POSNER, Circuit Judge.
A jury convicted the defendant of armed bank robbery, 18 U.S.C. § 2113(a), and the judge sentenced him to the statutory maximum of 240 months, id., in part because of his previous convictions for that crime. The appeal presents two issues; we begin with the lesser one, which involves the exclusion of a witness for the defense on the ground that he was an alibi witness and the defense had not given the prosecution the notice required before trial by Fed.R.Crim.P. 12.1(a). The defendant argues that the witness he wanted to call was not an alibi witness and so the rule doesn't apply.
The robbery occurred in Palatine, Illinois. The defendant was a personal trainer in Chicago, and had an appointment for a training session with one of his clients that began two hours after the robbery. The distance from the bank to the gym where the defendant did his personal training is only 28 miles, a distance easily covered by car in a good deal less time than two hours; and the defendant does not claim that extreme weather conditions, or an accident or other untoward event, might have prevented his arriving at the gym within two hours after leaving Palatine — in which event he could not have been the robber. So the client could not have given the defendant an alibi in the usual sense. This should make one wonder why the defendant wanted to call him. He argues that the client would have testified that the defendant was "calm, friendly and professional" at all their training sessions (the client did not recall the particular session that had taken place the evening of the robbery, which occurred almost two years before he was approached by the defendant's lawyer), and that he would not have been calm, etc., had he committed an armed bank robbery only two hours earlier. Actually such testimony would have had no probative value even if the client had remembered the defendant's deportment at the session after the robbery. No one had been hurt in the robbery, which had lasted all of five minutes, and why would one expect the robber, having committed what he thought a successful crime that had enriched him, albeit modestly (his take was only $1146), to be visibly agitated two hours later, far from the scene of the crime and not pursued by police (he was not arrested until two years later)? And he was an experienced bank robber — the presentencing investigation report states that he admitted having committed 11 bank robberies between 1981 and 1985.
In any event it was alibi evidence that the defendant wanted to offer by calling his client as a witness, albeit alibi evidence of an unusual sort. The usual alibi evidence, if believed, proves that it was physically impossible for the defendant to have committed the crime that he's been accused of; suppose the training session had been held in Los Angeles rather than Chicago and there was a record of his having attended it. But the alibi in this case would have been that it was psychologically impossible for him to have committed the crime, because had he done so he would have been visibly agitated two hours later yet the alibi witness would have testified that he was never visibly agitated at their training sessions. This would be the obverse of evidence that the robber had been "nervous" and "jumpy" an hour after the robbery, as in United States v. Turner, 474 F.3d 1265, 1278 (11th Cir.2007). It would have been weak evidence of innocence, as we said — "the fact that [the defendant] was not nervous and that he did not act violently is easily explained, because it would not have been in his interest to act in those ways," United States v. Boulanger, 444 F.3d 76, 89 n. 17 (1st Cir. 2006) — but still evidence.
Notice to the prosecution of proposed alibi evidence is required because an alibi defense is at once compelling if accepted and easy to concoct, so the prosecution is justified in wanting an opportunity to investigate it in advance of trial. Williams v. Florida, 399 U.S. 78, 81, 90 S.Ct. 1893, 26 L.Ed.2d 446 (1970); United States v. Pearson, 159 F.3d 480, 483 (10th Cir.1998). That is true of alibi evidence premised on psychological impossibility as well as the more common type. And so the district judge was right to exclude the evidence because of the defendant's failure to have complied with Rule 12.1(a).
We move to the second and more substantial issue — a challenge to the photo array shown the bank's manager, whom the robber had confronted after forcing an entry into the bank shortly after the bank had closed for the day. When police arrived after the robbery the manager had told them that although the robber had worn a dust mask that covered his nose and mouth, the manager could tell that the robber was a white man with "a very pale complexion" and "light colored eyebrows and freckles around his eyes."
