
572 F.3d 878 (2009)
UNITED STATES of America, Plaintiff-Appellant,
v.
Mahendra Pratap GUPTA, Cardinal Care, Inc., Marshal Medical Services, Inc., Defendants-Appellees.
No. 08-12248.
United States Court of Appeals, Eleventh Circuit.
June 23, 2009.
*880 Leif M. Johnson, Billings, MT, Anne R. Schultz, Asst. U.S. Atty., Miami, FL, for U.S.
Neal R. Sonnett, Miami, FL, for Defendants-Appellees.
Before BARKETT and PRYOR, Circuit Judges, and EDENFIELD,[*] District Judge.
PRYOR, Circuit Judge:
This third appeal by the United States, see United States v. Gupta (Gupta II), 463 F.3d 1182, 1188 (11th Cir.2006); United States v. Gupta (Gupta I), 363 F.3d 1169, 1170 (11th Cir.2004), involves fundamental errors about the resentencing of Mahendra Gupta, who was convicted a decade ago of Medicare fraud involving millions of dollars, and an overarching issue about whether to reassign the case to a different district judge to conduct a fourth sentencing hearing. The United States argues that the district court erred in applying the Sentencing Guidelines, *881 abused its discretion when it declined to order restitution, and imposed an unreasonable sentence, and the United States, for the second time, see Gupta I, 363 F.3d at 1177, urges us to reassign the case to preserve the appearance of impartiality. Because we agree with the United States about the procedural errors in applying the Guidelines, the statutory mandate of restitution, and the need for reassignment, we need not evaluate the substantive reasonableness of Gupta's sentence. We vacate Gupta's sentence and remand for resentencing with an instruction that the case be reassigned to a different district judge.

I. BACKGROUND
In September 1997, a federal grand jury in the District of Montana indicted Gupta, three other persons, Allegheny Management Company, and ten home healthcare agencies on 16 counts stemming from Medicare fraud. Gupta I, 363 F.3d at 1170-71. The indictment charged that the defendants violated the related-party regulation, 42 C.F.R. § 413.17, which required home healthcare agencies to report services provided by related companies and provided that, subject to cost caps, Medicare would reimburse the agency for only the cost, not the profits, to the related company.
Gupta's fraud was complicated and extensive. By using "false claims, straw owners, and other deceptive actions to conceal the close relationship between the various persons[,]" Gupta I, 363 F.3d at 1170-71, Gupta positioned himself on both sides of consulting contracts between Allegheny and the home healthcare agencies, charged the agencies a higher price for the contracts and services he provided through Allegheny, and obtained reimbursement of that profit from Medicare. See Gupta II, 463 F.3d at 1188.
Edward Quinlan, one of the other individual defendants, was the putative owner of Allegheny, but Gupta created, funded, and profited from the management company. Id. Through Allegheny, "Gupta was able to charge Medicare between $50 and $150 per hour for the employees' services as opposed to approximately $17 per hour. In the first six months of Allegheny's business operations, it billed Gupta-owned health care agencies more than $1 million for consulting." Id. at 1188 n. 4. Between 1991 and 1997, the home healthcare agencies claimed reimbursement for Gupta's and Allegheny's consulting fees without disclosing the relationships between the parties. Id. at 1190. "From 1991 to 1997, Medicare reimbursed Corporate Defendants and [one of the dismissed corporate defendants] more than $15 million in Allegheny's fees." Id. Some of Gupta's straw owners were family members, including Gupta's father, Chandra Shekhar; his brother, Vijay Gupta; and his brother's in-laws, Dev Raj and Shanno Devi, who may have supported Gupta in exchange for immigration assistance. See id.
In July 1998, the case was transferred to the Southern District of Florida. Gupta I, 363 F.3d at 1171. The district court severed the trial of one individual defendant and the three home healthcare agencies he owned, and the government later dismissed the charges against those four defendants. Id. at 1171 & n. 3. The district court also dismissed all charges against two other home healthcare agencies.
Gupta, Quinlan, Kuldeep K. Hajela, Allegheny, and five home healthcare agencies proceeded to trial. The district court dismissed 13 counts of the indictment, which left only one count of conspiracy to defraud Medicare, 18 U.S.C. § 286, and two counts of mail fraud, id. §§ 1341, 1342, for trial. Gupta I, 363 F.3d at 1171. Before trial, the government submitted an expert *882 report prepared by federal auditor Gary Young, who opined that Allegheny received approximately six million dollars in profits over a six-year period from consulting fees paid by related agencies. Trial commenced in October 1999. At the close of the government's case, all nine defendants moved for a judgment of acquittal. The district court granted Hajela's motion and reserved ruling on the motions of the other defendants. Id.
