OPINION

SILER, Circuit Judge.

Douglas Coley, an Ohio state prisoner, was convicted in Lucas County of aggravated murder, attempted murder, kidnapping, aggravated robbery and firearm specifications. He was sentenced to death on the aggravated murder charges. Coley then petitioned for state postconviction relief, but was turned down at all levels of the state judiciary. He subsequently sought habeas corpus relief in federal court. The district court denied his petition for a writ of habeas corpus. For the reasons set forth below, we AFFIRM the judgment of the district court.

I. BACKGROUND

A. Factual Background

1. Kidnapping, Aggravated Robbery and Attempted Murder of David Moore

On December 23, 1996, around 7:30 p.m., while David Moore was unloading his light blue, four-door Ford Taurus at his residence, Joseph Green asked Moore for directions. As Moore obliged, Coley appeared. When Moore moved to leave, Coley and Green held pistols on Moore and forced him into the car. Coley then drove the car away, demanded Moore's cash, and eventually told Moore to get out of the car. While Moore backed out, Coley shot him in the stomach. Moore then ran away, but one of the men chased him, other shots were fired, and Moore fell down. Moore pretended that he was dead, and his assailant walked away.

Moore had been shot in the head, stomach, arms, and twice in the hand. A gun identified as Coley's had ejected the shell casings found on Green Street and fired the bullet removed from Moore's wrist.

On an evening shortly before Christmas, Tyrone Armstrong, a cousin of both Coley and Green, saw Coley and Green in a light blue, four-door Ford Taurus. That same evening, Armstrong witnessed Coley and Green with the same .25 caliber semiautomatic pistols that Armstrong had seen each of them previously carry, and heard Green make up a rap song with the words "I shot him five times and he had dropped." Green also pointed his gun at Coley and said, "You better never snitch on me." Coley mimicked the action to Green, repeating, "Better never snitch on me."

Armstrong identified State Exhibit 32 as the pistol Coley previously carried and also State Exhibit 33 as a pistol belonging to Green. Coley's girlfriend also recognized State Exhibit 32 as a gun she had seen around her house. On December 27, 1996, police recovered Moore's car in an area near the residence of Coley's girlfriend.

2. Kidnapping, Aggravated Robbery, and Murder of Samar El-Okdi

Samar El-Okdi was found dead in an alley behind West Grove Place on January 7, 1997. She had been shot with a .25 caliber bullet from a gun fired at a distance of approximately twelve to eighteen inches. She was wearing the same white shirt, black shoes, and black trousers that she wore to work on January 3. At the scene, police found a live .25 caliber bullet and a .25 caliber shell casing near her body.

El-Okdi had last been seen around 8 p.m. on January 3, 1997. That same day, around 8:45 p.m., as Rosie Frusher left a friend's house at West Grove Place, she heard two gunshots and saw a car nearby in an alley. The car had taillights similar to a Pontiac 6000, the vehicle driven by El-Okdi. Frusher saw a man outside the car bending over and another man sitting in the driver's seat.

That same weekend, Armstrong saw Coley driving a gray Pontiac 6000 that he later identified as El-Okdi's car. On the night his cousins were arrested, Armstrong bought for Green and Coley some cigars and two bottled drinks, which police later found in the Pontiac. Armstrong also admitted that Green and Coley had keys for the Pontiac.

On January 6, El-Okdi's friend was parked on a street waiting to distribute missing-person flyers for El-Okdi and saw El-Okdi's car. The friend identified the car by its dented rear fender and a distinctive bumper sticker, although the license plate was different. The friend followed the Pontiac until the driver parked at an apartment complex and two men got out. Then, after talking with police, the friend and a Toledo detective returned to where the stolen Pontiac was parked. It bore an Ohio license plate which had been stolen from another Pontiac 6000 on January 4, 1997. Police staked out the car until Green, Coley and a woman with a baby got into the Pontiac and drove away. Police forced the Pontiac to stop and arrested Green and Coley.

