GILMAN, J., delivered the opinion of the court, in which MARTIN, J., joined. BOGGS, J. (pp. 107-08), delivered a separate dissenting opinion.
OPINION
RONALD LEE GILMAN, Circuit Judge.Byron Black, who was tried in state court and sentenced to death in 1989 for committing three murders, appeals the district court’s denial of his petition for a writ of habeas corpus. He raises various issues related to the court’s 2001 denial of his original habeas petition as well as the court’s 2008 denial of his amended petition based on Atkins v. Virginia, 536 U.S. 304, 122 S.Ct. 2242, 153 L.Ed.2d 335 (2002). For the reasons set forth below, we AFFIRM the district court’s denial of Black’s habeas petition regarding his non-Atkins claims, VACATE the court’s judgment regarding his Atkins claim, and REMAND the case for further proceedings consistent with this opinion.
I. BACKGROUND
Black was convicted on three counts of first-degree murder for the killing of his girlfriend Angela Clay and her two minor daughters, Latoya, age nine, and Lakeisha, age six. He was also convicted on one count of burglary arising out of the same incident. Black received a death sentence for the murder of Lakeisha, consecutive life sentences for the other two murders, and fifteen years of imprisonment for the burglary.
A. Factual background
Black was born on March 23, 1956. He was 33 years old when the murders were committed in 1988. The Tennessee Supreme Court, in deciding Black’s claims on direct appeal, summarized the facts of this case, in part, as follows:
It appears that these bizarre and tragic murders occurred in the early morning hours of Monday, March 28, 1988. The bodies of the three victims were found Monday evening around 9:30 p.m. At the time of the murders, the Defendant was on [a] weekend furlough from the Metropolitan Workhouse in Davidson County....
The Defendant was the boyfriend of Angela Clay, who had separated from her husband, Bennie Clay, about a year before her death. Bennie Clay was the father of Latoya and Lakeisha. Bennie Clay testified that at the time of Angela Clay’s death, he and Angela were attempting to reconcile, but the Defendant was an obstacle to the reconciliation. He further testified that Angela began a relationship with the Defendant after their separation and that at times she was seeing both the Defendant and himself. In December, 1986, the Defendant and Bennie Clay had an altercation during a dispute over Angela____The Defendant pled guilty to the shooting [of Bennie Clay] and received the workhouse sentence, which included weekend furloughs.
State v. Black, 815 S.W.2d 166, 170-71 (Tenn.1991).
*85On the night of the murders, Black drove the victims to the home of Angela’s mother. Angela and her two daughters were last seen that evening by her mother at around 11 p.m. Angela’s mother testified that Angela telephoned her at approximately 11:20 p.m. that evening after Angela returned home. That phone call was the last time that any of the witnesses spoke to Angela before her death. The police arrived at Angela’s apartment at approximately 9:30 p.m. the following night. They did not find any signs of forced entry into the apartment, but they found a pool of blood on the bed and the body of a small child on the floor. Id. The Tennessee Supreme Court continued its summary of the relevant facts, citing the testimony of Dr. Charles Harlan, Chief Medical Examiner for Davidson County:
Investigation revealed the bodies of Angela and her nine year old daughter, Latoya, in the master bedroom. Angela, who was lying in the bed, had apparently been shot once in the top of the head as she slept and was rendered unconscious immediately and died within minutes ....
Latoya’s body was found partially on the bed and partially off the bed, wedged between the bed and a chest of drawers. She had been shot once through the neck and chest....
The body of Lakeisha, age six, was found in the second bedroom lying face-down on the floor next to her bed. She had been shot twice, once in the chest, once in the pelvic area....
The receiver from the kitchen telephone was found in the master bedroom. The telephone from the master bedroom was lying in the hallway between the two bedrooms. The Defendant’s fingerprints were the only prints recovered from the telephones. Two of his fingerprints were found on the phone in the hallway, and one was on the kitchen telephone receiver found in the master bedroom.
Id. at 171-72. A substantial amount of additional circumstantial evidence connected Black to the killings. Id. at 172-73.
B. Procedural history
In 1991, the Tennessee Supreme Court denied Black’s numerous claims on his direct appeal. Black then filed a petition for post-conviction relief in the Davidson County Criminal Court. The trial court denied the petition after an evidentiary hearing, and the Tennessee Court of Criminal Appeals (TCCA) affirmed. Black’s petition to appeal the denial of his post-conviction claims to the Tennessee Supreme Court was. denied. The United States Supreme Court subsequently denied his petition for a writ of certiorari.
Black then filed a petition for a writ of habeas corpus in the district court, based on 28 U.S.C. § 2254, seeking relief on a number of evidentiary, procedural, and substantive grounds relating to both the guilt and penalty phases of his trial, as well as to issues that arose in his various state-court appeals. The district court denied all 34 of Black’s habeas claims, including several subclaims, in December 2001. Black v. Bell, 181 F.Supp.2d 832 (M.D.Tenn.2001). It then issued Black a Certificate of Appealability (COA) for all of the claims that it decided on the merits and denied a COA regarding the claims that it dismissed as procedurally defaulted. Black timely appealed the court’s decision.
After the Supreme Court decided Atkins in 2002, this court granted Black’s motion to hold his case in abeyance so that Black could exhaust his Atkins claim in the state courts. Black then filed a motion in 2002 to reopen his post-conviction proceedings in the state trial court. That court determined that Black had made a sufficient *86showing for his case to be reopened based on his Atkins claim. It held an evidentiary hearing, but ultimately determined that Black is not mentally retarded under the Atkins standard. The TCCA affirmed this decision in 2006, and the Tennessee Supreme Court denied Black’s application for permission to appeal. The United States Supreme Court again denied Black’s petition for a writ of certiorari. This court then remanded Black’s pending appeal of the district court’s denial of his § 2254 petition back to the district court so that it could reconsider Black’s mental-retardation claim (which was one of Black’s original 34 claims that the district court denied) in light of Atkins.
The district court did so in 2008, ultimately dismissing Black’s Atkins claim on the basis that “the state court was not unreasonable in stating that the proof in the record did not support the conclusion, under a preponderance of the evidence standard, that [Black’s] I.Q. was below seventy before age 18.” It also dismissed Black’s additional claim that the issue of his mental retardation should have been submitted to the jury, ruling that the claim was beyond the scope of this court’s remand order, and also because the claim failed on the merits. But the district court granted Black a COA on his Atkins claim, and Black timely filed an appeal. We then granted Black’s motion to expand his COA to include the issue of whether he had cause to excuse the procedural default of his claim that the jury improperly weighed an unconstitutional felony-murder aggravating circumstance. But we denied Black’s motion to have two additional issues included in his COA.
Black’s appeal of the district court’s original dismissal of his habeas claims in 2001 and his appeal of that court’s denial of his Atkins claim in 2008 have been consolidated in the present appeal. We thus have before us the issues that are within his COAs from both decisions. Although Black’s COAs cover many issues, he has limited his appeal to a total of five.
