GIBBONS, J., delivered the opinion of the court, in which ROGERS, J., joined. MOORE, J. (pp. 417-20), delivered a separate dissenting opinion.
OPINION
JULIA SMITH GIBBONS, Circuit Judge.Petitioner-appellant Sidney Cornwell was convicted by an Ohio jury of (1) aggravated murder committed by prior calculation and design; (2) three counts of attempted aggravated murder, with a firearm specification attached to each count and; (3) attached to the aggravated murder count, a death penalty specification that the murder was committed as part of a course of conduct involving the purposeful killing of or attempt to kill two or more people. On direct appeal, the Ohio Supreme Court upheld Cornwell’s conviction and sentence, and the United States Supreme Court denied his petition for a writ of certiorari. After unsuccessfully pursuing post-conviction relief in Ohio state court, Cornwell sought a writ of ha-beas corpus in federal district court. The district court denied Cornwell’s petition but issued a certificate of appealability on three claims. We granted a certificate of appealability on a fourth claim. For the following reasons, we affirm the judgment of the district court denying Cornwell’s habeas petition.
I.
The facts, as recounted by the Supreme Court of Ohio, are as follows. Sidney Cornwell shot three-year-old Jessica Bal-lew in her chest and face at about 2:00 a.m. on June 11, 1996. The shooting was part of a war between the “Crips” and the “Bloods.”
The Crips and the Bloods were rival gangs in Youngstown, Ohio. On the afternoon of June 10, 1996, members of the two gangs had been involved in a shootout on Elm Street in Youngstown. During the exchange of fire, Crips member Edward McGaha saw fellow Crips member Sidney Cornwell using a black gun. Also during this exchange, a bullet grazed McGaha’s head. Later that afternoon, McGaha was released from the hospital and went to his *403mother’s residence on Elm Street. McGa-ha, Cornwell, and several other people were standing outside the residence when a carload of Bloods exited a vehicle and opened fire. McGaha saw Cornwell return fire with the same black semiautomatic weapon he had used earlier in the day. Shortly thereafter, McGaha, Cornwell, and other persons gathered at a residence on New York Avenue and began discussing retaliation for the shooting of McGaha. They decided to kill Richard “Boom” Miles, a Blood who had been present at the first shooting.
That night, the Crips set out in three ears, two of which were stolen, to find and kill Boom. McGaha and Edward Bunkley were in a stolen Buick. Antwan Jones and Gary Drayton were in a Chevrolet Che-vette. The third vehicle was a stolen light blue Pontiac Bonneville, which carried four Crips. In the driver’s seat of the Bonneville was Denicholas Stoutmire. Beside him in the front passenger seat was Damian Williams. Behind Williams, in the right rear passenger seat, was Leslie Johnson. And in the remaining rear passenger seat, behind Stoutmire and to Johnson’s left, sat nineteen-year-old Sidney Cornwell who was carrying a semiautomatic 9 mm black gun.
The three cars drove around Youngstown for about an hour looking for Boom and then went to an apartment building on Oak Park Lane, where Stoutmire thought he might be. Susan Hamlett was outside on the porch of her apartment talking to her friend Donald Meadows. At about 2:00 a.m., Hamlett’s three-year-old niece, Jessica Ballew, came to the doorway of the porch to ask for a drink of water. Two of the cars drove past her apartment, but the third, the light blue Bonneville, stopped. Cornwell’s voice called out from the Bonneville, asking for Boom.1 Hamlett and Meadows both said that he was not there. Cornwell asked where Boom was. Ham-lett said that he did not live there. Corn-well said, “Well, tell Boom this,” and fired six to nine shots. Meadows and two people in the apartment — Marilyn Conrad, another resident of the apartment, and a friend of hers visiting the apartment, Samuel Lagese — were wounded. Jessica Bal-lew was killed. She was hit in both the chest and face, but it was the shot to the face that was fatal.
After receiving a call about the matter, a Youngstown police officer pursued the three vehicles, two of which fit a description he received. He saw that the Bonneville was parked in the driveway of a vacant house. He turned off his headlights, pulled up behind the Bonneville, then turned his lights back on. The occupants of the Bonneville jumped out and ran. The officer ran after the occupant whom the officer believed had jumped out of the driver’s door and, after a brief chase, caught him. The individual caught by the officer was Cornwell.
At trial, Meadows and Williams identified Cornwell as the gunman. Evidence was introduced that several 9 mm Luger shell casings were found at the scenes of the first Elm Street shooting and the Oak Park Lane shooting. Evidence was also introduced that two 9 mm shell casings were found in the Bonneville. A forensic scientist testified that all the 9 mm Luger shell casings recovered from the Oak Park Lane shooting and the first Elm Street shooting came from the same handgun. The murder weapon was never recovered.
A jury found Cornwell guilty of aggravated murder committed by prior calculation and design. It also found him guilty of three counts of attempted aggravated *404murder, with a firearm specification attached to each count and, attached to the aggravated murder count, a death penalty specification that the murder was committed as part of a course of conduct involving the purposeful killing of or attempt to kill two or more people. Cornwell was sentenced to death on the conviction for aggravated murder and to prison for the other convictions. The Ohio Supreme Court affirmed. State v. Cornwell, 86 Ohio St.3d 560, 715 N.E.2d 1144, 1149, 1157 (1999), cert. denied, 528 U.S. 1172, 120 S.Ct. 1200, 145 L.Ed.2d 1103 (2000).
