," an unspecified amount in "reasonable" attorneys' fees and costs, restitution, disgorgement, rescission, a permanent injunction prohibiting defendants "from engaging in the conduct described herein," and "such other relief as the Court deems just."

The plaintiffs served the complaint on the defendants in November 2014. The defendants then timely removed the case to federal court. See 28 U.S.C. § 1446(b). The defendants asserted that removal was permitted under the Class Action Fairness Act of 2005 (CAFA), which provides for federal subject matter jurisdiction over class actions alleging state-law claims where certain conditions are met, including minimal diversity between parties and that "the matter in controversy exceeds the sum or value of $5,000,000." 28 U.S.C. § 1332(d)(2).

The plaintiffs moved to remand the case to state court. The plaintiffs' sole argument for remand was that the District Court lacked subject matter jurisdiction under CAFA because the defendants had failed to show that over $5 million was in controversy. The defendants responded with estimates of the amount in controversy that were based on the references in the plaintiffs' complaint to "registration fees" and "added expenses, including, but not limited to gas, food, and/or lodging."

The District Court denied the plaintiffs' motion to remand the case to state court. The District Court's explanation, in its entirety, was that the "[d]efendants hav[e] shown a reasonable probability that the amount in controversy in this case exceeds $5 million."

Alongside the dispute over jurisdiction, the defendants filed a motion to dismiss the case and compel mediation and, if mediation were to fail, arbitration of the plaintiffs' claims in accordance with the terms of the agreement that the plaintiffs entered into when they registered for the Mudderella event. The District Court granted that motion.

The plaintiffs then appealed. They argue that the District Court erred in concluding that the defendants met their burden of showing that over $5 million is in controversy in this matter and thus that federal subject matter jurisdiction exists under CAFA. The plaintiffs also contend that if CAFA jurisdiction exists, the District Court erred in dismissing the case and compelling mediation and arbitration of the dispute. Because we agree with the plaintiffs on the first point, we do not reach the second.

II.

We begin with the standard of review. We have distinguished between a district court's conclusion regarding the "ultimate question" whether it has subject matter jurisdiction under CAFA and the district court's resolution of specific factual disputes in the course of reaching that conclusion. See Amoche v. Guar. Trust Life Ins. Co., 556 F.3d 41, 48 (1st Cir.2009). The former determination, we have explained, is evaluated de novo, while the latter is reviewed for clear error. Id.

As we have noted, the District Court's order in this case was short: it held that the "[d]efendants hav[e] shown a reasonable probability that the amount in controversy in this case exceeds $5 million." Because the District Court simply resolved the ultimate question of the sum or value in controversy in this matter, our review is "entirely de novo." Id. at 47-48; see also Romulus v. CVS Pharmacy, Inc., 770 F.3d 67, 71, 81 (1st Cir.2014).

III.

CAFA was enacted with the stated purpose of expanding the number of class actions that could be heard in federal court. Amoche, 556 F.3d at 47, 49 (stating that, "[i]n CAFA, Congress expressly expanded federal jurisdiction largely for the benefit of defendants against a background of what it considered to be abusive class action practices in state courts," "which had `harmed class members with legitimate claims and defendants that had acted responsibly,' `adversely affected interstate commerce,' and `undermined public respect for our judicial system'" (alteration omitted) (quoting CAFA, Pub.L. No. 109-2, § 2(a), 119 Stat. 4, 4 (2005))). Congress effectuated that purpose "by imposing only a minimal diversity requirement, eliminating the statutory one-year time limit for removal, and providing for interlocutory appeal of a federal district court's remand order." Id. at 47-48 (citing 28 U.S.C. §§ 1332(d)(2), 1453(b), (c)).

But Congress did impose various limits on CAFA's reach. And among them is the one that is relevant in this case: that the amount in controversy exceed $5 million. See 28 U.S.C. § 1332(d)(2).

The defendants bear the burden of showing that this amount-in-controversy requirement has been met, as they seek removal under CAFA. See Amoche, 556 F.3d at 48-50 (justifying this burden in part by the "general rule of deference to the plaintiff's chosen forum"). To meet that burden, the defendants must show a "reasonable probability" that more than $5 million is in dispute in this case. Id. at 50. That standard is "for all practical purposes identical to" the preponderance of the evidence standard. Id. "Yet because questions of removal are typically decided at the pleadings stage where little or no evidence has yet been produced, the removing defendant's burden is better framed in terms of a `reasonable probability,' not a preponderance of the evidence." Id.

