POSNER, Circuit Judge.

A jury convicted Wynell Gray of Medicaid fraud, 18 U.S.C. § 1347, and conspiracy to defraud the U.S. government, id., § 371, and the judge sentenced her to 33 months in prison and ordered her to pay restitution of $846,115 to Indiana Medicaid. Her appeal presents a variety of issues, with emphasis on the government's alleged violation of the Brady rule, which requires prosecutors in some circumstances to provide exculpatory evidence in their actual or constructive possession to the defendant.

Randy Suddoth, a high school dropout and convicted felon charged with the fraud along with Gray, pleaded guilty, was sentenced to 24 months in prison, and testified for the government at Gray's trial. A doorman at the Drake Hotel in Chicago, Suddoth had decided in 2001 to start a company that he called "Dovies Medicar" to transport patients to hospitals and doctor's offices. He enlisted the aid of his friend Gray, the only college graduate he knew (she has a bachelor's degree in psychology and a master's degree in social work). He bought two vans and leased office space in Indiana, and while he and a cousin drove the vans Gray—Suddoth's second in command—ran the office.

Most of Dovies' clients were covered by Medicaid, and the fees for the services that Dovies provided to them were billed directly to Indiana Medicaid, the state agency that administers the federal-state Medicaid program in Indiana. According to the government's evidence, Gray both set up the billing system for the Medicaid services that the company rendered and did the billing, which was electronic. After her husband became ill in the summer of 2002, she worked mainly from home, mainly on Medicaid billing. Billing for services to other clients, particularly clients not on Medicaid, was handled in Dovies' office by another employee.

The company struggled until, according to Suddoth's testimony, Gray hit on the idea of billing Indiana Medicaid in accordance with the Medicaid billing codes for ambulance services—even though Dovies had no ambulances—because the billing rates for those services are much higher than the rates for van services. Dovies' revenues soared as a result of the change in billing. Gray testified that the change was Suddoth's idea, not hers, and that she didn't know that Dovies had no ambulances.

The company's revenues soon rose tenfold; by the end of the first quarter of 2004 Indiana Medicaid had reimbursed Dovies more than $550,000 for nonexistent ambulance services. But then EDS, a private company that Indiana Medicaid has hired to process and pay Medicaid claims, altered its electronic billing program so that firms like Dovies that were not certified to provide ambulance services could not bill for them electronically. Dovies adapted by filing Medicaid claims for nonexistent trips in its vans—one claim was for transporting a child more than 90 times when the actual number was in all probability three.

Dovies' surging revenues from Medicaid were deposited in a bank account to which both Suddoth and Gray had access. Gray withdrew hundreds of thousands of dollars that she used to buy a Subway franchise and a Curves franchise (Curves is a fitness chain). She worked mainly at the franchise outlets (whether because her husband was better or the financial opportunities provided by the franchises were irresistible), but continued billing Medicaid from her home after hours for services supposedly rendered by Dovies. She testified that the franchises weren't really hers, that she was fronting for Suddoth, who couldn't be listed as the owner because he was a felon.

Eventually Indiana Medicaid tumbled to the fraud, and Dovies closed its doors in May 2005. Suddoth then created a new medical transportation company, also fraudulent, with Gray again doing the billing, but it was soon shut down.

Gray testified that she had been ignorant of the fraud, that Suddoth had given her the billing codes and the phony bills and she had never known that she was billing for nonexistent services, whether ambulance services or van services. She testified that she never submitted a bill for which she hadn't been given a seemingly authentic trip ticket signed by a driver employed by Dovies; therefore any false billing must have been done by some other employee of Dovies.

Before the trial began, Gray's lawyer asked the government for Dovies' Medicaid billing records, so that she could determine the date, amount, and patient identification on each bill and the nature and date of the service billed for. The government obtained the information from EDS and gave a copy to Gray's lawyer.