Cornwell unsuccessfully sought relief via a Murnahan2 motion, see State v. Cornwell, 88 Ohio St.3d 1413, 723 N.E.2d 119 (2000), and state post-conviction proceedings, see State v. Cornwell, No. 96 CR 525 (Mahoning C.P. Oct. 6, 2000) (unpublished) (granting the State summary judgment), aff'd, No. 00-CA-217, 2002 WL 31160861 (Ohio Ct.App. Sept. 24, 2002) (unpublished), juris. denied, 98 Ohio St.3d 1413, 781 N.E.2d 1020 (2003).
In 2003, Cornwell filed a petition for a writ of habeas corpus in federal court. As amended in 2005, it raised sixteen claims. The district court denied Cornwell’s requests for experts and an evidentiary hearing and also denied the federal habeas petition. The district court granted a certificate of appealability (“COA”) on Corn-well’s claims that racial bias tainted his prosecution, that the trial court erred in admitting the testimony of eyewitness Donald Meadows, and that appellate counsel was ineffective in failing to challenge the admission of Meadows’s testimony.
This court expanded the COA to include a claim of ineffective assistance in the penalty phase to the extent it raises the following issue: whether there is a reasonable probability the result of the penalty phase would have been different had trial counsel discovered and corrected the misunderstanding of Dr. James Eisenberg regarding Cornwell’s childhood mastectomy in time for him to determine whether this information affected his evaluation of Cornwell. This court also certified the issue of whether the district court erred in denying Cornwell’s request for an expert on genetic disorders and the evidentiary hearing issue to the extent relevant to the certified portion of the claim of ineffective assistance of counsel in the penalty phase.
II.
A.
Cornwell filed his federal habeas petition after the effective date of the Anti-terrorism and Effective Death Penalty Act of 1996 (“AEDPA”); its standards therefore govern. Lindh v. Murphy, 521 U.S. 320, 326-27, 117 S.Ct. 2059, 138 L.Ed.2d 481 (1997). This court may not grant ha-beas relief on any claim adjudicated on the merits in state court unless the adjudication
1) resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States; or
2) resulted in a decision that was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.
28 U.S.C. § 2254(d). In analyzing whether a state court decision is contrary to or an unreasonable application of clearly established Supreme Court precedent, a federal court may look only to the holdings of the Supreme Court’s decisions, not their dicta. Williams v. Taylor, 529 U.S. 362, *405412, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). A state court decision on the merits is contrary to clearly established Supreme Court precedent only if the reasoning or the result of the decision contradicts that precedent. Early v. Packer, 537 U.S. 3, 8, 123 S.Ct. 362, 154 L.Ed.2d 263 (2002). A federal court may grant habeas relief under the unreasonable application clause if the state court decision (a) identifies the correct governing legal principle from the Supreme Court’s decisions but unreasonably applies it to the facts, or (b) either unreasonably extends or unreasonably refuses to extend a legal principle from Supreme Court precedent to a new context. Williams, 529 U.S. at 407-08, 120 S.Ct. 1495. To violate the unreasonable application clause, the state court application of Supreme Court precedent must have been “objectively unreasonable,” not simply erroneous or incorrect. Id. at 409-11, 120 S.Ct. 1495. State court factual findings are presumed correct unless rebutted by clear and convincing evidence. 28 U.S.C. § 2254(e)(1).
When a habeas claim is not adjudicated by a state court, we review de novo questions of law and mixed questions of law and fact. Maples v. Stegall, 340 F.3d 433, 436 (6th Cir.2003). We, however, review the district court’s factual findings for clear error. Wilson v. Parker, 515 F.3d 682, 691 (6th Cir.2008).
B.
1.
Cornwell argues that his counsel rendered ineffective assistance in the penalty phase by failing to discover and correct the misunderstanding of Dr. James Eisenberg regarding Cornwell’s childhood mastectomy in time for him to determine whether this information would affect his evaluation of Cornwell.3 In post-conviction proceedings, the state court of appeals denied this claim on the merits. The district court agreed that the claim was meritless. The Warden concedes that this claim has been preserved for habeas review but contends it is meritless. Cornwell concedes that AEDPA deference applies.
To establish ineffective assistance of trial counsel, Cornwell must show that (1) his counsel’s performance was deficient, that is, objectively unreasonable under prevailing professional norms, and (2) it prejudiced his defense. Strickland v. Washington, 466 U.S. 668, 687-88, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). The test for prejudice is whether there is a reasonable probability that, but for counsel’s unprofessional errors, the result of the proceedings would have been different. Id. at 694, 104 S.Ct. 2052.
Cornwell disagrees that he must show a reasonable probability that the outcome of the trial would have been different. He asserted in his Reply brief that Strickland’s prejudice prong “is not outcome determinative.” He is incorrect. True, “[a] reasonable probability is a probability sufficient to undermine confidence in the outcome,” Strickland, 466 U.S. at 694, 104 S.Ct. 2052, and this is less than a preponderance of the evidence. Id. at 693-94, 104 S.Ct. 2052; Kyles v. Whitley, 514 U.S. 419, 434, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995). But that measuring stick is still applied to whether the result of the proceedings would have been different but for counsel’s unprofessional errors. See Strickland, 466 U.S. at 694, 104 S.Ct. 2052.
