EASTERBROOK, Chief Judge.

After a trial in 1981, Murray Hooper was convicted of three murders and sentenced to death. The Supreme Court of Illinois affirmed the conviction but ordered a new penalty trial. People v. Hooper, 133 Ill.2d 469, 142 Ill.Dec. 93, 552 N.E.2d 684(1989). It ended in another capital sentence, which was affirmed. People v. Hooper, 172 Ill.2d 64, 216 Ill.Dec. 633, 665 N.E.2d 1190 (1996). Collateral review in state court left the convictions in place, but the Governor of Illinois commuted the sentence to life imprisonment. Federal collateral review began in 2010. The district court's order, 854 F.Supp.2d 546 (N.D.Ill. 2012), denying Hooper's petition under 28 U.S.C. § 2254, rejected all three of his contentions. The unusual caption of these proceedings — in which the lead respondent is the Director of the Arizona Department of Corrections — stems from the fact that Hooper is on death row in that state, following his convictions there for multiple murders. See State v. Hooper, 145 Ariz. 538, 703 P.2d 482 (1985); Hooper v. Schriro, 2008 U.S. Dist. LEXIS 84760, 2008 WL 4542782 (D.Ariz. Oct. 10, 2008) (denying Hooper's petition for relief under § 2254). Because relief remains possible on the Arizona convictions and sentence, however, Hooper's challenge to his Illinois convictions is justiciable.

Details about Hooper's crimes do not matter to the federal proceedings. Procedural details do matter. Hooper was indicted with William Bracy and Roger Collins. Bracy and Collins were tried and convicted together; Hooper was tried separately. The convictions of Bracy and Collins reached the Supreme Court of the United States because Judge Thomas J. Maloney of the Circuit Court of Cook County presided. Maloney was convicted of taking bribes, see United States v. Maloney, 71 F.3d 645 (7th Cir.1995), and one of the prosecutions on which the bribery conviction rests came between the Bracy-Collins trial and Hooper's trial. Bracy and Collins contended that Judge Maloney engaged in "compensatory bias" — that he ensured the conviction of defendants who did not pay bribes, both to make people more willing to pay his price and to make his record look acceptable to the voters when up for retention. The Supreme Court held that compensatory bias is a valid legal theory and remanded for exploration of that subject. Bracy v. Gramley, 520 U.S. 899, 117 S.Ct. 1793, 138 L.Ed.2d 97 (1997). Five years later, this circuit held that compensatory bias had not been established with respect to Bracy's and Collins's convictions. Bracy v. Schomig, 286 F.3d 406 (7th Cir.2002) (en banc).

Hooper argues that he has shown compensatory bias even though Bracy and Collins failed to do so. A state judge rejected that argument in 2007. The state's intermediate appellate court affirmed, and the Supreme Court of Illinois denied a petition for review. The federal district judge held that the state decision on the compensatory-bias subject is not marred by a legal error or any clearly erroneous factual finding. 854 F.Supp.2d at 563-67. Given our holding en banc in Bracy, we too conclude that the state judiciary's decision on this subject cannot be upset on collateral review. We also agree with the district court's conclusion, id. at 574-76, that Hooper has not provided an adequate reason to reject the state courts' denial of his contention that his confession should have been excluded from evidence. Hooper's third argument, however, is substantially stronger.

Five years after Hooper's trial, the Supreme Court held in Batson v. Kentucky, 476 U.S. 79, 106 S.Ct. 1712, 90 L.Ed.2d 69 (1986), that racial discrimination in jury selection could be shown not just by statistical data revealing a systemic problem, see Swain v. Alabama, 380 U.S. 202, 85 S.Ct. 824, 13 L.Ed.2d 759 (1965), but by the misuse of peremptory challenges in a single case. Batson applies to cases that were on direct appeal when it was released. Griffith v. Kentucky, 479 U.S. 314, 107 S.Ct. 708, 93 L.Ed.2d 649 (1987). Because Hooper's appeal was pending when Batson came down, the Supreme Court of Illinois ordered Judge Maloney to hold a hearing to determine whether the prosecutor had exercised peremptory challenges on racial grounds. In 1987 Judge Maloney found not; the Supreme Court of Illinois concluded in 1989 that his findings did not constitute clear error, 133 Ill.2d at 502-15, 142 Ill.Dec. 93, 552 N.E.2d 684; and 23 years later the federal district court concluded (854 F.Supp.2d at 567-74) that the state's decision is not "contrary to, or ... an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States" (28 U.S.C. § 2254(d)(1)) — a standard established by legislation in 1996 and applicable here because the federal collateral attack began in 2010. See Lindh v. Murphy, 521 U.S. 320, 117 S.Ct. 2059, 138 L.Ed.2d 481 (1997).