On November 5, 1999, the jury acquitted Quinlan and convicted Gupta, Allegheny, and the five home healthcare agencies. Id. Gupta, Allegheny, and the home healthcare agencies requested an extension of "at least three weeks" to file post-verdict motions, and the district court granted their request. Id. On November 29, 1999, Allegheny again moved for a judgment of acquittal, and on December 3, 1999, Gupta and the home healthcare agencies moved for a judgment of acquittal or, in the alternative, for a new trial. Id. at 1172. On January 27, 2000, the district court denied all pending post-trial motions. Id.
The presentence investigation reports also were disclosed in late January 2000, but sentencing was continued several times. Id. Gupta's report assigned a base offense level of six, with an additional 14 levels because the loss, according to the Young report, was more than five million dollars but not more than ten million dollars, United States Sentencing Guidelines § 2F1.1(b)(1)(O) (Nov.1999), two levels because the offense involved more than minimal planning, id. § 2F1.1(b)(2)(A), and four levels because Gupta was "an organizer or leader in a criminal activity that involved five or more participants or was otherwise extensive[,]" id. § 3B1.1(a), for a total offense level of 26. The report stated that the guideline range was 63 to 78 months of imprisonment with two to three years of supervised release and that Gupta could afford to pay a fine and restitution. Because Allegheny and the home healthcare agencies had repaid Medicare 1.2 million dollars, the report deducted that amount from the loss to Medicare calculated by Young and stated that "[r]estitution is owed to Medicare in the amount of $4,987,173." Gupta was 54 years old when the report was disclosed and disclaimed any history of mental or emotional problems, although he complained of anxiety and nausea.
Gupta objected to the calculation of the loss that formed the basis for the 14-level enhancement and the enhancements for more than minimal planning and a leading role in a criminal activity that involved five or more participants or was otherwise extensive. Gupta submitted an expert report prepared by Stanley Foodman, a certified public accountant, to substantiate his objection to the loss amount. Foodman opined that Medicare was not owed restitution because it did not reimburse the home healthcare agencies for any Allegheny profits. Gupta also objected to the lack of a downward adjustment for acceptance of responsibility and argued that "a downward departure ... is warranted" because "a level 26 ... `severely over-represents' the seriousness of the offense[,]" "the loss calculations vastly overstate the seriousness of the offense, the offense in which [he] was convicted is no longer a crime[,]" and he offered "extraordinary service to others[.]"
On January 25, 2001, Gupta and the five home healthcare agencies asked the district court to reconsider its denial of their 1999 motions for judgment of acquittal or a new trial. The government responded that the motion was untimely. The district court did not rule on that motion until more than a year and a half later.
*883 On January 26, 2001, the district court held its first sentencing hearing. The district court stated that it would not allow the four-level enhancement for a leading role in a criminal activity that involved five or more participants or was otherwise extensive because "[the fraud] may have extended across the country but it was a very simple thing with regard to whether you check off the, whether it is a related company." The district court did not impose any sentence and took the motions for judgment of acquittal under advisement. The government submitted a sentencing memorandum and moved the court to appoint an independent auditing expert. The district court did not appoint the expert and continued sentencing again, until September 2002, and then again, until the next month.
On October 16, 2002, almost three years after the original post-verdict motions were filed, the district court entered judgments of acquittal for Gupta and the five home healthcare agencies. For reasons that remain unclear, the district court also entered a judgment of acquittal for Allegheny even though Allegheny had never asked the district court to reconsider the earlier denial of its motion. Gupta I, 363 F.3d at 1172. The government appealed and argued that the district court lacked jurisdiction to entertain the motions because they were untimely under Federal Rules of Civil Procedure 29 and 33. Id. The government also requested a reassignment to a different district judge. Id. at 1177.
In March 2004, we ruled that the district court lacked jurisdiction to consider the late motions, vacated the judgments of acquittal, reinstated the jury verdicts, and remanded the case for resentencing, but we declined to order a reassignment on remand. Id. at 1176-77. We rejected the argument of the government that "a supposedly too-light sentence ... would be `preordained'" and stated that "there is no reason to doubt [the] judgment or impartiality [of the district judge]." Id. at 1177. We concluded that reassignment would "require significant and unnecessary use of judicial resources." Id.