*406Turning to the merits of this claim, Ei-senberg was an expert witness who testified for Cornwell in the mitigation phase of proceedings. Cornwell argues that had Eisenberg seen his medical records from a childhood surgery, Eisenberg might have suggested the possibility that Cornwell had Klinefelter’s Syndrome. Instead of the usual male XY sex chromosome, men with Klinefelter’s Syndrome have an extra sex chromosome, XXY. Symptoms include “enlarged breasts, sparse facial and body hair, small testes, and an inability to produce sperm.” Furthermore, men with the syndrome tend to be overweight and to have “some degree of language impairment.” Despite these abnormalities, “[n]ot all males with the condition have the same symptoms or to the same degree.” Indeed, many adults with the condition “live [social] lives similar to men without the condition.” Klinefelter’s Syndrome “is one of the most common chromosome abnormalities in humans.” One in every five hundred men has an extra X chromosome. National Institute of Child Health and Human Development, Klinefelter Syndrome, http://www.nichd.nih.gov/health/topics/ klinefelter — syndrome.cfm (last visited Nov. 14, 2008).
The relevant medical records reveal that Cornwell was thirteen years old at the time of his admission for “bilateral double mastectomies” with nipple transplants and that before surgery he had size DD breasts. The records further reveal that Cornwell had a hormonal imbalance and that he had underdeveloped genitalia. The discharge summary attached to the records gave Cornwell a final diagnosis of “testosterone deficiency syndrome with manifestations of macromastia.” Macro-mastia is “abnormal largeness of the breasts.” See toww.Dictionary.com. The American Heritage Stedman’s Medical Dictionary.
While he did not have the medical records from the mastectomy, Eisenberg reviewed some of Cornwell’s medical records prior to his testimony at the mitigation phase, including records involving occasions when Cornwell was shot, when he was in a car accident, and when a dog bit him. Thus, had Eisenberg been given the medical records from Cornwell’s hospitalization, presumably he would have reviewed them and utilized the information in them.
There are inconsistencies between the medical records from the surgery and the testimony of Eisenberg. While he was aware of the surgery, Eisenberg’s explanation of the surgery began with an account that other people made fun of Cornwell for being overweight. Cornwell “literally ask[ed] his mom to see if he [could] get a chest reduction.” As a result, Eisenberg added,
Not to be crude, but what he told me is that he didn’t want to have these titties and this — that kids were making fun of him at school. And he does. He does, in fact, at 13-year old, has a reduction. I asked him, “Some kind of liposuction?”4 Which is a pretty profound statement. It says something about his identity, self-image, self-worth, the way people are making fun of him. And he goes ahead and has this reduction.
Eisenberg’s references to a reduction arguably made the procedure seem cosmetic. Believing that Cornwell had an elective cosmetic procedure, jurors arguably may have viewed him less favorably than if they had known that a medical condition caused the enlarged breasts that were removed by *407double mastectomy when Cornwell was a teenager.
The Supreme Court has stated that capital defense counsel has an obligation to do a thorough and complete investigation and that the American Bar Association standards are to be used as guides to the reasonableness of counsel’s conduct. Rompilla v. Beard, 545 U.S. 374, 387, 125 S.Ct. 2456, 162 L.Ed.2d 360 (2005); see also Dickerson v. Bagley, 453 F.3d 690, 693 (6th Cir.2006). Under the 2003 ABA Guidelines for the Appointment and Performance of Defense Counsel in Death Penalty Cases, defense counsel must explore a defendant’s medical history when there has been a hospitalization. Dickerson, 453 F.3d at 693. This court has made clear that “counsel for defendants in capital cases must fully comport with these professional norms.” Id.
While these standards should not be read to require trial counsel to locate every tiny piece of information about a capital defendant, they do seem to require that an attorney locate medical records for a known, unusual, and likely traumatic procedure performed on that defendant as a child. Given the nature of a “chest reduction” performed on a thirteen year old boy, a reasonable attorney would have assumed that: (1) emotional distress would have resulted from the event, and (2) perhaps an underlying medical problem caused the rare condition. Both of these possibilities would have been useful mitigation evidence. Moreover, this was not a situation where it would have been sufficient to rely on the statements of Cornwell and his family. It is obvious from their testimony that Cornwell’s family did not understand the nature of the procedure. Beverly Terry, Cornwell’s mother, termed it a “cosmetic surgery” for breasts that were size 38, 39, or 40. LaShonda Cornwell, his sister, called him “lazy” and said that he had the surgery because he was fat and that it “got rid of his chest.” And Corn-well himself could not be expected to provide a full account of his medical history. He was thirteen years old at the time, has no medical training, and might well be embarrassed to give full details of the mastectomy. In addition to the fact that the medical records might contain a significant amount of mitigating evidence, defense counsel was aware of the surgery and thus knew that medical records concerning it existed. Thus, this is not a case where an attorney was looking for the “proverbial needle in a haystack and had good reason to doubt its existence.” Eady v. Morgan, 515 F.3d 587, 597 (6th Cir.2008).
It should be noted, however, that trial counsel otherwise did a fairly thorough investigation. For example, defense counsel interviewed several family members, friends, and a pastor, obtained school records, obtained other medical records5, and had a forensic psychologist meet with Cornwell and his family members. Moreover, defense counsel pulled together all of the known mitigating factors, such as Cornwell’s very unstable family environment, weight problems, and academic difficulties, to create a reasonably strong defense.