A few numbers show why there is a Batson problem. The venire drawn for Hooper's trial had 63 members. Of these, seven were black. Two of the seven were removed on challenges for cause. The prosecutor exercised peremptory challenges against the remaining five. The prosecutor used 11 peremptory challenges, removing 100% of the black members of the venire who had not already been removed for cause and 11% of the white or Asian members. Surprisingly, however, Judge Maloney concluded that the defense lacked even a prima facie demonstration of racial discrimination. Here is his analysis of the Batson issue:

See 133 Ill.2d at 504, 142 Ill.Dec. 93, 552 N.E.2d 684. There are the findings that the Supreme Court of Illinois held neither legally mistaken nor clearly erroneous. We think that, in reaching this conclusion, the Supreme Court of Illinois made at least four errors that were unreasonable applications of the Supreme Court's decisions, if not outright contradictions of them.

Hooper's principal argument to the state judiciary, and his principal argument now, is that the numbers speak for themselves. The prosecutor removed every black member of the venire, producing an all-white jury. The Supreme Court of Illinois held, however, that a judge is forbidden to infer a prima facie case of discrimination from a racially disproportionate use of challenges. "Allowing the trial court to find a prima facie case based solely on the fact that the State has used its peremptory challenges to exclude all the black jurors from the venire would negate consideration of all other relevant circumstances ... and would be inconsistent with Batson's mandate that all relevant circumstances be considered." 133 Ill.2d at 506, 142 Ill.Dec. 93, 552 N.E.2d 684. This conflicts with Batson, where the Court remarked that "total or seriously disproportionate exclusion of Negroes from jury venires ... is itself such an `unequal application of the law ... as to show intentional discrimination'" (476 U.S. at 93, 106 S.Ct. 1712, quoting from Washington v. Davis, 426 U.S. 229, 241, 96 S.Ct. 2040, 48 L.Ed.2d 597 (1976), and Akins v. Texas, 325 U.S. 398, 404, 65 S.Ct. 1276, 89 L.Ed. 1692 (1945)).

Under Batson's predecessor, Swain v. Alabama, statistics were the only way to show race discrimination in jury selection; nothing in the Court's opinion suggests that it swung to the other extreme by holding that statistics could not suffice even for a prima facie demonstration. By relying on employment-discrimination cases such as Washington v. Davis, the Court established in Batson that the usual means to show discrimination, including statistical analysis, are available.

Later decisions, such as Miller-El v. Dretke, 545 U.S. 231, 125 S.Ct. 2317, 162 L.Ed.2d 196 (2005), show that Batson was serious in its endorsement of statistical methods. Miller-El holds that striking 91% of eligible black members of the venire established a prima facie case of discrimination. The parties have debated whether, under § 2254(d)(1) and Teague v. Lane, 489 U.S. 288, 109 S.Ct. 1060, 103 L.Ed.2d 334 (1989), procedural elaborations on the Batson framework, such as those in Miller-El and Hernandez v. New York, 500 U.S. 352, 111 S.Ct. 1859, 114 L.Ed.2d 395 (1991), that were announced after the conclusion of Hooper's direct appeal, govern his situation. We need not resolve that question as a general matter, because to the extent that Miller-El and other decisions elucidate Batson they are not "new rules" for the purpose of Teague.

Some elaborations on the Batson framework do create new rules. For example, the parties agree that J.E.B. v. Alabama, 511 U.S. 127, 114 S.Ct. 1419, 128 L.Ed.2d 89 (1994), which extends Batson from race discrimination to sex discrimination, created a new rule that does not aid Hooper, even though the prosecutor struck one person for the stated reason of altering the jury's male-to-female ratio. Miller-El, by contrast, does not change anything substantive about Batson. Instead it illustrates the proper application of Batson's approach. Miller-El was itself decided on collateral review; the Justices did not see any problem in applying its understanding to a case in which direct review had ended years earlier.