Upon approaching the vehicle, police noticed that Coley had a metallic object in his hand. Later, on the Pontiac's rear floor, they found a loaded .25 caliber pistol (State Exhibit 32) near where Coley had been sitting. Inside the trunk, police found a black crochet purse that El-Okdi had with her on January 3 when she disappeared. Police also found one of El-Okdi's license plates underneath the stolen rear plate, and they found her other license plate in the car trunk.

A firearms expert examined the .25 caliber bullet removed from El-Okdi's brain, the .25 caliber bullet removed from Moore's wrist, three .25 caliber shell casings from the two crime scenes, and Coley's.25 caliber semiautomatic pistol recovered from the rear floor of El-Okdi's Pontiac. The firearms expert concluded that Coley's pistol was in operating condition and had fired the bullets into Moore and El-Okdi and had ejected the three crime-scene shell casings. After police searched Green's residence, they found an empty box that had contained .25 caliber ammunition.

While in jail, Coley admitted to Armstrong, who was being held on unrelated charges, that he "did it." Armstrong understood Coley to mean that Coley had shot El-Okdi. Coley also asked Armstrong to lie for him by claiming that Coley had obtained his weapon and the Pontiac from someone named Denny. Additionally, Moore recognized Green and Coley as the men who had shot him. See also State v. Coley, 93 Ohio St.3d 253, 754 N.E.2d 1129, 1134-37 (2001).

B. Procedural Background

In 1997, Coley was indicted by a grand jury on eight counts, including charges of kidnapping, aggravated robbery, and attempted murder of Moore, and three counts of aggravated murder, kidnapping, and aggravated robbery of El-Okdi.

In 1998, Coley was convicted by a jury as charged. The jury found both that Coley was the principal offender in the aggravated murder of El-Okdi and that he committed the offense with prior calculation and design. The trial court sentenced Coley to 58 years in prison for the noncapital counts, and followed the jury's recommendation of death for the aggravated murder of El-Okdi. Coley unsuccessfully sought relief via direct appeal, see State v. Coley, 93 Ohio St.3d 253, 754 N.E.2d 1129 (2001), and an application to reopen that appeal pursuant to Ohio Sup.Ct. Prac. R. 11, § 5(A) (West 2004). See State v. Coley, No. 98-1474, 94 Ohio St.3d 1483, 763 N.E.2d 1182 (Ohio Mar. 4, 2002) (unpublished). While Coley was appointed counsel to assist him in post-conviction proceedings, no post-conviction petition was timely filed on his behalf.

In 2003, Coley sought habeas relief in federal court under 28 U.S.C. § 2254. See Coley v. Bagley, No. 1:02CV0457, 2010 WL 1375217, at *1, 2010 U.S. Dist. LEXIS 33063, at *1 (N.D.Ohio Apr. 5, 2010). The district court denied relief, but granted a certificate of appealability ("COA") for the following issues: (1) ineffective assistance of trial counsel for failure to object to the indictment; (2) ineffective assistance of trial counsel for failure to request that the trial judge recuse herself; (3) prosecutorial misconduct for using inconsistent theories to convict; (4) ineffective assistance of counsel during mitigation; (5) ineffective assistance of counsel during mitigation for failing to request that trial judge recuse herself based on Moore's letter; (6) ineffective assistance of appellate counsel for failing to raise on appeal the issue of the trial court's review of the letter; (7) the trial court and jury did not consider mitigating evidence; and (8) the trial court's decisions to not provide Coley with grand jury transcripts and to not sever the Moore counts from the El-Okdi counts. See id. at *65-68, 2010 U.S. Dist. LEXIS 33063 at *185-92.