In most cases where the Supreme Court has found capital defense counsel to be insufficient, defense counsel almost entirely failed to investigate the defendant’s background or defense counsel stopped investigating even though it had no legitimate defense upon which to rely. For *408example, in Wiggins v. Smith, 539 U.S. 510, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003), defense counsel presented no evidence of the defendant’s severely dysfunctional childhood, which involved physical and sexual abuse and foster care. Id. at 516, 123 S.Ct. 2527. Instead, counsel relied only on a pre-sentence report and city social services records. Id. at 523-24, 123 S.Ct. 2527. The Court found the lack of further investigation particularly unreasonable given that counsel had not discussed any other mitigating evidence to at least create some kind of defense. Id. at 524-27, 123 S.Ct. 2527. Similarly, in Rompilla v. Beard, 545 U.S. 374, 125 S.Ct. 2456, 162 L.Ed.2d 360 (2005), the only mitigation offered by defense counsel were the pleas of the defendant’s family for mercy. Id. at 393, 125 S.Ct. 2456. In failing to do an investigation into the defendant’s background, defense counsel ignored “obvious” signs of a troubled childhood, alcoholism, and mental issues. Id. at 379, 125 S.Ct. 2456. Defense counsel was not, the Supreme Court held, permitted to simply rely on defendant’s claim that he had an unexceptional childhood given the absence of any other mitigating evidence. Id. at 377, 125 S.Ct. 2456. The court seemed particularly troubled in this case by defense counsel’s failure because a significant amount of mitigating evidence was located in defendant’s prior police record located in the same courthouse where defendant was then being tried. Id. at 389-90, 125 S.Ct. 2456. Defense counsel failed to examine that record even though the prosecution had made it known it planned to use that record. Id.
It could be argued that the level of investigation here greatly exceeded that done in Wiggins and Rompida so that a finding that counsel was not deficient would not be an unreasonable application of clearly established law. For purposes of this opinion, however, we assume, without deciding, that counsel’s performance was deficient.
We thus turn to whether this deficient performance prejudiced Cornwell’s defense. Cornwell’s post-conviction mental health expert, Dr. Kristen E. Haskins, indicates that “It would be important to know ... if [Cornwell] could possibly have a genetic disorder known as Klinefelter’s Syndrome, a primary symptom of which is enlarged breasts.” Dr. Haskins offers her opinion that “Cornwell’s endocrine, and perhaps genetic, problem was confounded with his weight problems,” a result that could have been avoided by careful review of the medical records. She adds, “[further information needs to be obtained to rule out ... a possible genetic disorder (Klinefelter’s Syndrome).” Cornwell also submitted a report about Klinefelter’s Syndrome, which described the condition and its symptoms. It noted that boys with the condition lack strength and agility and are not good at sports. They may be teased by their peers and may have lower self esteem than others during adolescence.
In evaluating whether it was unreasonable to conclude that Cornwell was prejudiced by the failure to provide medical records of the surgery to Eisenberg for review, we first note the impossibility of knowing whether Eisenberg would have suspected Klinefelter’s Syndrome had he seen the records. Nonetheless, we assume that he might have done so for purposes of this analysis. Whatever the status of Ei-senberg’s suspicions about Klinefelter’s Syndrome, Eisenberg would have had information not otherwise available to him. He would have known that Cornwell had underdeveloped genitalia and a testosterone deficiency, and he would have known the amount of breast tissue removed. He could have relayed this information to the jury.
*409Despite the new information that the medical records would have revealed, much of the evidence which might be presented if Cornwell were determined to have Klinefelter’s Syndrome is quite similar to mitigation evidence actually admitted at the penalty phase. The jury heard testimony about Cornwell’s weight problems, his large breasts, his learning difficulties, the teasing by other children, his poor performance at sports, and his low self esteem. They learned about the part all of these factors played in driving him to gang activity.
Ultimately, the difference between the proof the jury heard and the proof they would likely have heard had Eisenberg seen the medical records amounts to the additional information in the records. Potentially, they might also have heard that Cornwell had Klinefelter’s Syndrome. The end effect would have been that the jury would have understood that the surgery was related to a medical condition. To the extent that jurors thought that Cornwell had undergone a purely cosmetic procedure, this view would have been countered. And if Cornwell indeed had Klinefelter’s Syndrome, they would have learned that being overweight often accompanies the condition, thus countering any belief that Cornwell was overweight because he was lazy.
In evaluating prejudice, it is important to note that much mitigation proof not involving the surgery was presented to the jury. Moreover, proof of the aggravating factor — that the murder was committed as part of a course of conduct involving the purposeful killing or attempt to kill two or more people — was strong.
We are unable to conclude that it was objectively unreasonable for the state court to conclude that Cornwell was not prejudiced by any deficiency in counsel’s performance in failing to provide the medical records of the surgery to Eisenberg. The state courts could reasonably reject an assumption that jurors blame teenagers for their own weight problems and somehow consider those who are overweight or lazy or have cosmetic surgery more deserving of the death penalty than those who are thin or energetic or have surgery related to medical conditions. And the state courts could reasonably find that jurors would not focus on such factors in this case, given the other evidence of both mitigation and an aggravating factor. Our system of justice finds its foundation in the belief that average citizens can and will weigh all the evidence presented to them, follow the law, and reach a well-reasoned verdict. To conclude that jurors would consider Cornwell more culpable because he was overweight or lazy appears to reflect a distrust of the soundness of jury decisions — a view at odds with the guarantees of the Sixth Amendment and the underlying principles of our judicial system. The state court could reasonably have concluded that there was not a reasonable probability that the outcome of the trial would have been different if the medical records had been available to Eisenberg. Therefore, we affirm the district court’s denial of habeas relief as to this assignment of error.
2.
Cornwell argues that the district court erred in denying his motions for a genetic disorders expert and an evidentiary hearing. The district court denied an eviden-tiary hearing because, whether or not Cornwell had diligently sought to develop the factual bases of his claim in state court, he had not shown that an evidentia-ry hearing was necessary to develop the facts further. The district court denied the motion for a genetic disorders expert for the same reason. The Warden argues *410that both denials were proper. She does not address Cornwell’s diligence and, thus, neither contends nor implies that Cornwell failed to develop the factual bases of his claim in state court.