In addition to Black’s Atkins claim, the other ■ four district-court determinations that Black now challenges are (1) whether he was competent to stand trial and whether he was entitled to an evidentiary hearing on that issue, (2) whether his trial counsel was constitutionally ineffective in failing to fully investigate, present, and argue mitigating factors against the death penalty, (3) whether his trial counsel was constitutionally ineffective in failing to object to the prosecution’s comment during closing argument at the penalty phase of the trial that giving Black a life sentence for all three of the murders would “reward” him, and (4) whether the trial court erred by declining to clarify for the jury, upon its request, the effect of a life sentence.
C. Atkins background
Under Tennessee law, capital defendants are considered mentally retarded if (1) they have “[significantly subaverage general intellectual functioning as evidenced by a functional intelligence quotient (I.Q.) of seventy (70) or below; (2) [they have d]eficits in adaptive behavior; and (3) [t]he intellectual disability must have been manifested during the developmental period, or by eighteen (18) years of age.” Tenn.Code Ann. § 39-13-203(a).
Each side presented conflicting evidence concerning whether Black qualifies as mentally retarded. At Black’s post-conviction proceedings on his Atkins claim, he presented four lay and three expert witnesses, the affidavit of another expert, and numerous exhibits in support of his claim. The State presented two expert witnesses in opposition. In addition, the state court considered the testimony of numerous lay *87and expert witnesses who testified during the course of Black’s pre-Atkins proceedings.
1. Black’s numerical I.Q. scores
One major category of evidence dealt with Black’s numerical I.Q. scores. In its post-conviction opinion on Black’s Atkins claim, the TCCA observed that Black’s intelligence has been tested numerous times, from his grade-school years through 2001. Black v. State, No. M2004-01345CCA-R3-PD, 2005 WL 2662577, at *13 (Tenn.Ct.Crim.App. Oct. 19, 2005). These scores can be grouped into the following three categories: (1) tests that were administered while Black was in elementary school, with the scores ranging from 83 to 97; (2) tests that were taken in preparation for Black’s trial and during his first round of post-conviction proceedings, from 1988 to 1997, which ranged from 73 to 76; and (3) tests that were administered in 2001 by Black’s experts who testified at his Atkins hearing, which ranged from 57 to 69. In addition, Black took achievement tests in high school. Dr. Daniel Grant, a psychologist and one of Black’s expert witnesses, explained that Black’s scores on the Differential Aptitude Test in the ninth grade placed his level of intelligence in the mentally retarded range.
A major point of contention in the present case, and an issue that the TCCA did not resolve, is which set of scores most accurately reflects Black’s level of intelligence by the time he was 18 years of age. Although Black’s first set of I.Q. scores were taken during this key period of his life and are above 70, his experts challenge the accuracy of these scores based on the sparse information concerning the testing details as well as the questionable supervision of Black’s academic progress at his segregated elementary school.
Black’s I.Q. scores from 1988 through 1997 were also above 70, but Dr. Grant opined that, when adjusted for the “Flynn Effect” and/or the standard error of measurement (SEM) that applies to these tests, these scores should be considered 70 or below. As Dr. Grant explained, the Flynn Effect calls for adjusting downward the score that a subject receives on an older I.Q. test based on the idea that the general population’s level of knowledge increases over time, thereby raising the average score obtained on older tests. Dr. Patti van Eys, a clinical psychologist who submitted an affidavit regarding her evaluation of Black, noted that the Flynn Effect is “broadly accepted by the psychological community and recognized by the American Association on Mental Retardation (AAMR).”
On the other hand, State witness Dr. Susan Vaught, a clinical psychologist, testified that although the Flynn Effect is a recognized issue that a clinician might consider when interpreting an I.Q. test, she did not think that it should be used to adjust the numerical score that a subject received on his or her test. She explained that “[y]ou don’t apply a numerical correction to a score that you get based on the Flynn Effect. It’s not in that kind of use amongst clinicians who test[].” Dr. Eric Engum, the other clinical psychologist for the State, also rejected the practice of correcting for the Flynn Effect because “[o]ne cannot arbitrarily ... go back in time and ‘correct’ or ‘recalculate’ a previously obtained IQ based on [subsequent] changes in standardization.”
As for the SEM, Dr. Grant testified that because the I.Q. score achieved on any particular test is fallible, the scores generally involve a SEM of five points up or down from the given score. Dr. Vaught similarly stated in her report that it is “typical and expected” under the prevail*88ing standard of practice “to consider the [SEM] for any given test in order to determine if a patient’s score could fall below 70.”
The experts also disagree about the relevance of Black’s 2001 I.Q. scores. Dr. Vaught conceded that, based on these most recent I.Q. scores, Black “currently meets the first criterion for mental retardation.” Black, 2005 WL 2662577, at *14. But she and Dr. Engum were suspicious of the scores’ validity based on comparisons to other indications of Black’s level of intelligence. They suspected that Black was malingering (i.e., artificially deflating his scores) during these later tests. Black’s experts, on the other hand, specifically determined that he was not malingering, and they were highly critical of the opinion of the State’s experts that Black was malingering based solely on the written record, without having personally interviewed him.
Black’s experts determined that his I.Q. fell in the mentally retarded range by the time he was age 18, but the State’s experts disagreed. Dr. Vaught, in particular, noted that although Black’s poor academic performance was “highly suggestive of learning disability or borderline intellectual capacity,” she found “no compelling evidence that the lower-functioning picture I see now in Mr. Black’s intellectual testing emerged prior to 18.”
2. Black’s brain damage
Another key point of contention is whether Black suffered from brain damage at an early age. Dr. Albert Globus, an expert in psychiatry and neurology who examined Black in 2001 in order to assess his competency to stand trial, reexamined him just before the state court’s post-conviction hearing. In addition, Dr. Ruben Gur, an expert in neuropsychology, testified in a video deposition taken after the hearing regarding the cause of Black’s brain damage. Both Drs. Globus and Gur concluded, based on MRI and PET-scan images of Black’s brain, that Black has extensive brain damage that was likely caused by his mother’s drinking alcohol while pregnant, but might also have been caused by other occurrences during his childhood.
The State does not contest that Black currently has brain damage. But the source of his condition is highly disputed. This point is important to the assessment of Black’s level of intelligence by the time he was age 18. If his current brain damage existed at an earlier stage of his life, then his current level of intelligence is all the more probative of his intellectual capacity at that earlier stage because any symptoms resulting from his brain damage would have also been present earlier on. Moreover, if Black’s brain was damaged earlier in his life, that determination would impact the credibility of the conclusion by the State’s experts — who never personally met with Black — that he was malingering on his recent I.Q. tests. Rather than offer an alternative explanation for his brain damage, the State argues that Black did not sufficiently prove that his brain damage was caused by the time he was age 18.
3. Expert assessments of Black’s adaptive deficits
In addition to assessing Black’s numerical I.Q. level, the various expert witnesses at his state post-conviction Atkins hearing testified regarding his level of adaptive functioning. These experts explained how Black functions in society and when his relevant characteristics manifested themselves. They dispute whether Black displays adaptive deficits and, if so, when these problems arose.