On remand, the government filed a second sentencing memorandum and expert reports about loss prepared by Jeff Litvak and Shirill Garvey. Gupta II, 463 F.3d at 1195-96. Litvak calculated the profits Allegheny received from the home healthcare agencies. He opined that the loss to Medicare was 3.4 million dollars. Id. at 1196.
On November 5, 2004, the district court held a second sentencing hearing. The district court sentenced Gupta to three years of probation on each conviction, to run concurrently, and fined him $10,000. Id. at 1186. The district court sentenced the five home healthcare agencies to three years of probation. The district court fined only two of the agencies, Marshal Medical and Cardinal Care, because the other three businesses were closed. Id. Gupta and the five agencies were excluded from Medicare programs for five years. Id.
The district court imposed these sentences reluctantly and restated its view that no wrongdoing had occurred. The district court expressed concern that the hospital that provided some of the same services the Gupta agencies had provided charged more for those services:
[A]ll you did was throw out a home provider that charged less for us and got somebody who charged more. And if the government isn't concerned about it, I don't think anybody's suffered any loss, certainly not the government because they don't mind paying more money than they were paying before.
The government argued that the measure of the loss was the profit for which Allegheny *884 was reimbursed by Medicare and offered testimony from Litvak to that effect, but "[t]he [district] court denied the government's request to include the Litvak loss report in the sentencing record[,]" id. at 1196, and again stated that there was no loss to the government. The district court also stated, "Well, I've been through this before. And I made a decision back then. And I said I'm not going to find any loss. And I'll stand by that .... [T]he 11th Circuit can sort it all out for us." The government urged the district court to impose a sentence that included some confinement to deter other potential fraudsters from using "false invoices and false letters" and "straw people" to take "very deceptive" actions that "hid[e] the relationship between these parties." The district court reiterated its view that "no crime has been committed" and stated that "it's amazing to me that somebody could be convicted of a felony based upon a bureaucratic regulation. Now I know you say, Well, he made a false statement and/or mail fraud or something."
Gupta and the home healthcare agencies appealed their convictions and the government cross-appealed the sentences. Id. The government challenged the sentences on three grounds: (1) the district court failed to consider and enhance Gupta's sentence on the basis of Gupta's leading role in the extensive fraud; (2) the district court failed to calculate loss; and (3) the sentences were substantively unreasonable. The government did not request restitution. Gupta responded that an enhancement for a leading role in extensive criminal activity was unwarranted because the fraud was not extensive; the district court correctly calculated a loss of zero; and the sentences were substantively reasonable because the cost of the consulting services was below the Medicare cost caps and the related-party regulation no longer exists.
We affirmed all of the convictions and some of the sentences, but we granted the request of the government to vacate and remand the sentences for Gupta and two home healthcare agencies, Marshal Medical and Cardinal Care. Id. at 1200; see also id. at 1195-1200. We ruled that the district court erred when it declined to apply a leading-role enhancement to Gupta's sentence on the ground that Gupta's scheme was not "otherwise extensive." Id. at 1199. We stated that, "[c]ontrary to Gupta's assertions, the criminal activity was quite complex and is not susceptible to simple categorization as the failure to check a box on a medicare form." Id. at 1198. We remanded for the district court to determine whether Gupta was the leader or organizer of the scheme.
We ruled that the finding of zero as the amount of loss was error for all defendants. Id. at 1200. We stated that the district court erred when it "found that the loss was determined as the amounts by which each of the [corporate defendants] exceeded the applicable Medicare reimbursement caps, which was equal to zero as such companies operated ... below the applicable caps." Id. at 1199. We rejected the reasoning of the district court that "the government did not mind paying up to such caps" because a "`no harm, no foul' argument ... [was] an insufficient rationale by which to calculate loss." Id. at 1199, 1200. We stated that "the amount the Government paid in response to the false claims is an appropriate measure of damages." Id. at 1200. We remanded for the district court to award damages.
On remand, the government argued that the district court should calculate loss by determining the amount of profit to Allegheny that the related-party regulation prohibited. The government argued that Litvak's estimation of loss was reasonable *885 and that the report prepared by Foodman was inaccurate because Foodman did not attend the trial, used figures from internal revenue audits that did not consider the fraud in the case, and included as expenses fraudulent transfers from Allegheny to other companies. The government also contested Foodman's conclusion that the government sustained no real loss because Allegheny was paid the market rate on the grounds that market rates are irrelevant in fraud cases and the assumption that Allegheny provided only legitimate services is unsound. The government urged the district court to impose a sentence within the guidelines range of 57 to 71 months of imprisonment because other potential fraudsters would not be deterred if Gupta received only probation for his complex scheme.
