482 F.3d 956
7th Cir.
2007
POSNER, Circuit Judge.

The defendant, a cardiologist who had billed Medicare some $17 million over a five-year period, pleaded guilty to health care fraud and tax fraud. He admitted having received “substantial payments” for fraudulent claims (estimated in the presen-tence investigation report to be between $5 and $10 million) submitted to health insurers and having defrauded the government of more than $550,000 in income tax. After a 13-day sentencing hearing, the district judge threw up his hands and imposed an absurdly light sentence of five years’ probation for both the health fraud and the tax fraud (the sentences to run concurrently) plus restitution of $1,258.

The government appeals, but the defendant cross-appeals, contending that the government fell so far short of obtaining the relief it sought (an 18-year sentence), and engaged in such “vexatious” conduct (mainly inducing the defendant to hire a good and therefore expensive lawyer by threatening the defendant with a heavy punishment!), that he rather than the government should be regarded as the prevailing party within the meaning of Pub.L. 105-119, Title VI, § 617, Nov. 26,1997, 111 Stat. 2519 (which appears as a statutory note to 18 U.S.C. § 3006A and which the cases refer to as the “Hyde Amendment”), and should therefore be awarded his attorneys’ fees.

The cross-appeal is frivolous. The Hyde Amendment authorizes the court in a criminal ease to award a reasonable attorney’s fee to “a prevailing party, other than the United States,” if the court finds that the government’s position was “vexatious, frivolous, or in bad faith.” So even if the government’s position is vexatious, etc., the defendant cannot be awarded fees unless he is the prevailing party. A defendant who is convicted and sentenced is not the prevailing party even if the sentence is light; the government is the prevailing party. For the general principle, see Farrar v. Hobby, 506 U.S. 103, 111-14, 113 S.Ct. 566, 121 L.Ed.2d 494 (1992) (“the prevailing party inquiry does not turn on the magnitude of the relief obtained,” id. at 114, 113 S.Ct. 566), and Buckhannon Board & Care Home, Inc. v. West Virginia Dept. of Health & Human Resources, 532 U.S. 598, 121 S.Ct. 1835, 149 L.Ed.2d 855 (2001), and for its application to the Hyde Amendment see United States v. Campbell, 291 F.3d 1169, 1171-72 (9th Cir.2002), and United States v. Beeks, 266 F.3d 880, 883 (8th Cir.2001) (per curiam).

So we turn to the appeal of the government, which argues that the district judge committed two fatal sentencing errors. He miscalculated the loss caused by the defendant’s fraud, underestimating it by at least a factor of a thousand, and he imposed a sentence that would have been unreasonable even if his calculation of the loss had been defensible.

The judge ruled that the only loss the government had proved was the face amount of two checks that the defendant admitted having received for medical services he hadn’t performed. Yet the defendant had admitted in his plea agreement that he had knowingly: created fraudulent records, billed insurers for tests and other medical procedures that were not performed, and received insurance payments for services to patients who had died before the services allegedly had been rendered, for services allegedly rendered when he was not in the United States, for services on a single day that he could not have performed in fewer than 25 hours, and for still other services that he had not performed. He did not admit in the plea agreement to a specific amount of loss that his frauds had inflicted on the insurers, but it is inconceivable that the amount was as slight as the district judge thought.

As the length of the sentencing hearing suggests, the government presented extensive evidence in an effort to estimate the amount of money that the defendant had obtained by fraud. A number of patients for whose treatment he had billed insurers testified that he hadn’t treated them at all or had treated them much less frequently than the bills claimed. He was shown to have billed for more than 24 hours of work a day on 401 days. On a day when Chicago was paralyzed by a snowstorm he billed for 28 home visits. Visas stamped on his passport confirmed his admission to having billed almost $50,000 for work supposedly performed on days when in fact he was out of the country. His own expert, after adjusting for innocent double billing (see next paragraph), determined that in order to have performed the services for which the defendant billed he would have had to treat an average of more than 18.38 patients a day, seven days a week, for 5.3 consecutive years — not a physical impossibility (though this depends on the breakdown between house calls and office visits), yet highly improbable for a cardiologist, especially since he admitted he worked only six days a week, which would have required him to treat more than 20 patients a day.