The decision as to whether the defendants have met their burden "may well require analysis of what both parties have shown." Id. at 51. Thus, it is not enough for the plaintiffs to "[m]erely label[] the defendant's showing as `speculative' without discrediting the facts upon which it rests." Id. But in evaluating what both parties have shown, we may consider "which party has better access to the relevant information." Id.

Applying those standards to the facts of this case, we conclude that a remand to state court is required. The defendants' argument that over $5 million is in controversy in this matter is based on what the defendants contend is a reasonable estimate of the registration fees in controversy and a reasonable estimate of the gas, food, and lodging expenses that the putative class incurred as a result of the event's change in location. The plaintiffs respond that the defendants' estimates are not reasonable, and that the amount in controversy is in fact lower than the defendants contend.

The parties' positions, at first blush, may seem out of character, in that the plaintiffs seek to downplay the amount of damages that they seek while the defendants attempt to show how large the potential damages really are. But this reversal in the usual role of plaintiffs and defendants in litigation is not at all unusual in a case in which defendants seek removal under CAFA. And here we conclude that the plaintiffs have the better of the argument as to whether removal is allowed.2

A.

We begin with the registration fees. The defendants contend that all the registration fees for the event are in controversy — the fees of those who did not attend the event as well as the fees of those who did attend. The defendants base their argument on the complaint's "prayer for relief," which states that the plaintiffs seek "damages in amounts to be determined at trial." The plaintiffs respond that they are not seeking registration fees on behalf of the attendees.

The complaint supports the plaintiffs' contention. The complaint mentions registration fees only in conjunction with "all persons who ... did not participate." We thus conclude that the plaintiffs' contention that they do not seek a refund of registration fees for the attendees is "not an impermissible effort to defeat federal jurisdiction by narrowing the pleadings post-removal, but rather a fleshing out of the vague language of the [complaint]." Id. at 52 (citation omitted).

Accordingly, the only registration fees in controversy are the fees paid by the people who did not attend the event. The defendants tell us that the registration fees for the people who did not attend the event total $617,574.86. The defendants argue that it is reasonable to treble this amount because the plaintiffs would be entitled to treble damages were they to succeed on their chapter 93A claim. And the defendants contend that it is also reasonable to add to this calculation a 33% attorney's fee award. Accepting those premises, the amount in controversy with respect to the registration fees would come to $2,464,123.69, which would get the defendants almost halfway to the amount CAFA requires.

B.

To show that roughly another $2.5 million is in controversy, the defendants point first to their estimate as to gas and food expenses. The defendants argue that it is reasonably probable that each of the 4,347 people who attended the event spent an additional $35 on gas and an additional $56 on food as a result of the event's change in location.

The defendants estimate the gas expense using the gas price in Massachusetts in September 2014 and the round-trip distance between the Haverhill and Westbrook event locations. The defendants estimate the food expense by using the federal government's per diem reimbursement rate for federal employee travel in the Westbrook, Maine area.

There is good reason to doubt whether, at least with respect to the food expense, it is reasonable to assume each attendee incurred that expense, as will become clear when we discuss the problem with the defendants' contention about lodging expenses. But taking the figures at face value for the moment, and after accounting for treble damages and attorney's fees, the additional amount in controversy attributable to gas and food expenses would be $1,578,352.23. If we then add that figure to the figure for registration fees, which totaled just shy of $2.5 million, the overall amount in controversy would be $4,042,475.92.

But even accepting the defendant's calculations to this point, the defendants would still need to show that it is reasonably probable that approximately $1 million more is in controversy in this matter. Thus, the defendants need the lodging expenses to be at least that high. But defendants come up short in making that case, as we next explain.3

C.

The defendants make two arguments regarding lodging expenses. Neither works.