Black’s experts explained that he has difficulty interacting according to ordinary social conventions and that he is paranoid, *89delusional, naive, and inappropriately happy. They also determined that he has deficits in his communication and functional academic skills and that he displays symptoms of various psychiatric disorders. Based on Black’s childhood experiences, as well as the alleged early onset of his brain damage, Black’s experts concluded that he had adaptive deficits by the age of 18.
But the State’s experts determined that Black displayed adequate skills across a variety of practical, social, and intellectual categories of behavior. Although they thought that Black had various personality problems and that he might suffer from various mental disorders, they did not think that Black qualified as mentally retarded. The State’s experts also determined that to the extent Black displayed adaptive deficits, he either strategically presented himself in that way (according to Dr. Engum) or had deteriorated more recently and therefore did not display these characteristics by the age of 18 (according to Dr. Vaught). After recounting some of the expert testimony on these issues, the TCCA concluded that Black did not meet his burden of proof to show that he had sufficient deficits in his adaptive behavior by the age of 18.
4. Lay witnesses
Black presented four lay witnesses at his Atkins post-conviction hearing to testify regarding various aspects of his social and educational history. Mary SmithsonCraighead, who started working as an administrator at Black’s elementary school in 1965 and was in charge of Black’s grade level for, at most, a year and a half, testified regarding the conditions at Black’s school. Black’s sister, Melba Corley, talked about Black’s upbringing. A1 Dennis, Black’s high school football coach, discussed Black’s experience on the football team. Finally, Richard Corley, Black’s brother-in-law, testified about Black’s job as a courier at an insurance company. Both sides draw on various aspects of these witnesses’ testimony to support their respective positions concerning Black’s level of intellectual functioning and his adaptive behavior by the age of 18.
5. Prior decisions on Black’s Atkins claim,
The state trial court determined that Black’s post-conviction Atkins claim merited an evidentiary hearing. At this evidentiary hearing, Black had the burden of showing by a preponderance of the evidence that he met Tennessee’s definition of mental retardation under Atkins. After the hearing concluded, the court summarized what it viewed as the determinative evidence from the voluminous record and, based on this evidence, denied Black’s Atkins claim for post-conviction relief.
The TCCA affirmed the trial court’s rejection of Black’s claim. In its “Analysis” section, the TCCA mostly reviewed, without taking a stance on, the conflicting expert assessments of the factual record. But the TCCA did recognize that, according to Black’s experts, the Flynn Effect and/or the SEM brings his middle set of I.Q. scores into the mentally retarded range. Based on Howell v. State, 151 S.W.3d 450, 457 (Tenn.2004), however, the TCCA determined that it was prohibited from considering these scientific concepts in assessing Black’s numerical I.Q. score.
The TCCA’s assessment of the factual record also makes clear that it was skeptical of the opinions of Drs. Globus and Gur regarding when Black’s brain damage occurred. But the TCCA did not go so far as to make a definitive factual conclusion regarding the date of onset of Black’s brain damage. The court also discounted Dr. Grant’s conclusion that Black displayed deficits in his adaptive behavior *90because, although Dr. Grant observed that Black had never engaged in a number of commonplace activities, “there is no proof in the record that [Black] was unable to do these things.” Black, 2005 WL 2662577, at *15. It also pointed out that none of Black’s childhood I.Q. scores fell in the mentally retarded range. But the TCCA reached its ultimate conclusion that “the proof in the record simply does not support that [Black’s] I.Q. was below seventy or that [Black] had deficits in his adaptive behavior prior to age eighteen” without stating which pieces of evidence were essential to its conclusion. Id. at *17.
In denying habeas relief to Black on his Atkins claim, the district court approvingly referenced the TCCA’s rejection of the application of the Flynn Effect and the SEM based on Howell. It also concluded, based on a review of how other jurisdictions have dealt with the Flynn Effect, that the TCCA’s rejection of these concepts did not render the state process arbitrary, unreasonable, or less than full and fair.
The district court further rejected Black’s three remaining arguments in support of his Atkins claim. First, the court determined that the TCCA’s discounting of Dr. Grant’s adaptive-deficits assessment did not render the state court’s decision unreasonable. It found no basis to question the TCCA’s ruling that, although the record indicated that Black had not performed the commonplace daily tasks mentioned by Dr. Grant, there was no showing that Black could not perform these tasks. Second, the court concluded that because Black had not shown that an aptitude test is equivalent to an I.Q. test, his low ninth-grade Differential Aptitude Test scores did not mean that his I.Q. was 70 or below by age 18.
Finally, the district court noted that “the evidence before the state court ... may or may not indicate that [Black’s brain damage] existed and caused mental retardation” by the time Black was 18 years of age. The court based this observation on its determination that Drs. Globus and Gur were unable to point definitively to the cause of Black’s brain damage or establish that this injury was the cause of Black’s mental retardation. It also quoted the TCCA’s reference to “Dr. Vaught’s testimony explaining the difference between mental illness and mental retardation, and her conclusion that [Black’s] early difficulties were likely caused by mental health issues or learning disabilities, rather than mental retardation.”
II. ANALYSIS
A. Standard of review
Because Black filed his habeas petition after the enactment of the Antiterrorism and Effective Death Penalty Act of 1996 (AEDPA), AEDPA’s provisions apply to his case. Murphy v. Ohio, 551 F.3d 485, 493 (6th Cir.2009). This court in Murphy set out the standard of review under AED-PA as follows:
Under AEDPA, a federal court may grant a writ of habeas corpus with respect to a “claim that was adjudicated on the merits in state court proceedings” if the state court’s decision “was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States.” 28 U.S.C. § 2254(d)(1). A habeas petition may also be granted if the state court’s decision “was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.” Id. § 2254(d)(2). A state-court decision is contrary to clearly established federal law “if the state court applies a rule that contradicts the gov*91erning law set forth in [the Supreme Court’s] cases” or “if the state court confronts a set of facts that are materially indistinguishable from a decision of [the Supreme] Court and nevertheless arrives at a result different from [that] precedent.” Williams [v. Taylor, 529 U.S. 362, 405, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000) ]. A state-court decision is an unreasonable application of clearly established federal law if it “correctly identifies the governing legal rule but applies it unreasonably to the facts of a particular prisoner’s case,” id. at 407-08, 120 S.Ct. 1495, or if it “either unreasonably extends or unreasonably refuses to extend a legal principle from Supreme Court precedent to a new context,” Seymour v. Walker, 224 F.3d 542, 549 (6th Cir.2000).
Id. at 493-94. And, as the Supreme Court recently explained, our review under § 2254(d)(1) is “limited to the record that was before the state court.” Cullen v. Pinholster, — U.S. -, 131 S.Ct. 1388, 1398, 179 L.Ed.2d 557 (2011).
B. Atkins claim
Black claims that he is not subject to the death penalty because he is mentally retarded, so that his execution would violate Atkins v. Virginia, 536 U.S. 304, 122 S.Ct. 2242, 153 L.Ed.2d 335 (2002). A few months before Atkins was decided, the Tennessee Supreme Court also held as a matter of first impression in Van Tran v. State, 66 S.W.3d 790 (Tenn.2001), that the Eighth Amendment to the United States Constitution and Article I, Section 16 of the Tennessee Constitution prohibit the execution of mentally retarded individuals. Id. at 794, 812. Van Tran further held that its newly announced rule applied retroactively to cases on collateral review. Id. at 811.