The Supreme Court of Illinois made a second legal error when analyzing the data and concluding that they did not offer any support for a prima facie case. The state court observed that the prosecutor struck six white or Asian members of the venire while using peremptory challenges against five blacks. Because most of those struck with peremptory challenges were not black, the state court concluded, it is unlikely that race played a role. 133 Ill.2d at 510, 142 Ill.Dec. 93, 552 N.E.2d 684. This reflects confusion about how to use numbers. The right question is whether it is possible to understand the pattern of strikes on the hypothesis that race did not play a role. The denominator in such an analysis is the number of black and white persons in the venire, not the number of peremptory challenges exercised. We asked at oral argument whether anyone in either the state or federal litigation had performed a statistical analysis to determine whether, if 11 peremptory challenges had been exercised without regard to race, all five eligible black members of a 63-person venire would have been excused. No one hired a statistician to do the analysis. Our back-of-the-envelope calculation suggests that the probability is vanishingly small.

A third legal error comes on the same page of the state court's opinion. The court said that an inference of discrimination is undermined because Hooper, all three victims, and all of the principal witnesses are black. As it happens, the court was wrong on the facts; three of the principal witnesses are white (as the state concedes). See 854 F.Supp.2d at 571-72. But the main problem is legal rather than factual. Batson and its successors say that the rule against race discrimination in jury selection is designed to protect the interests of potential jurors and of the public at large, not just of the litigants. The Supreme Court of Illinois seems to have thought that using race in jury selection is tolerable as long as the defendant, victims, and witnesses all are of the same race. That's a serious legal blunder.

Finally, the state court erred in concluding, as Judge Maloney also had done, that a prima facie case can be defeated by a prosecutor's seemingly race-neutral explanation for the strikes. As Hernandez and other decisions show, and Batson itself said (476 U.S. at 97-98, 106 S.Ct. 1712), it is important to keep the sequence of proof straight. Evidence that raises an inference of discrimination creates a prima facie case; this in turn requires an explanation by the prosecutor and an evaluation by the judge whether the prosecutor is honest in articulating a non-racial reason for each challenge. To say "the prosecutor gave a reason, therefore there is no prima facie case" is to scramble the analysis in a way that potentially eliminates the need to evaluate the prosecutor's honesty. See Franklin v. Sims, 538 F.3d 661, 666(7th Cir.2008). No harm is done if on the way to saying "no prima facie case" the judge concludes that the prosecutor honestly had a race-neutral reason for each challenge, see United States v. Stephens, 421 F.3d 503, 516 (7th Cir.2005) — once a hearing has been held and a decision made on the ultimate issue, the whole structure of prima facie case and response can be discarded, see Postal Service v. Aikens, 460 U.S. 711, 714-15, 103 S.Ct. 1478, 75 L.Ed.2d 403 (1983) — but that did not occur here. The prosecutor did not articulate any reason for one of the strikes, and Judge Maloney did not evaluate the honesty of the reasons stated for the other four.

We conclude that the Supreme Court of Illinois applied Batson unreasonably to Hooper's situation in concluding that the evidence did not make out a prima facie case of race discrimination in jury selection. And because the prosecutor has not to this day articulated any reason for one of the five challenges to black members of the venire, it is impossible to sustain the state court's decision on alternative grounds. A single discriminatory peremptory challenge vitiates the judgment. See Snyder v. Louisiana, 552 U.S. 472, 478, 128 S.Ct. 1203, 170 L.Ed.2d 175 (2008). At least one additional challenge is suspect. The prosecutor justified this challenge by saying that the jury had too many women. We have explained why that confessed sex discrimination does not justify collateral relief, but the reference to the venire member's sex led the state judiciary not to ask why, of the many women still eligible to serve, the prosecutor challenged the one who was by that point the only black member of the venire. The prosecutor has never attempted to justify striking this particular woman, and if the prosecutor had chosen a woman at random the challenge most likely would have fallen on a white member of the venire.

Our analysis does not establish that the prosecutor engaged in racial discrimination. But it does remove the state court's ground of decision and entitle Hooper to an evidentiary hearing in federal court. See Cullen v. Pinholster, ___ U.S. ___, 131 S.Ct. 1388, 179 L.Ed.2d 557 (2011). If the state articulates a non-discriminatory reason for all of the five contested peremptory challenges, the district judge must decide whether each reason is honest. The judge will not owe any deference to Judge Maloney's views; a federal evidentiary hearing leads to an independent decision.

It seems unlikely that this can be done 32 years after the trial. We do not know whether the prosecutors who exercised these challenges are living or whether their memories (or notes) will enable a reliable resolution. The State of Illinois may think it prudent to forego the exercise and offer Hooper another trial — though that, too, would be hard to hold 33 years after the murders (which occurred on November 13, 1980) with much prospect of an accurate decision. But the state can have a Batson hearing, if it thinks that one would be fruitful.

The judgment of the district court is vacated, and the case is remanded for further proceedings consistent with this opinion.