The government’s expert witness, who tried to add up the fraudulent payments that the defendant had received, did commit errors. In some instances he classified a bill as fraudulent simply because it was the second one the defendant had submitted for the same procedure, though he had submitted it only because the first bill hadn’t been paid. And with respect to a few of the dead patients, he may have treated the patient’s spouse and mistakenly transposed the names.

Because of the errors committed by the government’s expert, the judge found himself unable to calculate the exact amount of fraudulent payments that the defendant had received. The inability was genuine, but did not justify the judge’s loss calculation. Suppose the evidence presented at a sentencing hearing shows that the loss inflicted by the defendant’s crimes was no less than $1 million or more than $5 million but it is impossible to be more specific. Then for sentencing purposes the estimate of loss should not be zero, which is the implication of the district judge’s approach in this case; it should be, at the very least, $1 million. United States v. Radtke, 415 F.3d 826, 842-43 (8th Cir.2005); United States v. Chichy, 1 F.3d 1501, 1509-10 (6th Cir.1993). For then the defendant cannot complain that his sentence is based on a loss estimate that the government failed to prove. He wouldn’t even be heard to complain if as in the Radtke case the judge had split the difference between the bottom and the top of the range of possible loss; for when precision in calculating the loss inflicted by a crime is unattainable, a reasonable estimate is all that the law requires. United States v. Spano, 421 F.3d 599, 608 (7th Cir.2005); United States v. Freitag, 230 F.3d 1019, 1025 (7th Cir.2000). When guilt beyond a reasonable doubt is duly determined, picking a sentence within the statutory range to punish the defendant for his crime does not require as much precision as the initial determination that he in fact committed the crime.

In defending the judge’s estimate, the defendant’s counsel reminded us that several of the patients who testified were unsure just how many house calls the defendant had made on them. One of the patients, who testified on direct examination that the defendant hadn’t treated her in her apartment, acknowledged on cross-examination that he may have treated her once. But her insurer was billed for 12 visits; and the resulting uncertainty as to whether the defendant had billed for 11 or for 12 fictitious visits made it impossible to quantify his overbilling. But while such evidence could not support a point estimate of the loss inflicted by the defendant’s frauds, it could support a minimum estimate.

The defendant testified that his record-keeping was sloppy; and sloppy records could generate unintentional false billing. If he made three house calls on a patient but he or his secretary inadvertently put a “1” in front of the “3” on the record of the visit, the result would be a false bill but not a knowingly false one. But the extensive admissions that the defendant made in connection with his plea of guilty to the charge of fraud made his false claims prima facie evidence of the amount of loss that the fraud inflicted, and placed on him the burden of producing evidence on how many of the false claims were innocent. E.g., United States v. Grant, 431 F.3d 760, 765 (11th Cir.2005); United States v. Khorozian, 333 F.3d 498, 509 (3d Cir.2003). It was not enough for him to point to his sloppy record-keeping. United States v. Pesaturo, 476 F.3d 60, 73 (1st Cir.2007); United States v. Caldwell, 820 F.2d 1395, 1404-05 (5th Cir.1987). To accept such a showing would create a perverse incentive.

Although the evidence presented at the sentencing hearing would have supported a finding that the defendant had caused a total loss of at least $5 million, and although the judge’s finding that the proven loss was only $1,258 was not just clearly erroneous but incomprehensible except as a consequence of confusing a point with a range, the government is willing to concede that the judge could have found that the loss was as little as $1.4 million. But a finding of any smaller loss would be clearly erroneous, and so on remand $1.4 million must be the floor for the judge’s reconsideration of the amount of loss.

Even if we were to assume that the judge’s loss estimate, and therefore the amount of restitution that he ordered, had been correct and that he hadn’t further erred in ruling that one of the victims of the fraud was not a health insurer, which it clearly was, probation was too light a sentence. For on those assumptions the sentencing guidelines applicable when the defendant was sentenced would have specified a sentencing range of 24 to 30 months in prison. U.S.S.G. § 2F1.1 (2000). Had the judge assessed a $1.4 million loss and corrected his error about the health insurer as well, the range would have shot up to 78 to 97 months. See § 2Fl.l(b)(l). Under the current guidelines, the range would have been higher still—121 to 151 months, § 2Bl.l(a), (b) (2006)—and although if a case is remanded for resen-tencing the district court “shall apply the guidelines ... that were in effect on the date of the previous sentencing of the defendant prior to the appeal,” 18 U.S.C. § 3742(g); United States v. Andrews, 447 F.3d 806, 812 n. 2 (10th Cir.2006), current guidelines can be used to help guide a judge who is minded to sentence the defendant outside the applicable guidelines range. United States v. Johnson, 427 F.3d 423, 427 (7th Cir.2005).