The Supreme Court held in Atkins that, in light of “our evolving standards of decency,” the Eighth Amendment prohibits the execution of mentally retarded offenders. Id. at 321, 122 S.Ct. 2242. But the Court in Atkins did not define what it means to be “mentally retarded,” instead “leavfing] to the States the task of developing appropriate ways to enforce the constitutional restriction upon their execution of sentences.” Id. at 317, 122 S.Ct. 2242 (brackets omitted) (quoting Ford v. Wainwright, 477 U.S. 399, 405, 416-17, 106 S.Ct. 2595, 91 L.Ed.2d 335 (1986) (dealing with the issue of insanity)).
Under Tennessee law, capital defendants are considered mentally retarded for the purposes of an Atkins claim if they have an “intellectual disability” under § 39-13-203(a) of the Tennessee Code. Howell v. State, 151 S.W.3d 450, 457 (Tenn.2004). Defendants will meet this standard if (1) they have “[significantly subaverage general intellectual functioning as evidenced by a functional intelligence quotient (I.Q.) of seventy or below; and (2) [they have deficits in adaptive behavior; and (3) [t]he mental retardation must have been manifested during the developmental period, or by eighteen (18) years of age.” Tenn.Code Ann. § 39-13-203(a). Under Tennessee law, defendants have the burden of showing, by a preponderance of the evidence, that they qualify under this statutory definition. See Tenn.Code Ann. § 39-13-203(e).
In Coleman v. State, 341 S.W.3d 221 (Tenn.2011), the Tennessee Supreme Court recently issued a significant decision explaining the Atkins standard under Tennessee law. The State argues that this “recent state-law decision can have no impact on the reasonableness of the state courts’ application of federal law or on the reasonableness of the state courts’ factual determinations in light of the evidence presented in state court.” This argument raises three distinct objections to our con*92sideration of Coleman, all of which we find have no merit.
1. Application of Coleman in the present case
First, citing Cullen v. Pinholster, — U.S. -, 131 S.Ct. 1388, 179 L.Ed.2d 557 (2011), the State argues that, under AED-PA, Black is limited to the record that was before the state court at the time the latter rendered its decision. But Cullen explicitly dealt with the parameters of the factual record that the district court may consider on habeas review. Id. at 1399-1400. Coleman, however, elucidates Tennessee’s interpretation of Atkins’s legal standard. Cullen therefore does not prevent us from considering Coleman’s interpretation of Atkins under Tennessee law.
The state also focuses on the fact that Coleman is a “recent state-law decision.” But the date of the Coleman decision does not prevent us from considering its impact on the present case because Atkins “has been made retroactive to cases on collateral review.” In re Bowling, 422 F.3d 434, 436 (6th Cir.2005).
And because “Atkins reserved for the states ‘the task of developing appropriate ways to enforce the constitutional restriction,’ ” id. at 436-37 (quoting Atkins, 536 U.S. at 317, 122 S.Ct. 2242), federal courts conducting habeas review routinely look to state law that has been issued after the defendant’s state conviction has become final in order to determine how Atkins applies to the specific case at hand. See Hill v. Anderson, 300 F.3d 679, 682 (6th Cir.2002) (remanding Hill’s Atkins habeas claim to the Ohio state courts to “develop [their] own procedures for determining whether a particular claimant is retarded and ineligible for death”); Wiley v. Epps, 625 F.3d 199, 208 (5th Cir.2010) (assessing whether the defendant qualified for an evidentiary hearing on his Atkins claim based on the Mississippi Supreme Court’s standard even though “Wiley was convicted before Atkins was decided, and although he filed his state post-conviction application before the Mississippi Supreme Court established the state’s requirements for obtaining an Atkins hearing”). We will therefore consider Coleman in our review of Black’s Atkins claim under AEDPA. See Fulcher v. Motley, 444 F.3d 791, 822 (6th Cir.2006) (Clay, J., concurring) (explaining that even where a Supreme Court precedent applies retroactively, a federal court conducting habeas review of a state-court decision must still determine whether the decision was “contrary to” the retroactively applicable Supreme Court precedent).
2. Signiñcantly subaverage intellectual functioning
Under the Tennessee Code, the first requirement that a defendant must meet in order to be considered mentally retarded under Atkins is that he or she must have “[significantly subaverage general intellectual functioning as evidenced by a functional intelligence quotient (I.Q.) of seventy (70) or below.” Tenn.Code Ann. § 39-13-203(a). The Tennessee Supreme Court has determined that the statute’s incorporation of an I.Q. score of 70 is a “bright-line cutoff’ that does not account for “a standard error of measurement in the test scores nor consideration of any range of scores above the score of seventy.” Howell v. State, 151 S.W.3d 450, 458-59 (Tenn.2004). But even this bright-line cutoff allows for the consideration of more than one single source in determining a defendant’s I.Q. Because the Tennessee statute “does not provide a clear directive regarding which particular test or testing method is to be used” to determine whether an individual is mentally retarded for purposes of death-penalty eligibility, “[a] *93court may certainly give more weight to one test, but should do so only after fully analyzing and considering all evidence presented.” Id. at 459.
One of the defendant’s full-scale I.Q. scores in Howell was a 73 on the WAIS— III test. Id. at 453. In support of his Atkins claim, the defendant presented the testimony of Dr. Daniel Grant (who also testified on Black’s behalf in the present case) that a score on an I.Q. test represents a ten-point range of possible scores based on a five-point SEM in either direction. Id. When the SEM was considered, according to Dr. Grant, the defendant’s I.Q. score of 73 in Howell fell in the mentally retarded range. Id. at 453-54. But the Tennessee Supreme Court determined that Tennessee law provides a “bright-line cutoff’ for determining whether a defendant’s I.Q. is 70 or below. Id. at 458-59. The Court therefore agreed with the trial court’s refusal to interpret “the requirement of an I.Q. of seventy or below, as contained in the Tennessee statute, ... as representing a range of scores between sixty-five and seventy-five or below.” Id. at 457. Based on this reasoning, the defendant’s score of 73 was not in the mentally retarded range. (But the Court in Howell remanded the case for an evidentiary because the lower court imposed an overly demanding burden of proof on the defendant. Id. at 465, 467.)
Turning now to the case at hand, Black argues that the Flynn Effect and the SEM should be considered in determining his functional I.Q. level. Black’s experts, as explained above, applied the Flynn Effect to correct for the outdated nature of the I.Q. test that was taken. I.Q. scores are sealed so that the average score on any test should be 100, but the Flynn Effect postulates that the longer that an I.Q. test has been in existence, the higher the average score will be. See United States v. Davis, 611 F.Supp.2d 472, 486 (D.Md.2009) (explaining that “the Flynn Effect means ... that over time, the test norms become outdated, such that the average score is no longer 100, but something higher”). This increase in the general level of factual information that leads to higher average scores on older tests explains why I.Q. test scores would increase with the age of the test “without a corresponding increase in actual intelligence in the general population.” Wiley v. Epps, 625 F.3d 199, 203 n. 1 (5th Cir.2010). According to the Flynn Effect, scores on outdated tests thus need to be corrected for this upward deviation in the average score. Id. The SEM, on the other hand, “is an index of the variability of test scores produced by persons forming the normative sample” that “allows the evaluator to know the amount of error that could be present in any test.” Thomas v. Allen, 607 F.3d 749, 753 (11th Cir.2010).