We review the district court’s denial of discovery in a habeas proceeding for an abuse of discretion. Williams v. Bagley, 380 F.3d 932, 974 (6th Cir.2004). Because a request for experts is a request for discovery, the discovery standard applies. For good cause shown, the district court has the discretion to permit discovery in a habeas proceeding, see Rule 6(a) of Rules Governing Section 2254 Proceedings for the United States District Courts, “provided that the habeas petitioner presents specific allegations showing reason to believe that the facts, if fully developed, may lead the district court to believe that federal habeas relief is appropriate.” Lott v. Coyle, 261 F.3d 594, 602 (6th Cir.2001). “Conclusory allegations are not enough to warrant discovery under Rule 6; the petitioner must set forth specific allegations of fact.” Williams, 380 F.3d at 974 (brackets and internal quotation marks omitted); see also id. (“Rule 6 does not sanction fishing expeditions based on a petitioner’s conclu-sory allegations”) (internal quotation marks and citation omitted)).
“This court reviews a district court’s decision whether to hold an eviden-tiary hearing for an abuse of discretion.” Vroman v. Brigano, 346 F.3d 598, 606 (6th Cir.2003). “If the petitioner has not failed to develop the factual basis of a claim in state court, the federal court may hold a hearing [when] the petitioner’s factual allegations, if proved, would entitle him to relief.” Id. However, “prisoners who are at fault for the deficiency in the state-court record must satisfy a heightened standard to obtain an evidentiary hearing.” Williams v. Taylor, 529 U.S. 420, 433, 120 S.Ct. 1479, 146 L.Ed.2d 435 (2000). Because the Warden does not contend that Cornwell was at fault or lacked diligence in developing the factual basis of the claim, we turn to consideration of whether the district court abused its discretion.
The district court did not abuse its discretion in denying the motion for a genetic disorders expert because the facts, if fully developed, would not have led the district court to believe that federal habeas relief was appropriate. This is true because, “in order to establish prejudice, the new evidence that a habeas petitioner presents must differ in a substantial way — in strength and subject matter— from the evidence actually presented at sentencing.” Hill v. Mitchell, 400 F.3d 308, 319 (6th Cir.2005).
In determining that Cornwell did not establish the prejudice prong of his ineffective assistance claim under Strickland, we took into account the possibility that Cornwell might have been determined to have Klinefelter’s Syndrome even though such a determination was speculation in the absence of further investigation by a genetics expert. We concluded, however, that a diagnosis of Klinefelter’s Syndrome would not have affected the outcome of the penalty phase or at least would not have rendered the state court finding of no prejudice objectively unreasonable. Given this conclusion, it can hardly have been an abuse of discretion for the district court to have denied discovery that would not have affected the outcome of the penalty phase.
C.
1.
Cornwell argues that racial bias tainted his prosecution. He asserts that the “state’s witness Edward Bunkley balked at putting Cornwell’s life at risk by making his testimony fit with the State’s theory of the case.” Cornwell also asserts *411that, in response to Bunkley’s reluctance, a Mahoning County prosecutor asked Bunk-ley: “Do you give a f* * * if we fry your n* * * * * or not?” Cornwell contends that this question “evinces obvious racial animus that tainted all of the proceedings against Cornwell” in violation of his rights to equal protection and due process.6
In post-conviction proceedings, the state court of appeals held that the trial court had not erred in denying this claim because, among other reasons, Cornwell had failed to demonstrate or produce any evidence that similarly situated individuals of a different race were not prosecuted. The district court held that the state court rejection of this claim was not contrary to, or an unreasonable application of, clearly established Supreme Court precedent.
“It is appropriate to judge selective prosecution claims according to ordinary equal protection standards.” Wayte v. United States, 470 U.S. 598, 608, 105 S.Ct. 1524, 84 L.Ed.2d 547 (1985). Thus, Cornwell must show that the prose-cutorial policy had a discriminatory effect and was motivated by a discriminatory purpose. Id. “To establish a discriminatory effect in a race case, the claimant must show that similarly situated individuals of a different race were not prosecuted.” United States v. Armstrong, 517 U.S. 456, 465, 116 S.Ct. 1480, 134 L.Ed.2d 687 (1996).
Assuming the prosecutor made the alleged statement with racial animus would at most show discriminatory purpose. As the state court of appeals correctly noted, Cornwell has completely failed to show discriminatory effect — that he was prosecuted while similarly situated individuals of a different race were not.
Denying that he must show a discriminatory effect, Cornwell argues that, under McCleskey v. Kemp, 481 U.S. 279, 107 S.Ct. 1756, 95 L.Ed.2d 262 (1987), he need only show that the decision makers in his case acted with discriminatory purpose. Reply at 17 (citing McCleskey, 481 U.S. at 292, 107 S.Ct. 1756). McCleskey, however, says that “a criminal defendant must prove that the purposeful discrimination had a discriminatory effect on him.” 481 U.S. at 292, 107 S.Ct. 1756 (internal quotation marks omitted). Armstrong, issued nine years later, clarified how that effect must be proven. 517 U.S. at 465, 116 S.Ct. 1480.
Consequently, we believe that the state court did not unreasonably apply clearly established Supreme Court precedent, nor did it make an unreasonable determination of the facts in light of the evidence presented.
2.
Cornwell argues that the state court and the district court improperly denied him an evidentiary hearing on his claim that racial bias tainted his prosecution. The state court argument is not cognizable in habeas corpus proceedings, which cannot be used to challenge errors or deficiencies in state court post-conviction proceedings. See Kirby v. Dutton, 794 F.2d 245, 247 (6th Cir.1986).