II. ANALYSIS

A. Standard of Review

"In a habeas corpus appeal, we review the district court's legal conclusions de novo, but will not set aside its factual findings unless they are clearly erroneous." Ivory v. Jackson, 509 F.3d 284, 291 (6th Cir.2007) (citation omitted). The standard for reviewing state-court determinations, by contrast, is governed by the Antiterrorism and Effective Death Penalty Act ("AEDPA"). See Frazier v. Huffman, 343 F.3d 780, 787 (6th Cir.2003) (citing Lindh v. Murphy, 521 U.S. 320, 336, 117 S.Ct. 2059, 138 L.Ed.2d 481 (1997)). Under AEDPA, a writ of habeas corpus should be denied unless the state court decision was contrary to, or involved an unreasonable application of, clearly established federal law as determined by the Supreme Court, or based on an unreasonable determination of the facts in light of the evidence presented to the state courts. See Slagle v. Bagley, 457 F.3d 501, 513 (6th Cir.2006) (citing 28 U.S.C. § 2254(d)). The petitioner carries the burden of proving that this standard has been met. Cullen v. Pinholster, ___ U.S.___, 131 S.Ct. 1388, 1398, 179 L.Ed.2d 557 (2011).

A state court's decision is "contrary to" Supreme Court precedent if (1) "the state court arrives at a conclusion opposite to that reached by [the Supreme] Court on a question of law[,]" or (2) "the state court confronts facts that are materially indistinguishable from a relevant Supreme Court precedent and arrives" at a different result. Williams v. Taylor, 529 U.S. 362, 405, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). A state court's decision is an "unreasonable application" under 28 U.S.C. § 2254(d)(1) if it "identifies the correct governing legal rule from [the Supreme] Court's cases but unreasonably applies it to the facts of the particular ... case" or either unreasonably extends or unreasonably refuses to extend a legal principle from Supreme Court precedent to a new context. Id. at 407, 120 S.Ct. 1495.

This analysis does not apply to claims that the state court resolved without deciding the federal constitutional issues, as when the claims were held procedurally barred. Instead, if the federal court reaches their merits, they are reviewed under pre-AEDPA law. Under that standard, we review mixed questions of law and fact de novo. Williams v. Coyle, 260 F.3d 684, 706 (6th Cir.2001).

B. Alleged Ineffective Assistance of Trial and Appellate Counsel

According to Coley, defense counsel were constitutionally ineffective both at trial and on direct appeal because counsel (1) at the penalty phase did not investigate and present evidence of his character, education, or employment history; (2) failed to demand that the judge recuse herself at the penalty phase or file an affidavit of disqualification with the Ohio Supreme Court; (3) failed to request that the judge recuse herself in the guilt phase; (4) at the appeal stage failed to raise trial counsel's ineffectiveness in not requesting that the judge recuse herself. Coley's first claim fails because he neglected to raise it in his state appellate proceedings.1 See Roberts v. Carter, 337 F.3d 609, 613 (6th Cir.2003). Even if not procedurally defaulted, it still fails on the merits because Coley has not shown any prejudice, for he has never shown what evidence he had which was not presented to the jury.

The factual basis of the judicial bias claims originates from the following: The court-appointed defense investigator discovered a letter sent to a witness in the trial. The letter, addressed to Coley's brother, asked him to get a rifle to a certain individual to "take care" of someone. The letter, allegedly authored by Coley, was delivered to Coley's defense attorney. The defense attorney consulted with the Supreme Court of Ohio Board of Commissioners, and made the trial judge aware of the contents of the letter. Only having heard about, but not having seen the letter, the judge contacted the police and the prosecutors, who began an investigation. After the court overruled a motion to quash, it furnished the letter to law enforcement. The defense attorney moved to withdraw, the motion was granted, and new trial counsel was appointed.

1. Counsel was not ineffective for not seeking removal of the trial judge because the court was impartial and unbiased during the penalty phase of Coley's trial