The dust mask was found shortly after the robbery 150 feet from the bank. DNA found on the mask was eventually matched with DNA that had been taken from a convicted bank robber named John Ford, the defendant in this case. In March 2009, 16 months after the robbery, a police officer presented the bank manager with an array of six head shots that included one of Ford; we attach a photo of the array at the end of this opinion. The manager picked the man in the middle of the top row as the robber; it was Ford. He was eventually arrested and at a suppression hearing in September 2010 challenged the bank manager's identification on the ground that the photo array had been irreparably suggestive. The district judge refused to suppress the identification, and at the trial, held one month later, the manager testified that he had indeed identified the defendant as the bank robber in the photo array.
The photo array was suggestive. First, instead of showing the six photographs to the bank manager one by one, the police officer placed them on a table in front of him all at once, side by side in two rows, as in the photo at the end of this opinion (except that that's a photo of all six photos, and what the manager was shown was the separate photos — but as he was shown them all at once, what he saw was equivalent to our composite photo).
The officer asked the manager whether he recognized the robber. The objection to this procedure is that the manager would probably think that one of the photos was of the robber, or at least of the person whom the police suspected of being the robber, which might have led the manager to pick the one who most resembled the robber even if the resemblance was not close, especially since so much time had elapsed since he had seen the robber and the robber had been masked when he saw him.
It is true that the police officer told the manager not to assume that a photo of a suspect would be among the photos shown him, a disclaimer that the cases recommend. See United States v. Williams, 522 F.3d 809, 811 (7th Cir.2008); United States v. Saunders, 501 F.3d 384, 391 (4th Cir. 2007); United States v. Gibson, 135 F.3d 257, 260 (2d Cir.1998) (per curiam). Several studies suggest that such a disclaimer indeed reduces the risk of misidentification. See, e.g., Gary L. Wells & Deah S. Quinlivan, "Suggestive Eyewitness Identification Procedures and the Supreme Court's Reliability Test in Light of Eyewitness Science: 30 Years Later," 33 Law & Human Behavior 1, 6-7 (2009); Beth Schuster, "Police Lineups: Making Eyewitness Identification More Reliable," 258 Nat'l Institute of Justice Journal 2, 3 (2007). But whether it eliminates the risk created by a simultaneous array may be doubted. A witness is likely to think that the array must include a suspect as otherwise there would be no point in showing it to the witness, unless the witness's verbal description was of such an unusual-looking person that only a handful of people in the area in which the crime took place could possibly match it; in that case the police could show him all the look-alikes, confident that one was the criminal and hopeful that he differed enough from the others that the witness would be able to pick him out of the array.
The array would have been less suggestive had the manager been shown the photos one by one (a "sequential" array). United States v. Brown, 471 F.3d 802, 804-05 (7th Cir.2006); see N.C. Gen.Stat. § 15A-284.52(b)(2); Wis. Stat. § 175.50(5)(b); Letter from N.J. Attorney General John J. Farmer, Jr., to All County Prosecutors et al. (Apr. 18, 2001), www.state.nj.us/lps/dcj/agguide/photoid.pdf (visited May 31, 2012). Witnesses shown a sequential lineup are more likely to compare each person in it only with their memory of the offender, rather than choose whichever person looks the most like what the witness remembers. Schuster, supra, at 4; Gary L. Wells & Elizabeth A. Olson, "Eyewitness Testimony," 54 Ann. Rev. Psychology 277, 288-89 (2003); Dawn McQuiston-Surrett et al., "Sequential vs. Simultaneous Lineups: A Review of Methods, Data, and Theory," 12 Psychology, Public Policy & Law 137, 138-39 (2006); Nancy Steblay et al., "Eyewitness Accuracy Rates in Sequential and Simultaneous Lineup Presentations: A Meta-Analytic Comparison," 25 Law & Human Behavior 459, 468 (2001); but see United States v. Lawrence, 349 F.3d 109, 114-15 (3d Cir.2003).