Gupta argued that we "misapprehended the basis for [the district court's] finding that there was no loss to Medicare in this case[,]" and that no loss occurred because "Allegheny made no profit on the work it did for Mr. Gupta's agencies." Gupta urged the district court not to adopt an "unfair ... focus on loss" and to "err on the side of caution." Gupta argued for a downward departure from the guidelines range on the grounds that "the loss calculations vastly overstate the seriousness of the offense[,]" "[he] did not personally profit from the violations[,]" and "[his] personal characteristics warrant a downward departure." Gupta also argued that a downward variance was warranted because "the violations in this case took place ... more than a decade ago"; "a new rule promulgated by [a federal agency] ... abolished the ... related party regulation"; letters provided "a glowing tribute to his extraordinary service to others"; he suffers from "bipolar mood disorder, alcohol dependency, depression, hypertension, hypothyroidism, gastritis, and other physical and emotional ailments"; a custodial sentence was not necessary to protect the public from businesses that had closed; and he, at almost 63 years of age, would be deterred without going to jail. Gupta urged the district court to impose a sentence of probation.
In March 2008, the district court held a third sentencing hearing. The district court stated that Gupta's base offense level was six with a two-level enhancement for more than minimal planning and a four-level enhancement for a leading role in an extensive offense. The district court stated that "[t]here's a lot of leeway going either way" between the Litvak and Foodman reports about loss and that "we have this range of 3.4 million down to zero between people who I assume all have good credentials and have made an analysis." The district court stated that it "detect[ed] advocacy on both sides."
The district court could not recall whether it had sentenced Allegheny and, upon being told that it had, suggested that it was confused about the moniker "defendant" for the purposes of the loss calculation. Although the district court was supposed to be sentencing Gupta, the parties were calculating loss by determining the gain or loss to Allegheny. The government explained, with no objection from Gupta's counsel, that we had upheld the finding of the jury that Gupta exercised control over Allegheny's profits, see Gupta II, 463 F.3d at 1190-93, and that Gupta, for example, once used those profits to pay a personal debt to a diamond merchant.
After Litvak testified, the district court expressed frustration and adopted a Solomonic approach of splitting the baby to fix the amount of loss:
You know, this isn't going to help me a whole lot. I've read these reports and figures until my eyes are going blind trying to understand all of this. I'm *886 sure there's advocates on both sides. The Court says that  and the guidelines don't say that  the Court has to make a reasonable estimate of the loss. I'm sure there was some loss. I think the government has overstated it. The defense has probably understated it. It's not a matter of restitution in this Court. I'm not going to award restitution. I'm going to let the Board decide those issues.
I'm just going to pick a figure, like any jury would, about half way in between. And I'll pick 1 million 5, and that will be the amount that is a reasonable estimate, I guess, that I make.
The district court used the 1998 Sentencing Guidelines to calculate an 11-level enhancement for the amount of loss, for a total offense level of 23.
The district court sua sponte asked defense counsel whether Gupta would accept responsibility: "The appellate court has now determined that this was a related company. Does he wish to accept responsibility at this time? He has no other place to go." Defense counsel replied, "I mean, in hindsight now, since there has been a determination by the jury and by the 11th Circuit ... that they were related parties, then I think it's fair to say he accepts responsibility for that."
The government stated that "an acceptance of responsibility here is absurd[,]" but the district court disagreed because it "thought [during earlier proceedings] that there might not be a crime." The district court reduced Gupta's offense level by two points, to 21. The government asked that Gupta personally articulate his acceptance of responsibility, but the district court declined the request. The district court stated that the guidelines range was 37 to 46 months of imprisonment.
The district court next considered Gupta's request for a downward departure. The district court stated that it must "determine what a fair and reasonable sentence would be" under the governing statute, 18 U.S.C. § 3553(a). The district court recalled that there had been "two refusals to prosecute this by other U.S. Attorneys, one in Chicago and one in Montana[,]" and "the regulation that was so obscure  I don't remember which one it was that was written by some bureaucrat. And they said it ought to be clarified. And the government said, Don't clarify. It gives us more flexibility that way." Defense counsel reiterated that the related-party regulation was withdrawn in 2001, the government recalled testimony from trial that Gupta knew that he was committing a crime, and the district court stated that it could consider the abolition of the related-party regulation as part of the "nature and circumstance of the offense" factor under section 3553. The district court stated that it "s[aw] that, this was not an act of greed" because Gupta "could have made these charges a lot more and still been within the cap. And the Government would have willfully paid it." The district court recalled testimony that Gupta had not controlled Allegheny and stated, "But the Court [of Appeals] said that he did control it. So we have to deal with that."