Coley argues that the trial judge was unconstitutionally biased and her removal, therefore, should have been sought by trial counsel and appellate counsel should have accused trial counsel of ineffectiveness for not doing so. We must therefore consider the underlying issue of whether the judge was indeed biased. Judicial bias is a deep-seated favoritism or antagonism that makes fair judgment impossible. See Mayberry v. Pennsylvania, 400 U.S. 455, 465-66, 91 S.Ct. 499, 27 L.Ed.2d 532 (1971). A biased decision-maker is constitutionally unacceptable. Withrow v. Larkin, 421 U.S. 35, 47, 95 S.Ct. 1456, 43 L.Ed.2d 712 (1975). "[T]he Due Process Clause clearly requires a fair trial in a fair tribunal before a judge with no actual bias against the defendant or interest in the outcome of his particular case." Bracy v. Gramley, 520 U.S. 899, 904-05, 117 S.Ct. 1793, 138 L.Ed.2d 97 (1997) (internal quotation marks and citation omitted); Tumey v. Ohio, 273 U.S. 510, 535, 47 S.Ct. 437, 71 L.Ed. 749 (1927).

The bias inquiry is objective, asking "whether the average judge in his position is likely to be neutral, or whether there is an unconstitutional potential for bias." Caperton v. A.T. Massey Coal Co., 556 U.S. 868, 872, 881, 129 S.Ct. 2252, 173 L.Ed.2d 1208 (2009) (internal quotation marks omitted) (citing Ungar v. Sarafite, 376 U.S. 575, 584, 84 S.Ct. 841, 11 L.Ed.2d 921 (1964)). Recusal is required when "the probability of actual bias rises to an unconstitutional level." Id. at 887, 129 S.Ct. 2252. Since judicial bias is a structural defect both when actual and when merely unconstitutionally probable, see Arizona v. Fulminante, 499 U.S. 279, 309-10, 111 S.Ct. 1246, 113 L.Ed.2d 302 (1991), if either type of judicial bias is proven, Strickland prejudice need not be proven. See Strickland v. Washington, 466 U.S. 668, 691-96, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984).

Coley maintains that counsel's failure to seek removal of the trial judge resulted in actual bias on the part of the judge at sentencing. Coley also argues that counsel, in the penalty phase, should have sought removal of the judge who had already presided over the guilt phase because she had been biased by information obtained even before the guilt phase began. To establish bias, Coley need not prove actual bias, but merely an unconstitutionally high probability of actual bias. Caperton, 556 U.S. at 887, 129 S.Ct. 2252. Coley believes the following factors create a high probability of actual bias: (1) the judge was exposed to bad facts about the defendant; (2) she passed that information on to law enforcement, which resulted in a separate grand-jury investigation; and (3) after the jury had recommended death, she had to independently determine whether that was the appropriate sentence.

These factors do not singly or cumulatively establish the requisite probability of actual bias. Exposure to bad facts about the defendant does not, as a per se matter, establish bias. See Esparza v. Mitchell, 310 F.3d 414, 424-25 (6th Cir. 2002), rev'd on other grounds, 540 U.S. 12, 124 S.Ct. 7, 157 L.Ed.2d 263 (2003). "The nature of the criminal justice system often requires judges to consider evidence and then dismiss it from their minds." Id. at 425. Even exposure to bad facts and formation of an opinion based on them are not enough to establish bias. See Liteky v. United States, 510 U.S. 540, 550-51, 114 S.Ct. 1147, 127 L.Ed.2d 474 (1994). Nor does the analysis change merely because the judge received the information in a pretrial proceeding. Id. at 551, 114 S.Ct. 1147. Therefore, even if the judge were to have viewed the letter as threatening, rather than relatively benign, and as indisputably coming from the defendant himself, her exposure to it does not establish an unconstitutionally high probability of actual bias.

Furthermore, Coley's judge did not dig deeper to learn whether there was a nexus between Coley and the letter. She did not even read it to learn whether, upon examination, it fell more on the "benign" or "death threat" end of the spectrum. Instead, she turned the information about the letter over to a detective, for him to take whatever steps he thought appropriate. Nor was she the one who proffered any charges against Coley. Cf. In re Murchison, 349 U.S. 133, 133-38, 75 S.Ct. 623, 99 L.Ed. 942 (1955). That leaves the trial judge as neither investigator nor prosecutor, but simply a judge to whom the presumption of impartiality applies.