At trial a dispute arose over how long it took to bill Medicaid for a transportation service (whether ambulance or van). The question was relevant because there were many thousands of billings, yet according to her testimony Gray was doing most of her billing at home, at night, devoting no more than eight to ten hours a week to the task. How long it took to bill for each service rendered (or pretended to be rendered) would affect Gray's claim that not she but other employees had done the billing for the nonexistent services. She testified that it took her about three minutes to bill for each service and at that rate she could not have billed for all the phony services in eight to ten hours a week. An expert witness for the defense who had studied the EDS data handed over by the government concurred in Gray's estimate, but the prosecutor contended that it took Gray only 40 seconds to bill for a service.

The government had not studied the EDS data, which in the form supplied by EDS was intelligible only to a software technician, and was surprised when the defense expert, having extracted from the data not only the number of bills but also the dates, found that at three minutes a bill it would have taken one person 71 hours to do all the billing that EDS's data showed Dovies had submitted to Medicaid on July 15, 2004. That would be feasible on Pluto, which has a 153-hour day, but not on our fast-spinning planet. So the government asked EDS whether it could determine not only the day on which, but also the time at which, each bill had been sent, so that the government could get a better sense of how long it takes to bill for Medicaid transportation services.

To extract these "timestamp" data EDS had to write a program and run its billing data through it. Because the trial was moving toward its close, EDS was able to obtain time information for only that one day, July 15, 2004, the day of the heaviest billing. Sure enough, it showed impossibly close billing times: the first two pages of the 17-page printout showed two bills separated by one second, two bills separated by two seconds, and two bills submitted the same second. Obviously there had been more than one biller that day. The additional biller (or billers) has not been identified.

Although the table of billing times had only three columns (billing number, date—all July 15, 2004, of course—and time), and was turned over to the defendant's lawyer within a few hours after the prosecutors received it from EDS, she did not use it at the trial. She used only her expert witness's testimony that even if every bill took only 40 seconds to submit, it would have taken Gray nearly 16 hours of continuous labor to submit all 1414 bills that Dovies submitted to Medicaid on July 15, 2004: 1414 × 40 ÷ 3600 [the number of seconds in an hour] = 15.71 hours (although the actual interval between the first billing on the printout and the last was actually 17 hours). So there must have been another biller, probably more than one, besides Gray.

The timestamp data, although they were not in the EDS file that the government had received initially and turned over to Gray's lawyer, could have been extracted from EDS's database, as was later done. Gray argues that the prosecution's failure to extract the data and turn them over to the defense in advance of trial violated the Brady rule and entitles Gray to a new trial.

If a prosecutor possesses exculpatory evidence that had it been disclosed to the defense might have induced a reasonable jury to acquit, failure to provide it to the defense would be a reversible error. Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963); see also Strickler v. Greene, 527 U.S. 263, 280-82, 289-90, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999); Kyles v. Whitley, 514 U.S. 419, 437-40, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995); Gantt v. Roe, 389 F.3d 908, 912-13 (9th Cir.2004). The rule has been expanded to take in investigators and other members of the "prosecutorial team" broadly understood. Kyles v. Whitley, supra, 514 U.S. at 437-38, 115 S.Ct. 1555; United States v. Wilson, 237 F.3d 827, 832 (7th Cir.2001); United States v. Hall, 434 F.3d 42, 55 (1st Cir.2006); United States v. Wood, 57 F.3d 733, 737 (9th Cir.1995). Otherwise investigators assisting in a prosecution could conceal from the prosecutors exculpatory evidence that the investigation had revealed and then the evidence would never be revealed to the defense. But EDS was not a part of the prosecutorial team. It had been hired as we said to process and pay bills submitted to Indiana Medicaid. It was not a private detective agency hired by the state agency to assist state and federal prosecutors in prosecuting Medicaid fraud. Medicaid fraud investigators were part of the prosecutorial team, but EDS was not. Because it does the billing for Indiana Medicaid, the company has records that can be useful as evidence in fraud prosecutions. But the defense had the same access to those records as the prosecutors did, and so there was no suppression of evidence. E.g., United States v. Earnest, 129 F.3d 906, 910 (7th Cir.1997); United States v. Morris, 80 F.3d 1151, 1170 (7th Cir.1996).