The district court reiterated its belief that Gupta's criminal activity had been overstated:
I would find that I think that the amount of money overstates the seriousness of this particular crime. I think you see what a mess we've had trying to even figure it out. And I even have accountants who are willing to come in and say that there was no loss. Obviously, the 11th Circuit is saying you can't find that there was no loss. There had to be some loss. So I've taken my best estimate, a reasonable estimate based upon the wide disparity of opinions. *887 And I still think that the amount of loss overstates the seriousness of the crime.
The district court stated that "[it] really d[id]n't see what can be accomplished with a man of this age, putting him in jail" and mentioned an appeal involving a child pornography conviction in which we rejected a sentence of probation because, in the words of the district court, "there are some real victims there."
The district court stated that "a reasonable downward departure would be to about a level 12" and first considered a sentence of probation with home confinement. Upon determining that incarceration is required for level-12 offenses, the district court next considered a sentence of imprisonment for ten months. Before the district court imposed sentence, defense counsel suggested that the district court depart an additional two levels downward, which would permit a sentence of probation with home confinement. The district court heard testimony from Dr. David Rooney, Gupta's psychiatrist, about how Gupta had been hospitalized, possibly for problems related to his alcohol dependency, and how "incarceration would have a negative affect on his well being with regards to his need for treatment ... of bipolar mood disorder." The district court "fe[lt] that due to the nature of this thing, that confinement would just be very hazardous to [Gupta's] health" and departed downward to a level ten.
The district court imposed a sentence of three years of probation, including 12 months of home confinement, and fined Gupta $25,000. The government requested restitution, but the district court stated that "[r]estitution is going to be decided by [the Provider Reimbursement Review Board]."
The government appealed. Although the government designated Gupta, Cardinal Care, and Marshal Medical as appellees, it says nothing in its brief about the sentences of the home healthcare agencies. The government has abandoned any argument about those sentences, and we need not review them. United States v. Lopez-Vanegas, 493 F.3d 1305, 1309 n. 6 (11th Cir.2007).

II. STANDARDS OF REVIEW
We review findings of fact for clear error and application of the sentencing guidelines de novo. United States v. Jackson, 276 F.3d 1231, 1233 (11th Cir. 2001). "A factual finding is clearly erroneous when although there is evidence to support it, the reviewing court on the entire evidence is left with the definite and firm conviction that a mistake has been committed." United States v. Robertson, 493 F.3d 1322, 1330 (11th Cir.2007) (internal quotation marks omitted). "Although review for clear error is deferential, a finding of fact must be supported by substantial evidence." Id. "When a defendant challenges one of the factual bases of his sentence ... the Government has the burden of establishing the disputed fact by a preponderance of the evidence. This burden must be satisfied with reliable and specific evidence." United States v. Sepulveda, 115 F.3d 882, 890 (11th Cir.1997) (internal quotation marks and citation omitted). We review a decision not to award restitution for abuse of discretion. United States v. Remillong, 55 F.3d 572, 574 (11th Cir.1995) (per curiam).

III. DISCUSSION
Our discussion of this appeal is divided in three parts. We first discuss the failure of the district court to calculate the guidelines range correctly; we next discuss restitution; and we then discuss reassignment of this case to a different district judge. *888 Because we conclude that a remand is necessary to correct procedural errors, we decline to evaluate the substantive reasonableness of Gupta's sentence. See United States v. Collins, 915 F.2d 618, 622 (11th Cir.1990). "We do not know what sentence the district court will impose on remand. Thus, we would be rendering an advisory opinion if we were to pick a sentence and declare it to be reasonable." Id.

A. The District Court Erred When It Calculated the Guidelines Range.
The district court committed two procedural errors when it calculated the guidelines range. First, it failed to calculate loss. Second, it erroneously reduced Gupta's offense level by two points for acceptance of responsibility. We discuss each error in turn.

1. The District Court Failed To Calculate Loss.
The "loss is the greater of actual loss or intended loss." U.S.S.G. § 2B1.1 cmt. 3(A); United States v. Manoocher Nosrati-Shamloo, 255 F.3d 1290, 1291 (11th Cir. 2001) (per curiam). "Actual loss" is the monetary harm that resulted from the offense and was reasonably foreseeable, U.S.S.G. § 2B1.1 cmt. 3(A)(I), (iii), and "intended loss" is the monetary harm "that was intended to result from the offense," id. cmt. 3(A)(ii), (iii).