The judge dipped far below even his erroneously calculated guidelines range to take account of what he considered to be the following mitigating factors: the defendant was “chronically inept as a businessman”; the prosecution had been protracted; the government had violated the doctrine of Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), by failing to turn over records of the defendant’s medical training; the defendant had spent a great deal of money on his legal defense; and the prosecution had stigmatized him and might cause him to lose his medical license (it has in fact been suspended). Only the last two of these factors (stigma and effect on professional opportunities) are admissible in determining a sentence, and perhaps only the last one.

A judge’s sentencing discretion is constrained by 18 U.S.C. § 3553(a), which lists the factors to be considered in deciding on a sentence. That a conviction for fraud imposes a “stigma cost” on a “respectable” professional person, such as a doctor, and may even lead to his expulsion from the profession, adds to the punishment inflicted by a prison term or fine. United States v. Dreske, 536 F.2d 188, 196 (7th Cir.1976); Jeffrey S. Parker & Raymond A. Atkins, “Did the Corporate Criminal Sentencing Guidelines Matter? Some Preliminary Empirical Observations,” 42 J. Law & Econ. 423, 426-27 (1999). And so it may justify a limited (but we stress “limited”'—see United States v. Repking, 467 F.3d 1091, 1096 (7th Cir.2006) (per curiam)) reduction in the term or the fine, because the consequences of a sentence for the defendant’s well-being are relevant to the deterrent, incapacitative, and retributive goals of sentencing, all recognized in section 3353(a).

But that a defendant spends heavily on lawyers is not a mitigating factor. It would not only encourage overspending; it would be double counting, since the pricier the lawyer that a defendant hires, the less likely he is to be convicted and given a long sentence. And as for governmental misconduct, nothing in section 3553(a) suggests that punishing the government is a proper goal of sentencing; two wrongs don’t make a right.

The Brady claim hovers on the border of cloud-cuckooland. The defendant’s lawyer himself describes the Brady materials as merely revealing that the defendant’s “cardiology professor had evaluated him as lacking even basic aptitudes in areas central to this case” and as being “generally incompetent in most phases of cardiology and cardiac catherization.” The defendant knew all that, so disclosure would have been redundant. United States v. Dawson, 425 F.3d 389, 393 (7th Cir.2005). And because Brady does not require disclosure of impeachment material before trial, United States v. Higgins, 75 F.3d 332, 335 (7th Cir.1996), a plea of guilty (remember that Sriram pleaded guilty) is not spoiled by a lack of access to materials that, if the defendant went to trial, would have to be revealed to him then. United States v. Ruiz, 536 U.S. 622, 629-30, 122 S.Ct. 2450, 153 L.Ed.2d 586 (2002).

In demoting the federal sentencing guidelines from mandatory to advisory status, the Booker decision did not authorize sentencing judges to pick any sentence within the applicable statutory sentencing range that strikes their fancy. Federal sentencing remains cabined by the duty first to determine the guidelines range and then to pick a sentence, whether inside or outside that range, that is consistent with the sentencing factors that 18 U.S.C. § 3553(a) lists as proper considerations in sentencing. E.g., United States v. Roberson, 474 F.3d 432, 435-36 (7th Cir.2007); United States v. Parker, 462 F.3d 273, 276 (3d Cir.2006). The district judge stumbled at both steps, as well as in finding that one of the victims of the defendant’s fraud was not a health insurer.

The judgment is reversed and the case remanded for resentencing. For guidance on remand we repeat that any loss estimate lower than $1.4 million would be clear error inviting summary reversal and that most of the mitigating factors that persuaded the district judge to sentence below the applicable guidelines range were irrelevant and must not influence the sentence that he imposes on remand. The defendant committed fraud on a large scale and should be punished accordingly.

REVERSED AND REMANDED.