The Warden asserts that the certificate of appealability did not include this issue. It is closely related to the certified claim, however, so that it would not be unreasonable to read the COA as including both the *412former and the latter, if Cornwell had asked the district court for such a hearing. It appears, however, that Cornwell did not request an evidentiary hearing on this issue.
Assuming, however, that he had made such a request, or that the district court believed that he had done so, and assuming the issue is included within the COA, a hearing is not required. We review the district court’s denial of an evidentiary hearing for an abuse of discretion. Abdus-Samad v. Bell, 420 F.3d 614, 626 (6th Cir.2005). “In deciding whether to grant an evidentiary hearing, a federal court must consider whether such a hearing could enable an applicant to prove the petition’s factual allegations, which, if true, would entitle the applicant to federal habeas relief.” Schriro v. Landrigan, 550 U.S. 465, 127 S.Ct. 1933, 1940, 167 L.Ed.2d 836 (2007). Cornwell wants to present evidence that the prosecutor made the offending statement. This evidence, however, at most demonstrates discriminatory purpose and does not establish discriminatory effect. Therefore, Cornwell cannot show that his factual allegations, if proven, would entitle him to relief. In order to fill this gap, Cornwell offers to present evidence showing that similarly situated individuals of a different race were not prosecuted. Cornwell presented no such evidence in state court and advances no argument now that he diligently tried to present this evidence in state court. Hence, the evidence in question, to gain admittance, must “establish by clear and convincing evidence that but for constitutional error, no reasonable factfinder would have found the applicant guilty of the underlying offense.” 28 U.S.C.A. § 2254(e)(2)(B). The evidence fails to meet this threshold. Evidence that other persons were not prosecuted is not evidence that Cornwell is not guilty. If the district court did deny a hearing on this claim, such a denial was not an abuse of discretion.
D.
Cornwell had the right to the effective assistance of appellate counsel on his direct appeal to the Ohio Supreme Court because it was his first appeal of right. See Ohio Rev.Code Ann. § 2953.02; Evitts v. Lucey, 469 U.S. 387, 394, 105 S.Ct. 830, 83 L.Ed.2d 821 (1985). In order to show ineffective assistance of counsel, Cornwell must show both deficient performance and prejudice. Strickland, 466 U.S. at 687, 104 S.Ct. 2052.
Cornwell argues that appellate counsel were ineffective on direct appeal to the Ohio Supreme Court in failing to raise his claim that the trial court erred in denying Cornwell’s motion to suppress the eyewitness testimony of Donald Meadows. This subclaim was originally raised in Corn-well’s Mumahan motion, which the state supreme court denied in a standard order. The district court held that the claim lacked merit.
Because the Ohio Supreme Court’s order was unexplained, Cornwell argues that AEDPA deference does not apply. He is correct. Instead, modified AEDPA deference applies. Where the state court disposes of a constitutional claim but fails to articulate its analysis, this court conducts “an independent review of the record and applicable law to determine whether, under the AEDPA standard, the state court decision is contrary to federal law, unreasonably applies clearly established law, or is based on an unreasonable determination of the facts in light of the evidence presented.” Howard v. Bouchard, 405 F.3d 459, 467 (6th Cir.2005). Such a review is not de novo but is deferential because we “cannot grant relief *413unless the state court’s result contradicts the strictures of AEDPA.” Id. at 467-68.
“[C]onvictions based on eyewitness identification at trial following a pretrial identification by photograph will be set aside on that ground only if the photographic identification procedure was so impermissibly suggestive as to give rise to 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). “[E]ach case must be considered on its own facts.Id. In determining whether an identification is admissible, this court follows a two part analysis. The court first considers whether the procedure was unduly suggestive. Wilson v. Mitchell, 250 F.3d 388, 397 (6th Cir.2001); Ledbetter v. Edwards, 35 F.3d 1062, 1070-71 (6th Cir.1994). The court must decide if the procedure .itself steered the witness to one suspect or another, independent of the witness’s honest recollection. Wilson, 250 F.3d at 397. “The defendant bears the burden of proving this element.” Ledbetter, 35 F.3d at 1071 (citation omitted). If the procedure was suggestive, the court then determines whether, under the totality of the circumstances, the identification was nonetheless reliable and therefore admissible. Wilson, 250 F.3d at 397 (citation omitted); Ledbetter, 35 F.3d at 1071.
Ohio law forbids the introduction of evidence that was not part of the trial court’s record on appeal. See State v. Ishmail, 54 Ohio St.2d 402, 377 N.E.2d 500, 502 (1978). Appellate counsel were not ineffective for failing to introduce additional evidence, as state law prohibited them from doing so. This subclaim, therefore, focuses on the evidence presented at the time of trial. In other words, Corn-well’s argument is that appellate counsel were ineffective in not contending that the trial court, based purely on the evidence presented at the time of trial, erred in denying his motion to suppress.
Prior to the suppression hearing, Meadows identified Cornwell four times:
1) On June 12, 1996 (the day after the shooting), while in the hospital and heavily medicated with morphine, Meadows picked Cornwell’s photo out of a six-person photo array. “At that time[,] he was in obvious pain and apparently under the influence of the medication.” State v. Cornwell, No. 96-CR-525 at 1 (C.P. Mahoning County) (order denying motion to suppress). At first, Meadows had not made an identification, either because he did not want to get involved (according to police testimony summarizing Meadows’s answers) or because he did not recognize anyone (according to Meadows’s testimony), but the officer handed Meadows the array again and told him to take his time and make sure whether anyone was recognizable. It was then that Meadows identified Corn-well as possibly the driver of the car in question. Id. at 2.2) The next day, on June 13, 1996, the police again visited Meadows. According to their testimony, he did not seem to be “in the same type of pain or discomfort” and did not seem under the influence of the medication. Id. He again picked Cornwell out of the same photo array.