"The court need only make a reasonable estimate of the loss[,]" id. cmt. 3(c) but "courts must not speculate concerning the existence of a fact which would permit a more severe sentence under the guidelines." Sepulveda, 115 F.3d at 890 (internal quotation marks omitted). "[A] district court must make factual findings sufficient to support the government's claim of the amount of fraud loss attributed to a defendant in a [presentence investigation report]." Gupta II, 463 F.3d at 1200. "We must decide whether the district court erred by finding ... that the loss attributable to [Gupta] could be reasonably estimated without impermissible speculation at [1.5 million dollars]." Sepulveda, 115 F.3d at 890-91.
The government argues that "[t]he district court's calculation of loss here was the very definition of speculation. The court merely picked a figure out of thin air... that was roughly between the parties' estimates of $0 and $3.4 million." The government identifies five issues about loss that the district court failed to resolve or even to discuss: (1) whether loss should be calculated using pretax or posttax income of Allegheny; (2) whether loss should be calculated by including in the income of Allegheny fraudulent expenses that had no benefit to the Medicare program; (3) what percentage of the income of Allegheny was derived from the defendant home healthcare agencies instead of three other home healthcare agencies owned by Gupta's brother, Vijay; (4) whether loss should be calculated by including in the income of Allegheny "bad debts" Allegheny owed to the home healthcare agencies; and (5) whether loss should be calculated by including in the income of Allegheny $400,000 that the Montana home healthcare agency paid in response to repayment demands from the government, or whether that money should be characterized as restitution.
Gupta states that "there is no dispute about the correct methodology of determining whether there was a loss to Medicare" and acknowledges that "any `loss' to Medicare could only be the amount of the profit made by Allegheny on the services provided to the defendant Home Healthcare Agencies." Gupta does not discuss the failures of the district court that the government mentions. Gupta again relies on the finding by Foodman that "Allegheny *889 had earned no profit from the Defendant home health agencies." Gupta attacks various assumptions of the Litvak report, argues that the government failed to provide reliable and specific evidence of the amount of loss, and argues that the district court "evaluat[ed] the strengths and weaknesses of both experts' theories on loss."
The government replies that "splitting the difference between a credible loss estimate and an incredible loss estimate is not reasonable." The government also replies that meaningful appellate review requires the appellate court to be able to reconstruct the reasoning of the district court, which is impossible when the district court simply "picks" a number between the parties' estimates. We agree with the government.
The district court failed to calculate loss, and the district court failed to make factual findings about several key issues. Although the district court considered both Foodman's and Litvak's expert reports, the district court failed to resolve any of the five issues the government raised about how to calculate the loss. Litvak testified that Foodman had erroneously relied on figures from a federal tax audit of Allegheny that would have been different if the Internal Revenue Service had known that Allegheny was related to the home healthcare agencies, and the district court also failed to resolve this issue. "[T]he district court clearly erred when it did not make specific factual findings upon which to base the loss amount[]." United States v. Medina, 485 F.3d 1291, 1304-05 (11th Cir.2007).
The error of the district court is not limited to its failure to make findings about these key issues. The cursory statements of the district court suggest that the district court made no findings about anything at all. The district court stated that it just "pick[ed] a figure, like any jury would, about half way in between."
The district court employed an arbitrary approach. It did not make a calculation. The district court described the loss amount of 1.5 million dollars as "the amount that is a reasonable estimate, I guess, that I make." There is no basis for the amount of 1.5 million dollars other than that it is "about half way in between" the parties' estimates. Even this basis cannot fully explain the amount: 1.5 million dollars is more than 10 percent below the halfway mark between the parties' estimates.
The arbitrary decision by the district court makes a difference. The decision spared Gupta one point on his offense level: a finding of $1,500,001 in loss would have required an additional point. The decision also precluded an accurate determination of restitution, which depends on the amount of pecuniary loss. See 18 U.S.C. § 3663A(b)(1)(B) (providing that the amount of restitution depends on the amount of the loss).
Because the district court identified no basis for the loss amount it found, meaningful appellate review of the amount is impossible. "Without further information from the district court, we cannot determine what factual basis was used to reach the conclusion ...." Medina, 485 F.3d at 1304. A remand is necessary.