As the TCCA noted, Black’s experts testified that his adult I.Q. scores, including pre-Atkins scores, “fell within the mentally retarded range when adjusted by the [SEM] and/or the Flynn Effect.” Black, 2005 WL 2662577, at *14. But the court refused to consider this testimony because it concluded that Howell’s bright-line cutoff prohibited accounting for these adjustments under Tennessee law. Id. Coleman directly addresses this interpretation of Howell.
a. The Coleman decision
The defendant in Coleman brought an Atkins claim to challenge his death sentence. As part of his proof that his I.Q. score was in the mentally retarded range under Tennessee law, Coleman offered evidence regarding the impact of the Flynn Effect and the SEM in determining his ultimate I.Q. score. But the TCCA in Coleman determined, based on Howell, *94that Tennessee law does not provide “for the application of any standard error of measurement, including the ‘Flynn effect,’ to establish an IQ range rather than the bright-line cutoff of 70.” Coleman v. State, No. W2007-02767-CCA-R3-PD, 2010 WL 118696, at *18 (Tenn.Crim.App. Jan. 13, 2010).
The Tennessee Supreme Court in Coleman acknowledged that Howell correctly interpreted the Tennessee statute in holding that “an expert’s opinion regarding a criminal defendant’s I.Q. cannot be expressed within a range (i.e., that the defendant’s I.Q. falls somewhere between 65 to 75) but must be expressed specifically (i.e., that the defendant’s I.Q. is 75 or is ‘seventy (70) or below1 or is above 70).” Coleman, 341 S.W.3d at 242. But the lower state courts had misinterpreted Howell by extending its reasoning too far. As the Tennessee Supreme Court explained,
following Howell v. State, some trial courts and the Court of Criminal Appeals have construed our holding that Tenn.Code Ann. § 39-13-203(a)(l) provided a “clear and objective guideline” for determining whether a criminal defendant is a person with intellectual disability to have established a mandatory requirement that only raw I.Q. test scores may be used to determine whether a criminal defendant has “significantly impaired general intellectual functioning” and that a raw I.Q. test score above seventy (70) may be sufficient, by itself, to disprove a criminal defendant’s claim that he or she is a person with intellectual disability.
Id. at 240.
The Tennessee Supreme Court noted in Coleman that the Tennessee Code “does not provide clear direction regarding how a person’s I.Q. should be determined and does not specify any particular test or testing method that should be used. In fact, the statute does not even employ the words ‘test’ or ‘score.’ ” Id. at 241 (citation omitted). The statute’s purpose is for the courts to arrive at the defendant’s true functional I.Q. score. Id. But “[b]eeause the statute does not specify how a criminal defendant’s functional I.Q. should be determined, we have concluded that the trial courts may receive and consider any relevant and admissible evidence regarding whether the defendant’s functional I.Q. at the time of the offense was seventy (70) or below.” Id. The practical import of this reasoning is that
if the trial court determines that professionals who assess a person’s I.Q. customarily consider a particular test’s standard error of measurement, the Flynn Effect, the practice effect [which refers to increasing test scores based on an individual being retested with the same or a similar test], or other factors affecting the accuracy, reliability, or fairness of the instrument or instruments used to assess or measure the defendant’s I.Q., an expert should be permitted to base his or her assessment of the defendant’s “functional intelligence quotient” on a consideration of those factors.
Id. at 242 n. 55.
Allowing for the consideration of these factors was also found by the Court to be “consistent with current clinical practice,” which may “require information from multiple sources.” Id. at 244. Intelligence tests are just one of these sources. And because intelligence tests “are indirect rather than direct measures of intelligence, experts in the field recognize that they, like other measures of human functioning, are not actuarial determinations, that these tests cannot measure intelligence with absolute precision and that these tests contain a potential for error.” Id. at 245 (citations, brackets, and internal quo*95tation marks omitted). Moreover, recent practice in the Tennessee courts
reflect[s] the parties’ and the courts’ existing awareness that, as a practical matter, a criminal defendant’s “functional intelligence quotient” cannot be ascertained based only on raw I.Q. test scores. More importantly, they also reflect the parties’ conclusion that Tenn. Code Ann. § 39-13-203(a) does not prevent them from presenting relevant and competent evidence, other than the defendant’s raw I.Q. test scores, either to prove or to disprove that the defendant’s “functional intelligence quotient” when the crime was committed was “seventy (70) or below.”
Id. at 247-48.
The Coleman decision also recognized that “[ascertaining a person’s I.Q. is not a matter within the common knowledge of lay persons. Expert testimony in some form will generally be required to assist the trial court in determining whether a criminal defendant is a person with intellectual disability for the purpose of Tenn. Code Ann. § 39-13-203(a).” Id. at 241. “In formulating an opinion regarding a criminal defendant’s I.Q. at the time of the offense, experts may bring to bear and utilize reliable practices, methods, standards, and data that are relevant in their particular fields.” Id. at 242. These expert opinions are subject to cross-examination, and the trial court is not bound to follow any particular expert. Id. But the trial court “must give full and fair consideration to all the evidence presented.” Id.
b. Applying Coleman to the present case
The Tennessee Supreme Court went to great lengths in Coleman to explain why its decision comported with its own prior precedent, Tennessee statutory law, other states’ statutes, current clinical practice (which Atkins itself noted is generally incorporated in the various statutory definitions), and current litigation practice. Id. at 240-48. Even absent the Court’s guidance in Coleman, the TCCA in the present case clearly misinterpreted the Flynn Effect’s relevance under Howell. Although Howell emphasized the need to reach a single functional I.Q. score under Tennessee law, the decision made no mention whatsoever of the Flynn Effect. The purpose of adjusting for the Flynn Effect, after all, is to determine the single specific score that most accurately reflects the subject’s I.Q. And unlike the SEM, adjusting for the Flynn Effect yields only one score. See United States v. Davis, 611 F.Supp.2d 472, 488 (D.Md.2009) (correcting for the Flynn Effect was found appropriate in order to more accurately determine whether the defendant met the “strict numerical cutoff’). Considering the Flynn Effect in determining a defendant’s I.Q. score is therefore entirely consistent with Howell’s stated goal of assessing whether a defendant’s single I.Q. score, rather than a range of scores, meets the statute’s “bright-line cutoff.”