3) Four days later (June 17, 1996), Meadows was videotaped picking Corn-well’s photo from the same array. Id.
4) At the preliminary hearing (July 1, 1996, two weeks and six days after the shooting), Meadows picked Cornwell out of the group of codefendants in the case, who were also present in the courtroom. It was then that Meadows, for the first time, identified Cornwell as the shooter. Id.
*414When denying the suppression motion, the trial court found that there was no evidence the police had used suggestive identification procedures:
The victim testified that the police in no way suggested any of the particular persons in the photographic array prior to any of the identifications, nor did they indicate approval of or encouragement upon the identifications being made. The photographs were not numbered until the video tape identification procedure[;] however, in each of the previous identifications made by the victim, the Defendant was the person picked out. The entire exact same photographic array was shown to the victim on each of the occasions he was asked to look at the array. There is further testimony that[,] at the preliminary hearing in the Youngstown Municipal Court, Defendant was in the Courtroom with others charged in the crime. The victim was able to identify the Defendant as the perpetrator of this offense when he observed the Defendant and the others together in the Courtroom. There was no testimony of any prompting or improper conduct of the police at the preliminary hearing.
In support of his argument that Meadows’s testimony should have been suppressed, Cornwell cites many of the facts mentioned above. He includes: the initial failure of Meadows to identify anyone, his having been in pain and under the influence of morphine when he made the first identification, and his failure to identify Cornwell as the shooter until the preliminary hearing. He also notes that as time passed, Meadows became more certain in his identification but changed his mind about where Cornwell was sitting (first in the driver’s seat, then Meadows was not sure, then Cornwell sat behind the driver). Cornwell also emphasizes the difficulty of seeing the shooter. Cornwell also argues there is a possibility that Meadows made an unconscious transference based upon Meadow’s admission that he possibly saw Cornwell sometime before the shooting.
All of these arguments, however, go to the reliability of the identification, the second step of the analysis. None of the arguments relate to the suggestiveness of that procedure. Even Meadows’s having been in pain and under the influence of morphine when he first identified Cornwell shows, at most, that he was susceptible to suggestion, not that it occurred. Hence, Cornwell needs to point to something else in the identification procedure in order to supply the missing ingredient; nonetheless, he fails to do so.
To the contrary, Cornwell argues that, in the time between the initial identification when Meadows tentatively called him the driver and the preliminary hearing when Cornwell was identified as the shooter, Meadows saw television reports identifying Cornwell as a suspect. This argument fails for two reasons. First, it again goes to reliability of identification, not suggestiveness of procedure. Second, the evidence cited by Cornwell does not support his allegation. In the cited evidence, Meadows, when asked whether he had seen Cornwell’s picture on television news reports, replied, “I seen [sic] mainly when the ambulance came and was taking me away. That’s all I remember seeing ...”
Cornwell also fails to cite any evidence that the police themselves supplied suggestiveness. In his brief, Cornwell conceded that at the suppression hearing, “Meadows testified that the police officers were not doing anything to encourage him to pick out a photograph. He said that the police told him that someone had been arrested[,] but they did not give him the name of the person who had been arrested.”
*415Cornwell never suggests that the relevant state court decisions, the trial court denial of the suppression motion, and the Supreme Court rejection of the Mumahan motion were based on unreasonable determinations of the facts in light of the evidence presented. He does not show that the relevant state court factual findings were clearly erroneous. As the trial court found when denying the suppression motion, the police did nothing to suggest to Meadows that Cornwell was the person he should identify.
Cornwell fails to establish undue suggestion in the identification procedure itself, which he has the burden to prove. See Ledbetter, 35 F.3d at 1071. He, therefore, fails to show prejudice, an issue on which he has the burden of proof. See Strickland, 466 U.S. at 687, 104 S.Ct. 2052. This subclaim would fail even if it were reviewed de novo, and thus, it fails under modified AEDPA deference. Rejection of this subclaim by the Ohio Supreme Court was neither contrary to, nor an unreasonable application of, clearly established Supreme Court precedent and was not based on an unreasonable determination of the facts in light of the evidence presented. We affirm the district court’s denial of this subclaim.
E.
1.
Cornwell argues that the trial court erred by denying his motion to suppress Meadows’s testimony. In state post-conviction proceedings, the court of appeals held this claim meritless because “[t]he evidence relied upon fails the threshold of cogency and lacks credibility.” The district court held that the state court rejection of this claim was neither contrary to, nor an unreasonable application of, clearly established Supreme Court precedent.7
As Cornwell impliedly concedes AEDPA deference applies. Specifically, the “contrary to” clause applies because the state court of appeals, while explaining that the claim failed for lack of cogency and credi*416bility and mentioning the federal rights of due process and confrontation, applied no Supreme Court precedent. See Packer, 537 U.S. at 8, 123 S.Ct. 362.