2. The District Court Erred When It Reduced Gupta's Offense Level for Acceptance of Responsibility.
The Sentencing Guidelines provide a reduction in a defendant's offense level by two points "[i]f the defendant clearly demonstrates acceptance of responsibility for his offense." U.S.S.G. § 3E1.1(a). The reduction "is not intended to apply to a defendant who puts the *890 government to its burden of proof at trial by denying the essential factual elements of guilt, is convicted, and only then admits guilt and expresses remorse." Id. § 3E1.1, cmt. n.2. When a defendant exercises his constitutional right to a trial without denying essential factual elements of his guilt, the reduction may apply. Id. Application of the reduction "will not be overturned unless it is without foundation[,]" United States v. Castillo-Valencia, 917 F.2d 494, 500 (11th Cir.1990), but "[Gupta] bears the burden of clearly demonstrating acceptance of responsibility." United States v. Sawyer, 180 F.3d 1319, 1323 (11th Cir.1999).
The government argues that the reduction is "egregious ... because Gupta never requested the reduction, and the Probation Office did not recommend it." The government argues that "there is no record of what responsibility Gupta accepted" and Gupta "contested every aspect of the prosecution[,]" including two essential factual elements of guilt: intent and control.
Gupta argues that he raised the issue of the reduction in his objections to the presentence investigation report, and that "[he] through counsel accepted responsibility for his crimes" at sentencing. Gupta argues that the reduction applies because he attempted "to resolve the Allegheny management fees on the basis of actual costs" during administrative proceedings before the Provider Reimbursement Review Board, his criminal conduct ended over a decade ago, and he stopped participating in any Medicare businesses. Gupta also argues that any error is harmless because the district court could have imposed a less severe sentence even if the reduction does not apply.
The district court clearly erred when it reduced Gupta's sentence for acceptance of responsibility. Gupta put the government to its burden at trial, contested two essential elements of his guilt, moved to vacate his conviction, and then appealed the reinstatement of the jury verdict. Gupta could not have made clearer that he thought he was innocent.
Nothing in the record supports an adjustment for acceptance of responsibility. Gupta allegedly "accepted responsibility" when the district court prompted him by stating that "[h]e ha[d] no other place to go," but Gupta's "acceptance" was explicitly based on the conclusions of our Court. Gupta's counsel stated, "I mean, in hindsight now, since there has been a determination by the jury and by the 11th Circuit... that they were related parties, then I think it's fair to say he accepts responsibility for that." That statement does not even make clear for what Gupta "accepted responsibility" or that he is remorseful.

B. The District Court Abused Its Discretion When It Declined To Order Restitution.
Although the presentence investigation report recommended it, restitution was not an issue in previous appeals because the district court found zero loss. The government has raised the issue now that the district court has found some loss but declined to order restitution on the ground that the issue would be decided by the Provider Reimbursement Review Board. The government argues that restitution is required by the Mandatory Victims Restitution Act of 1996, 18 U.S.C. § 3663A, and is not before the Provider Reimbursement Review Board. Gupta argues that restitution is within the discretion of the district court and that the Provider Reimbursement Review Board is in a better position than the district court to order restitution.
The district court must order restitution. Gupta's conduct is covered by the Mandatory Act, which requires district *891 courts to order restitution without regard for a defendant's ability to pay when an identifiable victim suffers a pecuniary loss. Id. Although the Mandatory Act ordinarily does not apply to offenses that occurred before it became effective on April 24, 1996, United States v. Siegel, 153 F.3d 1256, 1258-60 (11th Cir.1998), the Act applies to conspiratorial offenses that began before that date but concluded after it. United States v. Futrell, 209 F.3d 1286, 1290 (11th Cir.2000) (per curiam) ("The ongoing nature of the conspiracy enables application of the new statute without violating the Ex Post Facto Clause.").
The conspiracy in which Gupta was convicted of participating began before April 24, 1996, and continued beyond that date. Three counts of the indictment charged conduct that continued after April 24, 1996. The first count, the Medicare fraud count, charged conspiracy to submit false claims, 18 U.S.C. § 286, between May 1991 and September 22, 1997. The second and third counts charged mail fraud, id. §§ 2, 1341, between September 1991 and September 22, 1997. The government also proved that specific instances of conspiratorial conduct occurred after April 1996. The government proved that Gupta paid a straw owner in July 1996 after selling one of the dismissed corporate defendants to a hospital at a profit. On remand, the district court must determine how much is owed and order Gupta to pay restitution.