Whether Coleman’s holding regarding the SEM clarifies Howell or deviates from Howell is more ambiguous. On the one hand, Coleman affirmed Howell’s holding that the Tennessee statute requires that an expert’s assessment must be expressed in terms of a specific I.Q. score rather than a range of scores. Coleman, 341 S.W.3d at 242. On the other hand, the Court held that an expert should be permitted to consider “a particular test’s standard error of measurement [the SEM], the Flynn Effect, the practice effect,” or other “reliable practices, methods, standards, and data” in assessing the defendant’s I.Q. Id. at 242 & n. 55. Coleman might therefore best be read as clarifying that although Howell prohibits interpreting the Tennessee stat*96ute “as representing a range of scores,” Howell, 151 S.W.3d at 457, it does not prevent the SEM, as well as all other relevant scientific evidence, from being used by an expert in determining a defendant’s single most accurate functional I.Q. score. See Duncan v. United States, 552 F.3d 442, 444-45 (6th Cir.2009) (explaining that “a decision does not announce a new rule when it is merely an application of the principle that governed a prior Supreme Court case” (internal quotation marks omitted)). In any event, regardless of whether Coleman clarified Howell’s holding or changed it regarding the SEM, the Tennessee Supreme Court’s recent elucidation of the Atkins standard under Tennessee law must be applied in the present case in light of our earlier conclusion regarding Coleman’s retroactive applicability-
Coleman is particularly applicable because the TCCA’s decision in the present case was cited to support the TCCA’s conclusion in Coleman (before Coleman reached the Tennessee Supreme Court) that although evidence concerning the Flynn Effect or the SEM may be introduced into the record, neither of these factors may impact the court’s ultimate determination of the defendant’s specific I.Q. score. Coleman v. State, No. W200702767-CCA-R3-PD, 2010 WL 118696, at *18 (Tenn.Crim.App. Jan. 13, 2010). The TCCA in Coleman explained that “both in Black and the present case, a challenge is made to the veracity of the bright-line cutoff of 70 in establishing whether a defendant is not subject to the death penalty.” Id. It then held that because Coleman, like Black, was allowed to present evidence regarding the Flynn Effect and the SEM, the defendant’s due process rights were not violated. Id. But as the Tennessee Supreme Court explained in Coleman, allowing defendants to present evidence regarding the Flynn Effect and the SEM is not enough. Tennessee courts must also consider this evidence in assessing a defendant’s ultimate functional I.Q. Coleman, 341 S.W.3d at 241-42.
3. Onset by the age of 18
In addition to having an I.Q. of 70 or below, this low level of intellectual capacity must have manifested itself by age 18 in order for the defendant to qualify as intellectually disabled under Tenn.Code Ann. § 39-13-203(a). Based on this rule, the TCCA in the present case denied Black’s Atkins claim because it concluded that “the proof in the record simply does not support that [Black’s] I.Q. was below seventy ... prior to age eighteen.” Black, 2005 WL 2662577, at *17. But the TCCA did not explain the extent to which this conclusion relied on any of Black’s various I.Q. scores. Nor did it consider the potential impact of the Flynn Effect and the SEM, despite the court’s consideration of the expert testimony that discussed the impact of these factors on Black’s middle set of I.Q. scores.
Just as the TCCA misinterpreted Howell in its Coleman decision, it made the same error here in deciding whether Black had demonstrated by a preponderance of the evidence that he had an I.Q. of 70 or below by the time he was 18 years of age. Although Black’s experts testified regarding the value of the Flynn Effect and the SEM, the TCCA refused to consider these factors as a matter of law based on Howell rather than based on whether “professionals who assess a person’s I.Q. customarily consider a particular test’s standard error of measurement [or] the Flynn Effect.” See Coleman, 341 S.W.3d at 242 n. 55. The TCCA’s decision is therefore contrary to the latest Tennessee Supreme Court’s decision on this subject. See Williams v. Taylor, 529 U.S. 362, 405, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000) (holding that “[a] *97state-court decision will certainly be contrary to our clearly established precedent if the state court applies a rule that contradicts the governing law”). And because Atkins defers to the individual states to set out the standard for a defendant to qualify as mentally retarded, the TCCA’s misinterpretation of Hmuell is contrary to Atkins.
Where a state court’s analysis contradicts the governing law, we must conduct an independent review of that issue, unconstrained by 28 U.S.C. § 2254(d)(1) (which mandates deference to state-court proceedings unless they “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”). Fulcher v. Motley, 444 F.3d 791, 799 (6th Cir.2006) (holding that after a federal court conducting habeas review determines that the state court’s decision was contrary to clearly established Supreme Court precedent, the “federal court is unconstrained by § 2254(d)(1) and de novo review is appropriate” (brackets, citation, and internal quotation marks omitted)). We conduct this independent review because “we cannot grant habeas unless [the defendant] is ‘in custody in violation of the Constitution or laws or treaties of the United States.’” West v. Bell, 550 F.3d 542, 553 (6th Cir.2008) (quoting 28 U.S.C. § 2254(a)).
Because the TCCA reached its ultimate conclusion that Black did not show by a preponderance of the evidence that his I.Q. was below 70 or that he had adaptive deficits by the time he was age 18, without specifying which I.Q. scores it relied on and why, “[i]t is impossible to determine ... the extent to which the [TCCA’s] error with respect to its reading of [Howell] affected its ultimate finding” that Black did not meet his burden of proof. See Williams, 529 U.S. at 414, 120 S.Ct. 1495; see also Mask v. McGinnis, 233 F.3d 132, 140 (2d Cir.2000) (holding under AEDPA that the “state court’s determination of factual issues ... were so closely intertwined with the state court’s articulation of an erroneous legal standard, to which we owe no deference, that we can discern no independent factual issues to which we should defer”); State v. Strode, 232 S.W.3d 1, 16 (Tenn.2007) (holding that “the question of whether an individual is mentally retarded for purposes of eligibility [for] the death penalty is a mixed question of law and fact”).
4. Black’s adaptive behavior
Even if Black’s I.Q. was 70 or below by the time he was age 18, we recognize that he must also have had deficits in adaptive behavior by the time he was .18 in order to be considered mentally retarded under Tennessee’s Atkins standard. Tenn.Code Ann. § 39-13-203(a). We therefore now turn to the issue of Black’s adaptive behavior.
In addition to explaining Tennessee’s standard for determining a defendant’s level of intellectual functioning, Coleman clarified the adaptive-deficits element of Tennessee’s Atkins standard. The Tennessee legislature did not define what characteristics constitute “deficits in adaptive behavior,” but the Tennessee Supreme Court explained that “deficits in adaptive behavior ‘means the inability of an individual to behave so as to adapt to the surrounding circumstances.’ ” Coleman, 341 S.W.3d at 248 (brackets omitted) (quoting State v. Smith, 893 S.W.2d 908, 918 (Tenn.1994)).
Although Smith did not adopt the clinical definition of deficits in adaptive behavior, “Tennessee’s trial and appellate courts have repeatedly relied upon expert analysis of adaptive behavior or functioning *98predicated upon definitions advanced within the relevant medical and psychological community and authoritative texts such as the AAIDD Manual and the DSM-IV.” Id. These documents are, respectively, the Manual of the American Association of Intellectual and Developmental Disabilities and the American Psychiatric Association’s Diagnostic and Statistical Manual of Mental Disorders. As in Coleman, the TCCA in the present case looked to the definition of deficits in adaptive behavior that the Tennessee Supreme Court adopted in Van Tran v. State, 66 S.W.3d 790, 795 (Tenn. 2001), which in turn based its standard on the DSM-IV.