That's why Gray is reduced to arguing that in advance of trial the government should have directed EDS to create and run programs to extract data from its database that would be useful to the defense. That argument is a non-starter. E.g., id. at 1168-70. "We find the proposed extension of Brady difficult even to understand. It implies that the state has a duty not merely to disclose but also to create truthful exculpatory evidence." Gauger v. Hendle, 349 F.3d 354, 360 (7th Cir.2003), overruled on other grounds by Wallace v. City of Chicago, 440 F.3d 421 (7th Cir.2006). "The failure to create exculpatory evidence does not constitute a Brady violation." United States v. Alverio-Melendez, 640 F.3d 412, 424 (1st Cir. 2011); see also United States v. Monroe, 943 F.2d 1007, 1011-12 n. 2 (9th Cir.1991). As it happened, the government for its own purposes ran such a program during the trial and having done so, as we know, promptly turned over the results to the defendant because they were potentially exculpatory. It had no duty to go further and conduct the defense's investigation for it.

It may be helpful to distinguish between patent and latent exculpatory evidence. Patent exculpatory evidence is evidence that is exculpatory on its face; an example would be a confession by Suddoth, in the possession of the FBI, in which he took full responsibility for the fraud and described Gray as an innocent whom he had gulled. Such evidence is Brady material. Latent exculpatory evidence is evidence that requires processing or supplementation to be recognized as exculpatory. It is illustrated by the timestamp data in this case, the exculpatory character of which was unknown and unknowable until EDS wrote and ran the program that extracted the data from its database.

To charge prosecutors with knowledge of exculpatory evidence buried in the computer databases of institutions that collect and store vast amounts of digitized data would be an unreasonable extension of the Brady rule. The courts, rightly in our view, have refused to make it. The government is not "obliged to sift fastidiously" through millions of pages (whether paper or electronic). United States v. Warshak, 631 F.3d 266, 297 (6th Cir.2010). It is "under no duty to direct a defendant to exculpatory evidence [of which it is unaware] within a larger mass of disclosed evidence." United States v. Skilling, 554 F.3d 529, 576 (5th Cir.2009), vacated in part on other grounds, ___ U.S. ___, 130 S.Ct. 2896, 177 L.Ed.2d 619 (2010); cf. United States v. Joseph, 996 F.2d 36, 37, 39-41 (3d Cir.1993).

The Brady rule is not a rule of pretrial discovery (Fed.R.Crim.P. 16 is, but is not contended to be relevant to this case); under the Brady rule (an interpretation not of procedural rules, but of the due process clause) "disclosure even in mid-trial suffices if time remains for the defendant to make effective use of the exculpatory material." United States v. Higgins, 75 F.3d 332, 335 (7th Cir.1996); see also United States v. Allain, 671 F.2d 248, 255 (7th Cir.1982). In any event the government cannot make disclosure until the exculpatory evidence comes into its possession (actual or constructive—constructive if the actual possession is by a police investigator or other member of the prosecutorial team); that didn't happen here until mid-trial; nor was the delay deliberate or otherwise in bad faith. And as soon as the government received the evidence it turned it over to the defense—which had time to use it but did not do so.

Even if the timestamp evidence were Brady material that the prosecution had concealed from the defense, that concealment would not be a reversible error because the evidence would not have changed the outcome of the trial, assuming the jury was reasonable. (No one can gauge with confidence the effect of evidence on an unreasonable jury.) Remember that the defense lawyer had the timestamp evidence for July 15, 2004, the day of the heaviest billing. She could have waved it in front of the jury; she did not so much as mention it. She could have asked for a continuance to enable EDS to generate timestamp evidence for other heavy billing days, or if need be for all billing days. She didn't do that either. Maybe she dropped the ball, or maybe she was content to point out to the jury that even without timestamp evidence it was obvious from the number of bills submitted on July 15, 2004, that there had been more than one biller that day; and there were other heavy billing days as well. All this evidence the defense had before the trial began and used at the trial, and the timestamp evidence would have added little. United States v. Dawson, 425 F.3d 389, 393 (7th Cir.2005). The fact that Gray had accomplices (whether witting or unwitting) who helped her file phony bills would not exonerate her.