Finally, we presume "honesty and integrity in those serving as adjudicators." Withrow, 421 U.S. at 47, 95 S.Ct. 1456. The presumption of impartiality stems not merely from the judicial-bias caselaw, see id., but from the more generally applicable presumption that judges know the law and apply it in making their decisions, see Lambrix v. Singletary, 520 U.S. 518, 532 n. 4, 117 S.Ct. 1517, 137 L.Ed.2d 771 (1997), and the even more generally applicable presumption of regularity, see Parke v. Raley, 506 U.S. 20, 30-31, 113 S.Ct. 517, 121 L.Ed.2d 391 (1992); United States v. Chem. Found., Inc., 272 U.S. 1, 14-15, 47 S.Ct. 1, 71 L.Ed. 131 (1926). Coley must overcome those presumptions. See Strickland, 466 U.S. at 687-88, 104 S.Ct. 2052; see also Kimmelman v. Morrison, 477 U.S. 365, 375, 106 S.Ct. 2574, 91 L.Ed.2d 305 (1986) (included within defendant's burden to prove Strickland claim is a burden to prove the merit of the underlying claim). He does not; the claim fails.

2. Counsel was not ineffective for failing to raise judge recusal

a. Procedural Default

The parties contest whether Coley's claim that counsel were ineffective in the guilt phase in failing to request that the judge recuse herself is preserved and whether this court should consider the procedural-default issue sua sponte. We decline to engage in the debate, because even when reviewed de novo, the claim is meritless. In an attempt to prove the contrary, Coley cites State v. Gillard, 40 Ohio St.3d 226, 533 N.E.2d 272, 276 (1988), overruled on other grounds by State v. McGuire, 80 Ohio St.3d 390, 686 N.E.2d 1112 (1997) (ruling that "when the state seeks to obtain relief from discovery or to perpetuate testimony under Crim. R. 16(B)(1)(e), the judge who disposes of such a motion may not be the same judge who will conduct the trial."). See State v. Esparza, 74 Ohio St.3d 660, 660 N.E.2d 1194, 1196-97 (1996) (per curiam) (clarifying that Gillard is a state-law ruling granting the defendant more protection than the Constitution required). Even assuming the Gillard rule applies — or that trial counsel could have obtained a recusal by analogizing Coley's situation to Gillard's — there is still no prejudice.

b. The Merits of Coley's Trial Counsel Ineffectiveness Claim for Failing to Raise Judge Recusal

We have found no constitutionally actionable bias in capital cases just because the trial judge knew of such bad facts, but did not recuse herself. See Gillard v. Mitchell, 445 F.3d 883, 893 (6th Cir.2006) (from pretrial, ex parte hearing, judge knew that Gillard had been president of the Outlaws motorcycle gang and his brothers had threatened witnesses with harm if they testified against him); Esparza, 310 F.3d at 424-25 (from pretrial, ex parte hearing, judge knew about violent past of Esparza and about the fear of his girlfriend (and mother of his child) that his brothers would harm her for testifying). We presume the judge to have followed the Ohio state law which forbids considering nonstatutory aggravators while weighing aggravation against mitigation, to have known that law, and to have applied it in making her decision, see Ohio Rev.Code Ann. § 2929.03(D)(2)-(3) (West 2004) (amended 2005, 2008), before imposing the death penalty. See State v. Wogenstahl, 75 Ohio St.3d 344, 662 N.E.2d 311, syl. ¶ 1 (1996); State v. Johnson, 24 Ohio St.3d 87, 494 N.E.2d 1061, syl. (1986). That is the state of affairs when looking only at the underlying bias argument, before taking into account the requirement, under Strickland's prejudice prong, that she be presumed to have acted according to the law. See Strickland, 466 U.S. at 694-95, 104 S.Ct. 2052; see also id. at 700, 104 S.Ct. 2052.