The accuracy of a sequential array can be improved by making it appear to the witness that there are more persons in the array than he's been shown. The officer presenting the array could pause after showing the witness the first five photos and ask whether he'd spotted the robber yet. For if after having looked at the first five photos in an array of six (as in this case) the witness knew he was looking at the last one in the array, he might infer, if he hadn't identified any of the first five, that the sixth photo was of the robber, or at least of the man who the police thought was the robber. But we suspect that even with the suggested adjustment the risk of misidentification is greater when the witness is looking from photo to photo, because they're side by side, in an attempt to pick out the one that most resembles his recollection of the robber.
And since the robber had been masked, the men in the photos (including Ford) should have been shown wearing dust masks similar to the one the police had found. Furthermore, the same detective from the Palatine police department investigated the case, compiled the photo array, and showed the array to the bank manager. Assigning other officers (with a smaller stake in nailing Ford) to compile the photo array and show it to the manager would have reduced the likelihood of an officer's signaling him to identify Ford as the robber.
Still another respect in which the array was suggestive was that the other five men don't look like the robber, because, although all are adult Caucasian males of approximately the same age, none is pale or has freckles. The only description that the manager had given the police was that the robber was very fair and had freckles, and only Ford's photo matches that description. Of course the Palatine police department's collection of photos of suspicious-looking characters (all the photos in the array were mugshots) may not have contained photos of any light-complexioned men with freckles except Ford. But the department should have been able to borrow such photos from a larger police department, such as the Chicago Police Department — and Palatine is a Chicago suburb.
Of course it's impossible to find photos of persons who are identical to a suspect (unless he has an identical twin) — and also undesirable, because then the witness wouldn't be able to identify the suspect. But Ford's appearance is so unlike that of the other men in the photo array — and unlike them with respect to the only two features that the bank manager recalled of the masked robber — that the array suggested to the manager which photo he should pick as the one of the robber. See United States v. Downs, 230 F.3d 272, 275 (7th Cir.2000); United States v. Wiseman, 172 F.3d 1196, 1209-10 (10th Cir.1999); compare United States v. Howard, 142 F.3d 959 (7th Cir.1998) (per curiam).
As awareness of the frequency of mistakes in eyewitness identification has grown (see, e.g., Jon B. Gould & Richard A. Leo, "One Hundred Years Later: Wrongful Convictions After a Century of Research," 100 J.Crim. L. & Criminology 825, 841-42 (2010); Innocence Project, "Reevaluating Lineups: Why Witnesses Make Mistakes and How to Reduce the Chance of a Misidentification" 3-4 (2009), www.innocenceproject.org/docs/Eyewitness_ID_Report.pdf (visited May 31, 2012); Richard A. Wise et al., "How to Analyze the Accuracy of Eyewitness Testimony in a Criminal Case," 42 Conn. L.Rev. 435, 440-41 (2009); Sandra Guerra Thompson, "Beyond a Reasonable Doubt? Reconsidering Uncorroborated Eyewitness Identification Testimony," 41 U.C. Davis L.Rev. 1487, 1490-91, 1497-98 (2008); Brandon L. Garrett, "Judging Innocence," 108 Colum. L.Rev. 55, 60 (2008); Samuel R. Gross et al., "Exonerations in the United States 1989 Through 2003," 95 J.Crim. L. & Criminology 523, 542 (2005)), so has the need for judges to be especially wary about suggestive arrays shown potential witnesses, especially when as in this case the suspect was masked and a long time had elapsed between the crime and the display of the array to the witness.
It is true that the three other employees of the bank who were present when the robbery occurred could not identify the defendant from the photo array, and this is some evidence that the array was not suggestive. See United States v. Arrington, 159 F.3d 1069, 1073 (7th Cir.1998); Millender v. Adams, 376 F.3d 520, 525 (6th Cir.2004). But unlike the bank manager they had not gotten a close look at the robber; so far as appears, they didn't realize he was light-skinned and freckled.