First, the defendants contend that it is reasonable to assume that every person who signed up for the event incurred an additional lodging-related expense as a result of the change in location. The people who did not attend the event, the defendants argue, may have forfeited the cost of a hotel room in Haverhill or Amesbury, Massachusetts, when the event was moved. As for the people who did attend the event in Maine, the defendants contend that those people may have incurred the additional expense of a hotel room in Westbrook. The defendants explain that the additional expense would arise either because the attendees would not have required lodging in Massachusetts or because the attendees had already paid for a hotel room in Massachusetts, the entire price of which the attendees may have forfeited as a result of the change in the event's location.

The defendants further contend that because the federal per diem lodging reimbursement rate in Westbrook is $128 per night and $98 per night for Haverhill and Amesbury, the average of those two numbers — $113 — represents a reasonable estimate of the lodging expense attributable to the event's changed location for each person who registered. On that basis, the defendants contend that the lodging expenses that are in dispute amount to more than $1 million. They get that figure by multiplying $113 by the 11,307 people who registered for the event and by adding treble damages and attorney's fees. Using that estimate, and given the other expenses that the defendants contend are in dispute, the defendants would then have met their burden of showing that it is reasonably probable that more than $5 million is in controversy in this case.

Alternatively, the defendants argue that even if the only lodging expenses in controversy are the lodging expenses of those people who attended the event — as the complaint suggests is the case — those expenses, estimated at the Westbrook per diem of $128 per attendee, still exceed $1 million. The expenses are of that magnitude, the defendants explain, if one multiplies $128 by the 4,347 people who attended the event and then adds treble damages and attorney's fees.

These two arguments, however, suffer from the same flaw. The defendants' arguments rest on the assumption that each person who registered for the event lived far enough away from Haverhill, Amesbury, or Westbrook to require lodging at those locations. But the defendants have provided us with no information to support that premise.

In fact, defense counsel's representation at oral argument that the defendants "organiz[e] these highly challenging, physically rigorous obstacle course events all over the country" suggests that people could sign up for events relatively close to their homes. And, we note, the defendants conceded at oral argument that Massachusetts residents would not have required lodging for the event. That concession is at odds with the notion that all registrants needed lodging, as it is reasonably probable that the event attracted at least some registrants from Massachusetts, as that is the state in which the event was scheduled to take place.4

Nor do we find it reasonably probable that the registrants who did require lodging would have incurred additional lodging expenses (whether $113 or $128) in consequence of the defendants' having moved the event to Maine. It is by no means unusual for hotels to permit cancellation within a short time frame for no fee, and the defendants offer us no basis for concluding that such recourse would not have been available here. It is not apparent, therefore, that the people who did not attend the event in Maine and who had initially reserved a hotel room in Massachusetts (however many, if any, such persons there were) would have forfeited the entire cost of that room when they discovered, a week before the event, that the event had been relocated.

Moreover, on this record, only speculation could support a conclusion that all attendees (if any there were) who travelled far enough from home to require lodging for the Westbrook event would not also have required lodging for the race in Haverhill or Amesbury. Those two communities are only 79 and 71 miles, respectively, from Westbrook. Nor is it apparent that each of those attendees who had initially reserved lodging in Haverhill or Amesbury did then reserve lodging in Westbrook, given the proximity of Haverhill and Amesbury to Westbrook. And even if we could assume that each of the attendees who initially reserved lodging in Haverhill or Amesbury would have reserved lodging in Westbrook, we have no reason to assume that each would have forfeited the entire cost of the hotel room in Haverhill or Amesbury or that each would have incurred any other additional expense — such as a hotel cancellation fee — as a result of the change in hotel.5

In sum, the defendants' argument that all registrants incurred an additional lodging expense of $113 or, alternatively, that all attendees incurred an additional lodging expense of $128, fails. And that is because the defendants provide no support for the conclusion that the predicate assumptions underlying their estimate of lodging expenses are reasonably probable ones.

As a fallback, the defendants at oral argument offered a different way of justifying their calculation of lodging expenses. They contended that their approach accounts for the problematic assumptions that underlie their argument regarding those expenses. Specifically, they argue that the federal per diem lodging expense rates actually account for the fact that some people spend much more than those federal per diems on lodging and some people spend much less or, even, nothing at all because they do not travel at all. And so, by using that rate, the defendants say they are relying on an estimate that already accounts for the problematic uncertainties that we have just recounted.

