Sykes, Circuit Judge.

Miguel Adorno, an Illinois prisoner, was convicted of attempted murder using a firearm. On direct appeal he challenged certain remarks by the trial judge about the state's burden of proof. More particularly, he argued that the judge's comments — delivered impromptu during voir dire — invited the jury to convict on less than the reasonable-doubt burden of proof required by the Constitution's guarantee of due process of law. He also claimed that the judge's remarks violated state law. The Illinois Court of Appeals addressed only the state-law argument and rejected the claim; the court made no reference to federal law. Adorno then sought federal habeas relief under 28 U.S.C. § 2254. Applying de novo review, the district judge found a due-process violation and granted the petition.

We reverse the judgment. Because the state court did not specifically address Adorno's federal claim, our first task is to decide whether the Richter presumption applies. See Harrington v. Richter, 562 U.S. 86, 131 S.Ct. 770, 178 L.Ed.2d 624 (2011). When a state prisoner presents a federal claim to a state court and the court denies relief without explanation, Richter requires a federal habeas court to presume that the state court adjudicated the claim on the merits. Id. at 99, 131 S.Ct. 770. The presumption triggers deferential review under § 2254(d); the federal court must give the state-court judgment the benefit of any arguments or theories that could have supported the state court's judgment. Id. at 102, 131 S.Ct. 770.

The Richter presumption is rebuttable, but we do not need to decide whether it has been rebutted here. Even under de novo review, Adorno's claim fails. There is no reasonable likelihood that the jury convicted him on less than the reasonable-doubt standard.

I. Background

While attending a house party in the Hermosa neighborhood in Chicago, Adorno was accused of stealing an iPod and a laptop from one of the hosts. After the laptop was retrieved from the back seat of the car Adorno arrived in, he and his friends were asked to leave. A fistfight ensued between Adorno and Jeffery Nagamine, the host's brother. According to several witnesses, Adorno threatened to kill Nagamine and retrieved a gun from his friend's car to make good on the threat. As the other guests retreated back into the house, Adorno fired several shots into the crowd. The partygoers were lucky; no one was killed and only one person was hit, sustaining a gunshot wound to the arm.

Adorno was arrested and initially told police that he knew nothing about the house party. He claimed to have spent the entire evening with his mother. Later Adorno admitted his involvement in the shooting but claimed that he fired his gun at the crowd in self-defense. The State's Attorney charged him with attempted murder in the first degree while armed with a firearm.

The case proceeded to jury trial. During voir dire, the judge preliminarily informed the venire about the presumption of innocence and the burden of proof in criminal cases. He told the prospective jurors that Adorno was presumed innocent and that the presumption could be overcome only if the state proved his guilt beyond a reasonable doubt. The judge explained that Adorno was not required to present any evidence on his own behalf but could instead rely entirely on the presumption of innocence. The judge then discussed the standard of proof in greater detail:

The last sentence in this passage implies that a nonverbal hand gesture accompanied the judge's "scale" analogy, but no record was made of it.

A jury was seated, and at the close of the evidence, the judge read formal instructions about the presumption of innocence, the elements of the charged crime, and the state's burden to prove every element beyond a reasonable doubt. The jury convicted Adorno as charged, and the judge imposed a sentence of 30 years.

On direct appeal Adorno challenged the judge's attempt to explain the reasonable-doubt standard during voir dire. Citing Victor v. Nebraska, 511 U.S. 1, 114 S.Ct. 1239, 127 L.Ed.2d 583 (1994), he argued that the judge's remarks invited the jury to convict on less than the reasonable-doubt standard required by the federal Constitution's guarantee of due process. His argument relied almost exclusively on federal law, but he also alluded to Illinois common law, which precludes trial judges from defining reasonable doubt, and to Illinois Supreme Court Rule 431(b), which requires judges to verify that the jurors understand and accept the reasonable-doubt standard. He raised other challenges as well, though none are relevant here.

The state appellate court affirmed. In evaluating Adorno's challenge to the voir dire remarks by the judge, the court relied exclusively on state law and treated the claim as one alleging ordinary trial error rather than an error of constitutional magnitude. That is, the court applied the statelaw framework for evaluating improper judicial comments at trial and concluded that because the remarks were not prejudicial, Adorno was not entitled to relief.

Adorno skipped state postconviction proceedings and moved directly to federal court seeking habeas relief under § 2254, repeating his federal constitutional challenge to the judge's voir dire remarks. The district judge determined that the state court had not adjudicated Adorno's federal claim on the merits and thus reviewed it de novo, without the deference normally required by § 2254(d)(1). The judge concluded that the state trial judge's remarks improperly invited the jury to convict on a constitutionally insufficient standard of proof. Accordingly, the judge granted Adorno's § 2254 petition and ordered Illinois to release him or file notice within 30 days of its intent to retry the case against him. The State appealed.

II. Discussion

We review the judge's § 2254 ruling de novo. Thompkins v. Pfister, 698 F.3d 976, 983 (7th Cir. 2012). A state court's decision on a prisoner's federal claim ordinarily is entitled to substantial deference on federal habeas review; we will not set it aside unless it "was contrary to, or involved an unreasonable application of, clearly established Federal law" or "was based on an unreasonable determination of the facts in light of the evidence presented in the [s]tate court proceeding." 28 U.S.C. § 2254(d)(1), (2). The AEDPA1 standard is deliberately difficult, setting a high bar for relief; the prisoner must demonstrate that the state court's ruling was "so lacking in justification that there was an error well understood and comprehended in existing law beyond any possibility for fairminded disagreement." Richter, 562 U.S. at 103, 131 S.Ct. 770.