C. The Case Must Be Reassigned to Another District Judge.
"We have the authority to order reassignment of a criminal case to another district judge as part of our supervisory authority over the district courts in this Circuit." United States v. Torkington, 874 F.2d 1441, 1446 (11th Cir.1989) (per curiam). Reassignment is an extraordinary order, and we "do not order [it] lightly." Id. at 1447. "[W]here there is no indication of actual bias[,]" we consider at least three factors to determine whether to reassign a case: "(1) whether the original judge would have difficulty putting his previous views and findings aside; (2) whether assignment is appropriate to preserve the appearance of justice; (3) whether reassignment would entail waste and duplication out of proportion to gains realized from reassignment." Id. Reassignment is necessary when a district judge adheres to erroneous views after multiple remands, see United States v. Martin, 455 F.3d 1227, 1242 (11th Cir.2006) (ordering reassignment after second appeal, when district court changed sentence from probation to seven days of imprisonment), or when a judge "question[s] the wisdom of the substantive law he ha[s] to apply and challenge[s] the government's decision to prosecute [the defendant,]" Torkington, 874 F.2d at 1447 (ordering reassignment after second appeal, when district court "dismissed the case at the first opportunity by construing a motion for mistrial as a motion for entry of judgment of acquittal[,]" stated that the prosecution was "silly," and "demonstrated great difficulty in putting aside his prior conclusions about the merits of this prosecution").
The government argues that "[t]he greatest casualty in this proceeding is the appearance of a lack of impartiality"; the straightforward errors in calculating the guidelines range demonstrate that the district court "is willing to commit obvious error in order to avoid sentencing Gupta to a term of incarceration"; and reassignment would produce little duplication because "the district court has done little or nothing of record on the issue of loss," and, in any event, "retains only snippets of [the] long-ago proceeding [of the trial]." Gupta argues that the district court followed our mandate and there is no evidence that the district court is biased. *892 Gupta also argues that sentencing on remand would not be predetermined because "the transcript of sentencing and the record clearly reflect that [the district court] carefully reviewed the extensive written submissions, heard argument and testimony, and took into consideration the presentence report."
Although "[w]e do not question the district judge's actual ability, integrity and impartiality[,]" we order this case reassigned because "the trial judge has demonstrated great difficulty in putting aside his prior conclusions about the merits of this prosecution." Id. At the third sentencing hearing, the district court adhered to its erroneous belief that Gupta's behavior was not criminal, emphasized that other federal prosecutors had declined to prosecute Gupta, disparaged the merits of his prosecution, and committed two basic procedural errors in the most recent proceedings. The error of reducing Gupta's sentence for acceptance of responsibility was obvious and gratuitous, and we had warned the district court about failing to make a calculation of actual or intended loss. We stated in Gupta II that "the district court's finding of no loss is not a reasonable estimate. The district court did not apply relevant calculation as to the greater of intended or actual loss. The court's belief that no crime was committed does not nullify its duty to calculate the Guidelines loss amount." 463 F.3d at 1200. Despite that mandate, the district court failed to make any calculations at all on remand. Although the district court acknowledged its obligation to follow our mandate, the district court failed to fulfill that obligation. We see no basis for a belief that the district court will employ a different approach if given another chance.
Reassignment will not produce excessive duplication. Although the district court has considered the parties' expert reports about loss, the district court has not made any findings about key issues in those reports. A new judge would need to become familiar with the history of this appeal, but our published opinions in Gupta I and Gupta II provide much of the essential information.
We are especially persuaded that reassignment is necessary because of the protracted history of this action. The situation is qualitatively different now than it was in Gupta I or Gupta II. The refusal of the district court to set aside its feelings is more pronounced after a third appeal and a second request for reassignment, and we see no basis for a belief that the district court will adjust its view if given another chance. The district court has suggested that "[its] eyes are going blind trying to understand all of this" and that it is not capable of addressing the issues about loss that remain disputed.
Reassignment is necessary to preserve the appearance of justice. "We do not question the district judge's actual ability, integrity, and impartiality. Rather, we respond to the appearance of a lack of neutrality and act to preserve in the public mind the image of absolute impartiality and fairness of the judiciary. We do not order this case reassigned lightly." Torkington, 874 F.2d at 1447.

IV. CONCLUSION
We VACATE the order of the district court and REMAND for resentencing. We remand with the instruction to the Chief Judge of the Southern District of Florida that the case be REASSIGNED to a different district judge.
BARKETT, Circuit Judge, concurring in part and dissenting in part:
I agree that we must remand for a determination of actual loss and to consider *893 the issue of restitution which is dependent on the actual loss that occurred. However, I would not order the reassignment of this case to another judge. Having clearly explicated our reasoning in this complicated case, I believe the district judge can fairly make the determinations deemed necessary by this opinion. If it is going to be reassigned, it should be at the request of the judge presently presiding over this case.
NOTES
[*]  Honorable B. Avant Edenfield, United States District Judge for the Southern District of Georgia, sitting by designation.