The TCCA quoted the following passage from Van Tran that it had previously quoted in Coleman:
The second part of the definition— adaptive functioning — refers to how effectively individuals cope with common life demands and how well they meet the standards of personal independence expected of someone in their particular age group, socio-cultural background, and community setting. As discussed, a mentally retarded person will have significant limitations in at least two of the following basic skills: communication, self-care, home living, social/interpersonal skills, use of community resources, self-direction, functional academic skills, work, leisure, health, and safety. Influences on adaptive functioning may include the individual’s education, motivation, personality characteristics, social and vocational opportunities, and the mental disorders and general medical conditions that may coexist with Mental Retardation.
Black, 2005 WL 2662577, at *15 (quoting Van Tran, 66 S.W.3d at 795 (internal quotation marks omitted)).
The TCCA in Coleman determined that although “[Coleman] has established that he has deficits in academic performance, he has not established that he suffers substantial limitations in at least two adaptive behavioral skill areas. Accordingly, he has failed to establish that he has adaptive deficits by a preponderance of the evidence.” Coleman v. State, No. W200702767-CCA-R3-PD, 2010 WL 118696, at *29 (Tenn.Crim.App. Jan. 13, 2010). The Tennessee Supreme Court disagreed with the analysis of both the TCCA and the trial court. It determined that their erroneous interpretation of Howell led them to assess the possible causes of Coleman’s apparent deficiencies in adaptive behavior without the benefit of “testimony indicating that Mr. Coleman’s intellectual capacities rendered him intellectually disabled.” Coleman, 341 S.W.3d at 249.
The lower courts’ failure to properly consider this evidence concerning Coleman’s intellectual capacities might have had “a substantial and injurious impact on the trial court and the Court of Criminal Appeals’ decision-making in weighing the relative strengths of the causes of the seeming deficits in Mr. Coleman’s adaptive behavior.” Id. Notably, the Tennessee Supreme Court found that the lower courts’ assessment of Coleman’s adaptive deficits was flawed, even though they acknowledged that he had various personality problems, because they did not think that these personality problems could be characterized as deficits in adaptive behavior under Tennessee’s Atkins standard. See id.
This problem is equally present in the TCCA’s decision in the present case. Just as in Coleman, the TCCA here cited a number of expert assessments indicating that Black had various personality problems, but it concluded that these issues did not amount to deficits in his adaptive behavior. Black, 2005 WL 2662577, at *6-7, 10, 15-16. Even the State’s experts ac*99knowledged that Black has serious personality problems. Coleman’s conclusion that the erroneous exclusion of expert testimony concerning adjustments to Coleman’s I.Q. score might have had “a substantial and injurious impact on the [lower courts’] decision-making in weighing the relative strengths of the causes of the seeming deficits in Mr. Coleman’s adaptive behavior” is therefore equally applicable in the present case. See Coleman, 341 S.W.3d at 249.
The relevant question, however, is whether Black displayed the requisite deficits in his adaptive behavior by the time he loas 18 years of age. See Tenn.Code Ann. § 39-13-203(a). As with the TCCA’s analysis of Black’s level of intellectual functioning, its conelusory reliance on the record as a whole and the ambiguity of the conflicting evidence make the TCCA’s errors in assessing Black’s adaptive deficits extend to the determination of whether these adaptive deficits manifested themselves by the time Black was age 18. The TCCA’s analysis of the adaptive-deficits issue in the present case is thus contrary to Coleman.
In addition to connecting the analysis of adaptive deficits to the proper assessment of intellectual capacities, Coleman contains several legal principles regarding adaptive deficits that are relevant to the analysis in the present case. The Tennessee Supreme Court held that “the definition of ‘intellectual disability’ embraces a heterogeneous population ranging from persons who are totally dependent to persons who are nearly independent.” Id. at 231. This position supports the idea that a court reviewing whether a defendant is mentally retarded “must focus on Defendant’s deficits, not his abilities.” United States v. Lewis, No. 1:08 CR 404, 2010 WL 5418901, at *30 (N.D.Ohio Dec. 23, 2010). Various experts from both sides in the present case also testified that someone might be mentally retarded but still be able to carry out any of a number of everyday activities, such as maintaining a simple job or driving a car. A full, independent review of whether Black showed by a preponderance of the evidence that he displayed adaptive deficits by the time he was age 18 must therefore look at his weaknesses instead of at his strengths.
The Tennessee Supreme Court in Coleman also determined that the lower courts erred in
their decision to distinguish between Mr. Coleman’s mental illness and his intellectual disability as separate causes of his adaptive limitations. By concluding that Mr. Coleman’s adaptive deficiencies were caused by his mental illness alone, the lower courts treated Mr. Coleman’s mental illness and intellectual disabilities as separate dichotomous spheres rather than as interwoven causes.
Coleman, 341 S.W.3d at 249.
In making this point, the Tennessee Supreme Court explained that there is no consensus among the various state courts around the country, nor in the scientific literature, regarding “the role of causation with regard to assessing deficits in adaptive behavior.” Id. at 250. The Tennessee Supreme Court in Coleman did not resolve this conflict because it determined that the matter should be addressed only after the record was more complete. Id. at 252. But even with the less-than-complete record before it, the Court noted that the expert testimony in the record established that mental retardation and other mental disorders are not mutually exclusive. See id. at 252-53. Rather, mental retardation and any number of other factors may coexist as comorbid causes of a defendant’s deficient adaptive functioning. See id.
*100The Tennessee Supreme Court thus concluded that the TCCA had erred in holding that Coleman’s adaptive deficits were caused solely by his mental illness, without considering evidence that “intellectual disability and mental illness were inter-related and served to aggravate each other, combining to limit Mr. Coleman’s adaptive functionality.” Id. at 252. Moreover, although the Tennessee Supreme Court did not make a conclusive legal determination concerning the causal relationship between mental retardation and mental illness, the legal precedents and scientific literature that it cited explain that, at a minimum, courts must consider the possibility that a defendant’s mental retardation and other mental illnesses might be comorbid causes of a defendant’s personality problems. See id. at 251-53; Lewis, 2010 WL 5418901, at *32 (“Indeed, individuals with intellectual disability are three to four times more likely to have comorbid mental disorders than the general population.”). Coleman thus establishes that even where a defendant suffers from mental illness, that finding does not preclude a concomitant determination that the defendant’s personality problems constitute adaptive deficits under Tennessee’s Atkins standard.
The TCCA in the present case repeatedly cited evidence that it interpreted as supporting the existence of Black’s mental illness but not of his mental retardation. For example, the TCCA explained that Dr. Engum “believed that Petitioner suffered from personality problems, delusional problems, or psychological difficulties, [but that] those issues are separate and apart from the issue of whether Petitioner was mentally retarded.” Black, 2005 WL 2662577, at *16. The TCCA also concluded, based on Dr. Vaught’s testimony, that mental retardation “has nothing, however, to do with mental illness.” Id. at *10. This reasoning is similar to the TCCA’s error in Coleman of treating “Mr. Coleman’s mental illness and intellectual disabilities as separate dichotomous spheres rather than as interwoven causes.” Coleman, 341 S.W.3d at 249. On remand, a proper analysis of Black’s case under Coleman must consider the potential relationship between mental retardation and mental illness.