This judge was not biased under the Constitution and therefore Strickland prejudice is not presumed but must be proven. Strickland's prejudice test "focuses on the question whether counsel's deficient performance renders the result of the trial unreliable or the proceeding fundamentally unfair. Unreliability or unfairness does not result if the ineffectiveness of counsel does not deprive the defendant of any substantive or procedural right to which the law entitles him." Lockhart v. Fretwell, 506 U.S. 364, 372, 113 S.Ct. 838, 122 L.Ed.2d 180 (1993) (citations omitted). No substantive or procedural right entitles a defendant to one judge instead of another. See Sinito v. United States, 750 F.2d 512, 515 (6th Cir.1984). Moreover, the test asks whether there is a reasonable probability that, but for counsel's unprofessional errors, the result of the proceedings would have been different. Strickland, 466 U.S. at 694, 104 S.Ct. 2052. Confidence in the outcome is not undermined simply because unbiased Judge A, rather than unbiased Judge B, sat. Coley fails to show an unconstitutionally high probability of actual bias, and there is no prejudice. Therefore, his Strickland claim fails.

c. The Merits of Coley's Appellate Counsel Ineffectiveness Claim for Failing to Raise Judge Recusal

In his final challenge to his counsel's ineffectiveness, Coley argues that appellate counsel was ineffective because he failed to raise trial counsel's ineffectiveness in not requesting that the judge recuse herself. Although AEDPA deference applies, this claim fails even if reviewed de novo. The underlying arguments are meritless; it could scarcely be ineffective of appellate counsel not to raise them. See Rashad v. Lafler, 675 F.3d 564, 571 (6th Cir.2012). Omitting meritless arguments is neither professionally unreasonable nor prejudicial. See also Allen v. Harry, No. 10-1304, 2012 WL 3711552, at *10 (6th Cir. Aug. 29, 2012) (unpublished) (citing Hoffner v. Bradshaw, 622 F.3d 487, 509 (6th Cir.2010), cert. denied, ___ U.S. ___, 131 S.Ct. 2117, 179 L.Ed.2d 910 (2011)).

C. Alleged Trial Court Error: Grand Jury Transcript

Coley argues that the trial court erred in denying his pretrial motion for disclosure of the grand jury transcript. Coley, who was indicted twice — first without capital charges and second in a capital indictment — argued on direct appeal that the reindictment demonstrated the "particularized need" required under Ohio law to justify unsealing the grand jury transcripts. The Ohio Supreme Court held the claim meritless, noting that a presumption of regularity supports prosecutorial decisions to present additional evidence to another grand jury and, for that discrete point, cited Supreme Court precedent. Otherwise citing only state law, the court held that Coley had failed to show a particularized need for the grand jury testimony. In federal habeas proceedings, the district court held this a state law claim, whose rejection by the Ohio Supreme Court was not contrary to or an unreasonable application of clearly established Supreme Court precedent. We agree. Coley does not meet his burden of proving that state court rejection of his claim was contrary to or an unreasonable application of clearly established Supreme Court precedent. See Pinholster, 131 S.Ct. at 1398. This claim fails.

D. Alleged Trial Court Error: Not Severing Counts

Coley argues that the trial court erred in denying his motion to sever the Moore counts from the El-Okdi counts. The prejudice he alleges is that the jury improperly considered the acts involving Moore when deciding Coley's guilt of the aggravated murder of El-Okdi. The district court held that this was a state law issue and that nothing in the Ohio Supreme Court decision was contrary to or an unreasonable application of clearly established Supreme Court precedent. The Warden contends this claim is both defaulted — because raised in state court only as a matter of state law — and meritless. The claim is preserved, however, because Coley's brief alleged that improper joinder of the offenses denied him his rights under the Sixth, Eighth, and Fourteenth Amendments. See Sheppard v. Bagley, 657 F.3d 338, 347 (6th Cir.2011); West v. Bell, 550 F.3d 542, 557-58 (6th Cir.2008). We review the merits under AEDPA's contrary-to clause because, under currently controlling caselaw, that is the clause that applies when the state court cited only state law. See Early v. Packer, 537 U.S. 3, 8, 123 S.Ct. 362, 154 L.Ed.2d 263 (2002).2