But the defendants provide no support for that most unlikely description of what the federal per diem rate represents. The federal government has little interest in determining how much to reimburse an employee who incurs no expense. The federal per diem reimbursement rates for Haverhill or Amesbury ($98), and Westbrook ($128), thus would seem to reflect an estimate of the average expense of lodging in Haverhill, Amesbury, and Westbrook for an employee who actually books a room overnight there.

Thus, in order for those federal per diem rates to be reasonably probable estimates of the lodging expenses at issue in this case, it would have to be reasonably probable that each person who did not attend the event in Maine forfeited the cost of a hotel room in Haverhill or Amesbury, Massachusetts. It would also have to be reasonably probable that, in consequence of the change in location of the event, each attendee either booked a room in Westbrook and then forfeited the cost of a hotel room in Massachusetts or booked a room in Westbrook that the person would not have needed had the event been held in Massachusetts as originally planned. But, as we explained, those assumptions are not reasonably probable ones.

Nor will we venture to come up with our own estimate of a reasonably probable lodging expense incurred per registrant. The defendants have given us no guidance as to how to go about making such an estimate beyond their unconvincing argument that the federal per diem rate of $128 is such an estimate.

Similarly, we will not venture to guess that, even if we reject the defendants' chosen means of estimating lodging expenses, the total additional lodging expenses incurred by all registrants as a result of the change in location must nevertheless be something north of $1 million. To guess as much, we would need to find it reasonably probable that 1,875 people who attended the event — over 43% of all attendees — incurred additional lodging expenses at the $128 rate, or that 2,074 people who registered for the event — over 18% of all registrants — incurred additional lodging expenses at the $113 rate. Only then would the added value of those expenses, including treble damages and attorney's fees, increase the total amount in controversy to just over $5 million. But those are not small numbers of persons. And there simply is nothing before us that would support a conclusion that either of those numbers, given how big they are, is a reasonably probable estimate of the number of people who incurred additional lodging expenses.

D.

Part of the reason that we will not engage in such speculation, moreover, is that, as we noted at the outset, we may take into account "which party has better access to the relevant information." See Amoche, 556 F.3d at 51. And here that party is the defendants.

The defendants conceded at oral argument that they have access to the home addresses of everyone who registered for the event. With that information, the defendants could have come up with a reasonably accurate estimate of the number of people who might have had to travel far enough from home for the event so as to require lodging. But they did not do so. Nor have they attempted to support the assumptions that they ask us to accept with any historical data that they might possess, such as how far people generally travel to attend the defendants' events, or, for that matter, any other relevant knowledge that they possess in consequence of their having organized these events in the past.

Given that the defendants had potentially illuminating information and yet chose not to use it, and given that they have offered us no other information to support their assertion regarding lodging expenses, we conclude that we cannot accept the assumptions on which their estimate of lodging expenses depends. We thus conclude that, as in Amoche, the defendants have not met their burden to show that more than $5 million is in controversy in this case. Here, as in Amoche, the defendants rely on unsupported assumptions about the operation of their business and "failed to present" information "reasonably within [their] control" that might have provided "some insight" into the amount in controversy. Id. at 52-53.

E.

In attempting to counter this conclusion, the defendants refer us to our statement in Romulus that "[t]he defendant has no duty to investigate or to supply facts outside of those provided by the plaintiff." Romulus, 770 F.3d at 75. But that statement was made in the context of our consideration of a different issue from the one before us in this case.

We held in Romulus that CAFA's 30-day clock for filing a notice of removal is triggered when the plaintiff's complaint or the plaintiff's subsequent "paper" provides the defendant with sufficient information to easily determine that the matter is removable. Id. And so the language from Romulus on which the defendants rely was meant to clarify only that the defendant need not look outside such papers to determine whether the 30-day clock has been triggered. Id. Our conclusion on that score does not mean that where, as here, defendants timely remove to federal court on the ground that the plaintiffs' complaint shows that the amount in controversy requirement has been met, we cannot consider who has access to the information needed to determine whether the party seeking removal has met its burden to show that amount has been met. In fact, Amoche is clearly to the contrary on that point. See Amoche, 556 F.3d at 51.

IV.

The decision of the District Court is reversed, and this case is remanded to the District Court with instructions to remand the case to state court for lack of jurisdiction, without prejudice to removal at a later date.