The defense points to the following passage in the prosecutor's closing argument to the jury: "when you want something as badly as [Gray] wanted it, you will do anything to get it, including staying up for hours on end to bill nonstop. . . . And it isn't three minutes to bill an item. . . . Even defendant's own expert admitted that you get much better at it as you go along. . . . You don't have to wait 3 minutes to call them up. She can go back to what she billed a week ago, a day ago, a month ago, a year ago and pull it up and save herself the time and do it in the 40 seconds. Forty seconds a claim. And there's only one, one day like that. One day with 1400 services provided for 14 people. Fourteen people. Because the defendant really needed that money, really wanted that money."

Gray argues that the prosecutor was telling the jury that even on July 15, 2004, Gray was the only biller. He didn't say that in so many words, but he implied it. Gray's lawyer could have objected—but didn't, maybe because the time it takes to bill really wasn't an important issue, since, as we just said, the fact that Gray may have had accomplices would not exonerate her; the evidence that she was centrally involved in Dovies' fraud was compelling.

Gray makes other arguments for reversal besides the timestamp evidence, but only one of them merits discussion. Suddoth completed his direct testimony at the end of the first day of trial and was scheduled to be cross-examined at the start of the second day. He arrived at court on time but refused to enter the courtroom. A court security officer told the judge that Suddoth was lying on the floor outside the courtroom, that he had thrown up in the elevator, and that he appeared to have the "dry heaves." The judge joked, "If he pukes on my carpet, he goes directly to prison," then told the prosecutor to call another witness. Defense counsel objected, but the judge overruled the objection.

Trial resumed and the judge told the jury: "Mr. Suddoth did come to the building today, but he has what appears to be some type of intestinal problem. He's been throwing up this morning in the bathroom [sic—it was the elevator]. He was about to come in the courtroom and had another attack, so he's being medically looked at." During the next recess the judge talked to the paramedic who had been summoned to treat Suddoth. The paramedic said that Suddoth had refused to be hospitalized or to have any tests performed on him, and that he (that is, the paramedic) didn't know whether Suddoth had actually been ill. Suddoth told the courtroom security officer that he just needed a bottle of water; he blamed his distress on a foot-long Subway sandwich that he'd eaten for breakfast that morning. At the end of the recess the judge told the jury that "I've been informed that more likely than not it is something that he had for breakfast, and he's feeling better. He's drinking water and probably will be available to complete his testimony," and in fact he completed his testimony that afternoon.

Gray complains that the judge excluded pertinent information, namely Suddoth's refusal of treatment, and "testified" without any basis in evidence that Suddoth's failure to testify as scheduled was attributable to something he'd eaten rather than to fear of cross-examination.

The judge's declining to tell the jury that Suddoth had refused treatment was proper. Gray argues that Suddoth's refusal of treatment was an admission that he was faking nausea. But a person often will refuse medical treatment because he's feeling better. It's not an admission of malingering. For that matter the fact that a witness becomes sick to his stomach at the prospect of being cross-examined is not, as Gray argues, an admission that he was lying on direct examination. An aggressive cross-examiner might induce nausea in a truthful witness.

It would have been better had the judge said nothing about Suddoth's physical condition. All he need have told the jury was that although Suddoth had been scheduled to be the first witness that morning, the schedule had changed and he would testify later and another government witness would testify first. But the judge's remarks about Suddoth's condition cannot be thought reversible error. Gray argues that they created sympathy for Suddoth and an excuse for what he claimed in his testimony under cross-examination were failures of recollection. But the jury can't have had much sympathy for Suddoth, as he had pleaded guilty to conspiring with Gray to commit Medicaid fraud. And Gray's lawyer could have cross-examined Suddoth about his "refusal of treatment" but did not. That's an indication that she didn't think the judge's comments about Suddoth's condition would predispose the jury to believe his testimony.

AFFIRMED.