Misjoinder is not per se unconstitutional, but rises to that level if it results in prejudice so great as to deny a defendant his due process right to a fair trial. See United States v. Lane, 474 U.S. 438, 446 n. 8, 106 S.Ct. 725, 88 L.Ed.2d 814 (1986). The harmless-error rule governs. See id. at 446, 106 S.Ct. 725. In federal habeas proceedings, we ask whether the error had "substantial and injurious effect or influence in determining the jury's verdict." Brecht v. Abrahamson, 507 U.S. 619, 623, 113 S.Ct. 1710, 123 L.Ed.2d 353 (1993) (internal quotation marks omitted); see also Fry v. Pliler, 551 U.S. 112, 121-22, 127 S.Ct. 2321, 168 L.Ed.2d 16 (2007). "[A] risk of undue prejudice exists whenever joinder of counts permits introduction of evidence of other crimes that would otherwise be inadmissible." Davis v. Coyle, 475 F.3d 761, 777 (6th Cir.2007). However, in Coley's case, the evidence of other crimes was not otherwise inadmissible. The Ohio Supreme Court specifically held that evidence of the Moore offenses was admissible under Ohio R. Evid. 404(b) "to prove Coley's identity as El-Okdi's killer." Coley, 754 N.E.2d at 1139.

Coley does not directly challenge that holding, but argues that the introduction of this evidence denied him a fair trial. This is not a winning argument. Other evidence presented against Coley included the facts that: Green and Coley were found traveling in El-Okdi's stolen car three days after she disappeared; inside was the black crocheted purse she had with her; her front license plate had been stowed in the trunk; her rear plate was still in position, but covered by another license plate, stolen from a different car; and the bullet found in her brain and the shell casing at the crime scene had come from Coley's gun. Additionally, there was evidence of Coley's inculpatory statements: "I did it but Joe [Green] shouldn't have snitched on me," and asking his cousin to lie for him by claiming that the gun and stolen car were given to him by a man named Denny.

Any error in joining the offenses was harmless and Coley was not denied a fair trial. The state court's rejection of this claim was not contrary to clearly established Supreme Court precedent.

E. Alleged Prosecutorial Misconduct: Inconsistent Theories

Coley insists that prosecutorial misconduct so infected his trial with unfairness as to result in a denial of due process. Specifically, he alleges that the prosecution engaged in misconduct by using inconsistent theories of criminal culpability: arguing at the trial of codefendant Green that Green was the principal offender, but at the subsequent trial of Coley that Coley was the principal offender.

1. Procedural Default

"Federal habeas relief is available to state prisoners only after they have exhausted their claims in state court." O'Sullivan v. Boerckel, 526 U.S. 838, 839, 119 S.Ct. 1728, 144 L.Ed.2d 1 (1999) (citing 28 U.S.C. § 2254(b)(1)). A habeas petitioner has not exhausted his claims in state court unless he has "properly presented" his claims to a state court of last resort. Id. at 848, 119 S.Ct. 1728 (emphasis omitted). The state's argument in the present appeal is that because Coley failed to raise his prosecutorial misconduct claim before the Ohio Supreme Court,3 the federal courts are precluded from ruling on the merits of the claim.

We will consider the merits of a procedurally defaulted claim in a habeas petition, however, where the petitioner "show[s] that there was cause for the default and prejudice resulting from the default, or that a miscarriage of justice will result from enforcing the procedural default in the petitioner's case." Lancaster v. Adams, 324 F.3d 423, 436 (6th Cir.2003), (quoting Seymour v. Walker, 224 F.3d 542, 550 (6th Cir.2000)).