"An identification infected by improper police influence, our case law holds, is not automatically excluded. Instead, the trial judge must screen the evidence for reliability pretrial. If there is `a very substantial likelihood of irreparable misidentification,' Simmons v. United States, 390 U.S. 377, 384, 88 S.Ct. 967, 19 L.Ed.2d 1247 (1968), the judge must disallow presentation of the evidence at trial. But if the indicia of reliability are strong enough to outweigh the corrupting effect of the police-arranged suggestive circumstances, the identification evidence ordinarily will be admitted, and the jury will ultimately determine its worth." Perry v. New Hampshire, ___ U.S. ___, 132 S.Ct. 716, 720, 181 L.Ed.2d 694 (2012). This is a demanding test for exclusion, but may have been met in this case, and if so it was a mistake to allow the bank manager to testify at the trial about his previous identification of the defendant as the robber. (He did not attempt to identify the defendant as the robber in person, that is, at the trial.)
But we think the error was harmless. There was no doubt that the dust mask found outside the bank was the robber's, and the DNA found on the dust mask matched the defendant's DNA. Moreover, even if not permitted to identify the defendant as the robber, the manager would have been permitted to testify that the robber was a pale-visaged freckled white man, for that is what he had told the police immediately after the robbery; and the jurors could have compared the description with the defendant sitting in front of them. The jury also could have compared the bank manager's description with the pictures of the robber taken by the bank's surveillance camera during the robbery and shown at the trial. The manager had described the robber to the police as 5'10" and he testified at trial that the robber was close to his own height of 5'10". Still frames from the surveillance footage reveals that the two men are indeed of approximately the same height.
The defendant makes much of the fact that the day after the robbery the bank manager had thought he recognized the robber among the bank's customers, and that the police had investigated and determined that the man in question was not the robber. It is not surprising that the day after being held up at gunpoint the manager was nervous and would make such a mistake. Another possibility, we grant, is that he was overconfident of his ability to identify the robber — but his initial mistake should have made him less confident later, when he viewed the array.
Oddly, though, the government does not argue harmless error. When asked at argument why not, the government's lawyer replied that there was "substantial" doubt that the jury would have convicted the defendant without the eyewitness identification. The defendant's lawyer added that at trial the DNA evidence had been challenged, although a forensic scientist from the Illinois State Police testified that the probability that the DNA on the dust mask was not the defendant's was only 1 in 29 trillion.
The lawyers' statements indicate a misunderstanding of the harmless-error rule. An error can be harmless even if, had it not been committed, the defendant would have been acquitted. The criterion of harmlessness is whether a reasonable jury might have acquitted; if not, the error was harmless. The cases usually say a "rational" jury rather than a "reasonable" jury, but they are using "rational" to mean "reasonable." It would not necessarily be "irrational" for a jury to vote to convict a person whom it did not think guilty beyond a reasonable doubt — the jury might think the government's burden of having to prove guilt beyond a reasonable doubt too heavy. But it would be "unreasonable" because it would be flouting the judge's instructions.
It is because not all juries are reasonable that prosecutors sometimes take out insurance against erroneous acquittals by presenting evidence (if the judge permits) that should have been excluded. The evidence reduces the likelihood of acquittal, and does so without providing grounds for reversal, provided that a reasonable jury would not have acquitted had the evidence been excluded as it should have been, though because some juries are unreasonable (or dominated by an unreasonable member or unreasonable members) the actual jury might have acquitted. See Alexandra White Dunahoe, "Revisiting the Cost-Benefit Calculus of the Misbehaving Prosecutor: Deterrence Economics and Transitory Prosecutors," 61 NYU Annual Survey of American Law 45, 93-94 (2005); Bennett L. Gershman, "The New Prosecutors," 53 U. Pitt. L.Rev. 393, 429-31 (1992).