Cornwell claims that the trial court erred in denying the suppression motion. He states in the heading in his federal habeas petition:
A TRIAL COURT ERRS WHEN IT DENIES A DEFENSE MOTION TO SUPPRESS THE TESTIMONY OF AN EYEWITNESS WHEN THAT WITNESS’S TESTIMONY IS UNRELIABLE AND THE RESULT OF A SUGGESTIVE PHOTOGRAPHIC LINE UP, IN VIOLATION OF U.S. CONST. AMEND. XIV
The body of the claim makes the same argument. Cornwell did ask this court to certify for appeal subclaims that trial counsel were ineffective in regard to the suppression hearing. As he did not set out the law, state or federal, governing such hearings, this panel did not certify them, and it is now too late for Cornwell to seek rehearing. See Slagle, 457 F.3d at 528-29.
Cornwell argues that the trial court erred in denying the suppression motion because evidence not presented or discovered until post-conviction proceedings shows that, after Meadows had tentatively picked out one photo, a police officer allegedly commented, “that’s the one guy we picked up[;] so far you doing good, Mr. Meadows.” He argues that this comment improperly enhanced Meadows’s certainty that he had identified the correct person. In further support of his argument, Corn-well cites evidence that also was not presented until post-conviction proceedings and that attacks the reliability of Meadows’s identification. He cites(l) the post-conviction admission by Meadows that, when the shootings occurred, he was under the influence of more marijuana and alcohol than he admitted at trial; and (2) firearm tests casting doubt on Meadows’s ability to see the shooter’s face by the light produced by the gunshots. None of this evidence is relevant to a claim of trial court error. The court did not err by failing to consider evidence it was unaware of at the time of trial.
To the extent this post-conviction argument is viewed as one asserting trial court error based on the evidence before it, the argument does not succeed. It fails for the reasons explained above with respect to the subclaim for ineffective assistance of appellate counsel. Essentially, the trial court did not err in denying the motion to suppress because Cornwell’s arguments relate to the weight to be given to the identification, not its admissibility.
It is unnecessary to consider Cornwell’s contention that the state court of appeals decision was based on an unreasonable determination of the facts in light of the evidence presented. That court found only that the post-conviction evidence lacked credibility. Even if it should have been found credible, it still was irrelevant. It was not contrary to clearly established Supreme Court precedent for the state court of appeals to find that irrelevant evidence was irrelevant or lacked “cogency.” We affirm the judgment of the district court denying this claim.
2.
Cornwell argues that he should have been granted an evidentiary hearing on the suppression both in state court and in federal court. The state court argument is not cognizable here.
The Warden responds that the federal court issue was not included within the COA. Assuming the issue has not been forfeited and that it was included within the COA because it was somewhat closely related to the certified claim, the argument *417fails. Any post-conviction evidence is irrelevant to this claim. Therefore, Corn-well cannot show that his factual allegations, if proven, would entitle him to relief. The district court did not abuse its discretion in denying an evidentiary hearing.
III.
For the foregoing reasons, we affirm the judgment of the district court denying Cornwell’s petition for habeas relief.
. Boom had been at the apartment earlier in the evening.
. State v. Murnahan, 63 Ohio St.3d 60, 584 N.E.2d 1204, 1209 (1992) (Ohio’s vehicle for bringing appellate counsel ineffectiveness claims).
. As the Warden contends, Cornwell’s brief at points encompasses generalized claims of failure to investigate that fall outside the scope of the certification. We confine our opinion to resolution of the certified issue.
. At various points Cornwell suggests that Ei-senberg referred to the surgical procedure as a "liposuction” at trial. In fact, Eisenberg calls it a "chest reduction.” Eisenberg uses the word "liposuction” only in recounting his question to Cornwell.
. For example, Eisenberg was given medical records about Cornwell's gunshot wound, car accident, and dog bite.
. Cornwell asserts that his rights under the Fifth Amendment were violated. We construe his claim as one brought under the Fourteenth Amendment, not the Fifth Amendment, because Cornwell was prosecuted by the state and the Fourteenth Amendment applies to state action. See San Francisco Arts & Athletics, Inc. v. U.S. Olympic Comm., 483 U.S. 522, 543 n. 21, 107 S.Ct. 2971, 97 L.Ed.2d 427 (1987).
. The opening paragraph of this claim, as stated in the federal habeas petition, states: “The trial court erred in failing to suppress the tainted, unreliable eyewitness testimony of Donald Meadows. The photo line up [sic] was so suggestive as to be unreliable.” Interpreting these two sentences as separate sub-claims, the district court held that the first had been raised during state post-conviction proceedings (as summarized above), but the second had only been raised in the Mumahan motion, and then as part of an ineffective assistance of appellate counsel claim. Despite this, the district court held that both subclaims had been preserved for habeas review.
It may be questioned whether the second quoted sentence represents a separate sub-claim, as opposed to a development of the argument begun in the first sentence: the trial court should have suppressed Meadows's unreliable testimony because it was the product of an unduly suggestive identification process. If this reading is accurate, the so called second subclaim is really just part of the post-conviction argument that the trial court erred in denying the motion to suppress the testimony of Donald Meadows.
If, on the other hand, Cornwell is advancing a second subclaim, there is still no need to consider whether he forfeited it in state proceedings, because he forfeited it here. Nowhere in his brief does he attack the photo lineup itself (the position of the photos in the array, the similarity or dissimilarity of Corn-well’s photo to the others, or the choice of which photo of Cornwell to use). Instead, he attacks, the photo lineup procedure: the allegedly suggestive comment the police officer made while Meadows was being shown that lineup. To the extent that Cornwell may be trying to advance some other photo lineup argument, it is forfeited. See United States v. Elder, 90 F.3d 1110, 1118 (6th Cir.1996) ("[I]t is a settled appellate rule that issues adverted to in a perfunctory manner, unaccompanied by some effort at developed argumentation, are deemed waived”) (internal quotation marks omitted).