2. The Merits of Coley's Prosecutorial Misconduct Claim

Pre-AEDPA law controls because we reach the merits of a claim whose merits the state courts did not reach. See Maples v. Stegall, 340 F.3d 433, 436-37 (6th Cir.2003). Legal and mixed questions receive de novo review. Id. at 436. The district court understood Coley to be complaining of the alleged prosecutorial misconduct only to the extent used to obtain his conviction, and Coley does not challenge the district court's understanding, even while raising the issue on appeal. Therefore, Coley forfeits any penalty-phase aspect of this claim, see Hill v. Mitchell, 400 F.3d 308, 335 (6th Cir.2005) (appellant forfeits objection to component of district court ruling if appellant, on appeal, does not object to that component), because it leaves in place the district court's understanding that Coley did not advance such an argument below. Coley may not argue here what he did not argue there. See Brown v. Marshall, 704 F.2d 333, 334 (6th Cir.1983). The penalty-phase argument was not raised in the habeas petition and was not included in the COA, and may not be considered now.4

That leaves Coley with the guilt-phase argument. According to Coley, the prosecution argued in Green's trial that Green was the shooter, but argued in Coley's trial that Coley was the shooter, i.e., the principal offender. He contends that the prosecution's use of these inconsistent theories of culpability constituted misconduct. Assuming the accuracy of Coley's summary of the prosecution's argument in Green's trial, and assuming for the sake of argument that such inconsistent arguments violate due process, this claim still fails.

In Bradshaw v. Stumpf, 545 U.S. 175, 125 S.Ct. 2398, 162 L.Ed.2d 143 (2005), the Supreme Court confronted the question whether the use of such inconsistent theories voided Stumpf's guilty plea. See id. at 177-82, 186-87, 125 S.Ct. 2398.5 Without deciding whether such prosecutorial behavior was a due-process violation, id. at 187, 125 S.Ct. 2398, the Court held that any error was harmless — or, "immaterial," because under Ohio law Stumpf, even if not the shooter, was guilty of aggravated murder under an aider-and-abettor theory "so long as the aiding and abetting is done with the specific intent to cause death." Id. at 184, 186-87, 125 S.Ct. 2398 (relying on In re Washington, 81 Ohio St.3d 337, 691 N.E.2d 285, 286-87 (1998); State v. Scott, 61 Ohio St.2d 155, 400 N.E.2d 375, 382 (1980)); see also State v. Coleman, 37 Ohio St.3d 286, 525 N.E.2d 792, syl. ¶ 2 (1988).

The same reasoning applies here. Coley was convicted of prior-calculation-and-design aggravated murder and two counts of aggravated felony murder, all of which required that he "purposely" caused the victim's death and "specifically intended" to cause that death. See Ohio Rev.Code Ann. § 2903.01 (A)-(B), (D) (West 1997) (amended 1997, 1998, 2002, 2011). Purpose and specific intent are one and the same. See State v. Treesh, 90 Ohio St.3d 460, 739 N.E.2d 749, 775 (2001) ("A person acts purposely when he or she specifically intends to cause a certain result."). Thus, Coley was found to have specifically intended to cause El-Okdi's death. And therefore, whether aider or abettor or actual shooter, Coley was equally guilty of those three counts of aggravated murder. He was also convicted of the death specification to each aggravated murder count: that the aggravated murder was committed in conjunction with kidnapping or aggravated robbery and either he was the principal offender in the aggravated murder or, if not the principal offender, committed the aggravated murder with prior calculation and design. Even though the jurors specifically found that he was the principal offender, they also found that he caused El-Okdi's death with prior calculation and design. Classifying Coley as shooter or aider and abettor makes no difference to his guilt of this specification. As the district court held, any error in the guilt phase was harmless.

F. Failure to File Post-Conviction Petition

Coley claims that appellate counsel was ineffective for not filing a state post-conviction petition but does not argue the claim in his brief. See United States v. Layne, 192 F.3d 556, 566 (6th Cir.1999) ("[I]ssues adverted to [on appeal] in a perfunctory manner, unaccompanied by some effort at developed argumentation, are deemed waived...."). This claim was not certified for appeal. Hence, we lack the authority to address it. See Hill, 400 F.3d at 329, 335. To the extent that this argument is another aspect of Coley's already-addressed ineffective assistance of appellate counsel claim, it is meritless for the reasons stated here.

Similarly, while the district court granted a certificate of appealability on three additional issues, Coley has abandoned those issues on appeal.

AFFIRMED.