Although the defendant's lawyer tried to throw dust in the jurors' eyes by a vigorous challenge to the DNA evidence, and might have succeeded with another jury, the challenge had no merit. What is involved, very simply, in forensic DNA analysis is comparing a strand of DNA (the genetic code) from the suspect with a strand of DNA found at the crime scene. See "DNA Profiling," Wikipedia, http://en.wikipedia.org/wiki/DNA_profiling (visited May 31, 2012). Comparisons are made at various locations on each strand. At each location there is an allele (a unique gene form). In one location, for example, the probability of a person's having a particular allele might be 7 percent, and in another 10 percent. Suppose that the suspect's DNA and the DNA at the crime scene contained the same alleles at each of the two locations. The probability that the DNA was someone else's would be 7 percent if the comparison were confined to the first location, but only .7 percent (7 percent of 10 percent) if the comparison were expanded to two locations, because the probabilities are independent. Suppose identical alleles were found at 10 locations, which is what happened in this case; the probability that two persons would have so many identical alleles, a probability that can be computed by multiplying together the probabilities of an identical allele at each location, becomes infinitesimally small — in fact 1 in 29 trillion, provided no other comparisons reveal that the alleles at the same location on the two strands of DNA are different. This is the same procedure used for determining the probability that a perfectly balanced coin flipped 10 times in a row will come up heads all 10 times. The probability is .510, which is less than 1 in 1000.
Because the DNA sample taken from the dust mask was incomplete, 10 was all the locations that could be profiled; but that was enough to enable a confident estimation (the 1 in 29 trillion) that the probability that DNA on the dust mask was not the defendant's was exceedingly slight. No evidence was presented to cast doubt on the validity of the DNA test conducted in this case or on the odds stated by the government's expert witness; nor did the cross-examination of the witness, though vigorous, undermine his testimony. The combination in this case of the unimpeached DNA evidence with the bank manager's description of the robber would have persuaded any reasonable jury beyond a reasonable doubt that the defendant was the robber.
It might seem that by failing to argue harmless error the government forfeited that ground for affirming and so we must reverse. Normally that would be true. But Wood v. Milyard, ___ U.S. ___, 132 S.Ct. 1826, 1832, 182 L.Ed.2d 733 (2012), confirming the Supreme Court's earlier decision in Granberry v. Greer, 481 U.S. 129, 134, 107 S.Ct. 1671, 95 L.Ed.2d 119 (1987), states that a court can base decision on a ground forfeited by a party if the ground is "founded on concerns broader than those of the parties," id. at 1833, and that is true of harmless error — and so we and other courts have sometimes affirmed a criminal judgment on the basis of the harmless-error rule even though the government had not invoked it. As we explained in United States v. Giovannetti, 928 F.2d 225, 226-27 (7th Cir. 1991) (per curiam) (citations omitted), in accordance with Granberry, "we are authorized, for the sake of protecting third-party interests including such systemic interests as the avoidance of unnecessary court delay, to disregard a harmless error even though through some regrettable oversight harmlessness is not argued to us. If it is certain that the error did not affect the outcome, reversal will not help the party arguing for reversal beyond such undeserved benefits as he may derive from delay. And reversal will hurt others: not merely the adverse party, whose failure to argue harmlessness forfeits his right to complain about the injury, but innocent third parties, in particular other users of the court system, whose access to that system is impaired by additional litigation. Costs to third parties are an established reason for a court's declining to honor an agreement by the parties, and the same principle applies when a court is belatedly requested to decline to give effect to a forfeiture — which is the equivalent of an implied agreement. When these third-party costs are taken into account, reversal may be an excessive sanction for the government's having failed to argue harmless error, at least if the harmlessness of the error is readily discernible without an elaborate search of the record." See also United States v. Hatfield, 591 F.3d 945, 951 (7th Cir.2010); Jenkins v. Nelson, 157 F.3d 485, 494 n. 1 (7th Cir.1998); United States v. Ghane, 673 F.3d 771, 787 (8th Cir.2012); United States v. Gonzalez-Flores, 418 F.3d 1093, 1100 (9th Cir.2005); United States v. Rose, 104 F.3d 1408, 1414-15 (1st Cir.1997).
The judgment is therefore
AFFIRMED.
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