But deferential review under AEDPA "applies only to claims that were actually `adjudicated on the merits in [s]tate court proceedings.'" Harris v. Thompson, 698 F.3d 609, 623 (7th Cir. 2012) (quoting § 2254(d)). For all other claims, we apply the pre-AEDPA standard of 28 U.S.C. § 2243 and review de novo. Id.

In its decision resolving Adorno's direct appeal, the Illinois Appellate Court did not explicitly address the federal claim. Though Adorno's briefing squarely challenged the trial judge's voir dire remarks on federal due-process grounds, the court made no mention of federal law in its opinion. The court's only hint of a nod to a claim based on federal law is a single sentence that contains faint echoes of the Victor standard: "We do not believe that the court's comments during voir dire could reasonably be construed as inviting the jury to convict [the] defendant based on less than the reasonable doubt standard."

Even when a federal claim is wholly unaddressed by the state court, however, a question remains whether it was "adjudicated on the merits" for purposes of § 2254(d). Where, as here, a state prisoner adequately presents a federal claim to a state court and the court denies relief, the Supreme Court has instructed us to presume that the federal claim was adjudicated on the merits "in the absence of any indication or state-law procedural principles to the contrary." Richter, 562 U.S. at 99, 131 S.Ct. 770; see also Keith v. Schaub, 772 F.3d 451, 454 (7th Cir. 2014). In Johnson v. Williams, 568 U.S. 289, 292, 133 S.Ct. 1088, 185 L.Ed.2d 105 (2013), the Court held that the Richter presumption applies in cases like this "when a defendant convicted in state court attempts to raise a federal claim, either on direct appeal or in a collateral state proceeding, and a state court rules against the defendant and issues an opinion that addresses some issues but does not expressly address the federal claim in question." See also Lee v. Avila, 871 F.3d 565, 571 (7th Cir. 2017).

Although "the Richter presumption is a strong one that may be rebutted only in unusual circumstances, it is not irrebuttable." Williams, 568 U.S. at 302, 133 S.Ct. 1088. The presumption may give way if "the state court relies exclusively on state law, and the state standard is less protective than the federal one"; or if the governing federal standard was simply "`mentioned in passing in a footnote or ... buried in a string cite'"; or if the prisoner can show that the claim was overlooked "`as a result of sheer inadvertence.'" Brady v. Pfister, 711 F.3d 818, 825 (7th Cir. 2013) (quoting Williams, 568 U.S. at 301-03, 133 S.Ct. 1088). We do not need to decide whether the Richter presumption has been rebutted here; the due-process claim fails on plenary review.

The Fourteenth Amendment's guarantee of due process includes the requirement in criminal cases that the state prove every element of a charged offense beyond a reasonable doubt. In re Winship, 397 U.S. 358, 364, 90 S.Ct. 1068, 25 L.Ed.2d 368 (1970). As a matter of Illinois common law, trial judges are instructed not to attempt to define reasonable doubt for the jury. People v. Thomas, 191 Ill.App.3d 187, 138 Ill.Dec. 568, 547 N.E.2d 735, 741 (1989). In contrast, "the [federal] Constitution neither prohibits trial courts from defining reasonable doubt nor requires them to do so as a matter of course." Victor, 511 U.S. at 5, 114 S.Ct. 1239. Accordingly, the voir dire remarks by the trial judge in Adorno's case will amount to federal constitutional error only if "there is a reasonable likelihood that the jury understood the [remarks] to allow conviction based on proof insufficient to meet the [reasonable-doubt] standard." Id. at 6, 114 S.Ct. 1239.

There is no reasonable likelihood of that here. The trial judge expressly recognized that under Illinois law there is no need for a judicial definition of the term "reasonable doubt." He told the prospective jurors that it was "up for you to decide in words" what the term means. That was not, as Adorno argues, an invitation to the jury to convict on some lesser standard of proof.

The judge's reference to the civil burden of proof using the metaphor of a scale likewise did not invite the jurors to convict on a constitutionally insufficient standard of proof. The judge invoked the civil standard solely for the purpose of distinguishing it from the criminal reasonable-doubt standard, explaining that proof by preponderance of the evidence is insufficient for criminal cases. And he emphasized that "reasonable doubt is the highest burden of proof in our country and in our [s]tate." Finally, at the close of the case, the judge formally instructed the jury on the presumption of innocence, the elements of the offense, and the state's burden to prove each of the elements beyond a reasonable doubt. The propriety of those instructions was and is unchallenged.

The judge's voir dire comments must be viewed "in the context of the entire charge," not in isolation. Jones v. United States, 527 U.S. 373, 391, 119 S.Ct. 2090, 144 L.Ed.2d 370 (1999). Taken as a whole, nothing in the judge's remarks creates a reasonable likelihood that the jury "underst[ood] the phrase [`reasonable doubt'] to mean something less than the very high level of probability required by the Constitution in criminal cases." Victor, 511 U.S. at 14, 114 S.Ct. 1239. Put slightly differently, the judge's remarks do not suggest that the jurors would have understood that they were free to convict Adorno on less than proof beyond a reasonable doubt. Because the conviction was not tainted by a due-process violation, the order granting habeas relief was unwarranted and is

REVERSED.

Bauer, Circuit Judge. Concurring.

Attempts at defining reasonable doubt have always occasioned problems. Both "reasonable" and "doubt" are words in common usage and are constantly used in the language of law. No matter how glib the speaker, it is necessary to use other words that require further definition in trying to refine the terms "reasonable" or "doubt." The language used by this learned trial judge makes that point clearly.

Illinois Pattern Instructions and the Seventh Circuit Criminal Instructions make this point emphatically. Judges and lawyers must accept the fact that we select jurors who presume to be reasonable and who understand through years of normal living what is meant by "doubt."

It is with a sore heart then, that I concur in the opinion.