5. Conclusion on Black’s Atkins claim
Overall, the record is rife with conflicting testimony regarding Black’s level of intelligence and adaptive deficits by the time he was age 18. The TCCA’s decision is of little help because the court made so few definitive factual determinations leading up to its ultimate conclusion that Black did not show by a preponderance of the evidence that he qualifies as mentally retarded. Moreover, the TCCA did not have the benefit of Coleman’s guidance when it refused to consider either the Flynn Effect or the SEM in evaluating the mental-retardation issue. Habeas review by the district court was similarly constrained.
The rules governing what factors may be considered in determining whether a defendant qualifies as mentally retarded under Atkins deal with questions of law. See Clark v. Quarterman, 457 F.3d 441, 444 (5th Cir.2006) (holding that the rules regulating the factors involved in the ultimate determination of whether a defendant qualifies as mentally retarded under Atkins raise questions of law); see also Murphy v. Ohio, 551 F.3d 485, 510 (6th Cir.2009) (reviewing the state court’s resolution of the defendant’s Atkins claim under AEDPA’s standard for questions of law). The TCCA’s assessment of Black’s level of intellectual and adaptive functioning was therefore contrary to Coleman under AEDPA’s legal standard.
Ordinarily, where the state court’s decision is contrary to clearly established *101law under AEDPA, we will conduct an independent review of the record in order to determine whether the defendant is “in custody in violation of the Constitution or laws or treaties of the United States.” West v. Bell, 550 F.3d 542, 553 (6th Cir.2008) (quoting 28 U.S.C. § 2254(a)); Fulcher v. Motley, 444 F.3d 791, 799 (6th Cir.2006) (holding that when we determine that the state court contradicted the governing law, we must conduct an independent review, unconstrained by 28 U.S.C. § 2254(d)(1)). But we will refrain from reaching any independent conclusions ourselves because no court has yet analyzed Black’s Atkins claim according to the proper legal standard, which was set out by the Tennessee Supreme Court in Coleman. See Alley v. Bell, 405 F.3d 371, 372 (6th Cir.2005) (en banc) (granting rehearing en banc and remanding the case for the district court to determine in the first instance whether it had jurisdiction to consider the death-row inmate’s motion for relief from judgment in light of an intervening case that the district court did not originally consider); see also Thaddeus-X v. Blatter, 175 F.3d 378, 399 (6th Cir.1999) (vacating the district court’s grant of summary judgment on the plaintiffs retaliation claim and remanding the case for the district court to apply the correct legal standard in the first instance).
A complete review must apply the correct legal standard to all of the relevant evidence in the record. We therefore VACATE the district court’s denial of Black’s Atkins claim and REMAND the case for it to review the record based on the standard set out in Coleman and consistent with this opinion.
6. Response to Dissent
We note that our dissenting colleague vigorously argues that Coleman “does nothing to implicate [Black’s] Atkins claim,” that “AEDPA forecloses consideration of this state court precedent as a ground for relief,” and that a “[r]emand is unnecessary, inappropriate, and flatly contrary to federal law.” For all of the reasons set forth above in this Part II. B., we respectfully disagree.
Moreover, we believe that the dissent fails to recognize that this case raises a unique set of circumstances. Retroactively applicable new rules under AEDPA and under Teague v. Lane, 489 U.S. 288, 109 S.Ct. 1060, 103 L.Ed.2d 334 (1989), are exceedingly rare occurrences. See Ochoa v. Sirmons, 485 F.3d 538, 540 (10th Cir.2007) (explaining that “Atkins reflects one of the rare instances in which the Supreme Court has announced a new rule of constitutional law that it has also expressly made retroactively applicable to cases on collateral review”). For the Supreme Court to explicitly leave to the states the task of defining the contours of such rules is even more out of the ordinary. But these are the unique circumstances that we face in this case, which is why we are convinced that a remand to the district court for reconsideration of Black’s Atkins claim in light of Coleman is the proper resolution of this issue.
C. Competency to stand trial
Black also challenges the state court’s determination that he was competent to stand trial. He argues that, at the very least, the district court should have granted him an evidentiary hearing on this issue. To be competent to stand trial, a defendant must have “ ‘sufficient present ability to consult with his lawyer with a reasonable degree of rational understanding’ and ‘a rational as well as factual understanding of the proceedings against him.’” Filiaggi v. Bagley, 445 F.3d 851, 858 (6th Cir.2006) (quoting Dusky v. United States, 362 U.S. 402, 402, 80 S.Ct. 788, 4 *102L.Ed.2d 824 (1960) (per curiam)). “[Evidence of a defendant’s irrational behavior, his demeanor at trial, and any prior medical opinion on competence to stand trial are all relevant in determining whether further inquiry is required, but ... even one of these factors standing alone may, in some circumstances, be sufficient.” Drope v. Missouri, 420 U.S. 162, 180, 95 S.Ct. 896, 43 L.Ed.2d 103 (1975).
A defendant’s competence to stand trial is a question of fact. Filiaggi, 445 F.3d at 858. Under AEDPA, assuming that the state court’s legal standard for determining whether a defendant is competent is not contrary to or an unreasonable application of clearly established Supreme Court precedent, the court’s factual competency determination “must be upheld unless there is clear and convincing evidence to the contrary.” Id. (internal quotation marks omitted).
Black argues that neither his experts nor the State’s experts conducted a thorough evaluation of either his social history or his psychological and neurological impairments in assessing his competency to stand trial. But Black relies on evidence from his post-conviction proceedings, which was produced long after his trial, in order to support this claim. Although such after-the-fact evidence is relevant to competency determinations, “[t]he critical question is whether the evidence relied upon for determining a defendant’s competence at an earlier time of trial was evidence derived from knowledge contemporaneous to trial.” Bowers v. Battles, 568 F.2d 1, 4 (6th Cir.1977) (internal quotation marks omitted). Psychiatric opinions offered years after a habeas petitioner’s trial are therefore not nearly as relevant as those issued at the time of trial. Harries v. Bell, 417 F.3d 631, 636 (6th Cir.2005).
Black received a competency hearing shortly before his trial. At this hearing, a psychologist and one of Black’s attorneys testified on Black’s behalf that he was unable to understand the judicial process, did not understand his attorneys’ role, did not understand the consequences of the trial, and that he was unable to assist his attorneys. But the prosecution’s three mental-health experts all interviewed Black and testified that although his intelligence was at the lower end of the normal range and that he probably had a personality disorder, he was not delusional and was competent to stand trial.
The trial court then appointed another expert, a psychiatrist, to evaluate Black. This expert concluded that Black was “clearly competent.” The court adopted this conclusion. When Black’s attorneys raised the competency issue again after voir dire, this same expert reinterviewed Black and once more found that he was competent. The trial court then reaffirmed its ruling that Black was competent to stand trial. In reviewing Black’s competency claim on direct appeal, the Tennessee Supreme Court determined that Black “understood the nature and object of the proceedings against him and was able to consult with and assist counsel in preparing his defense.” State v. Black, 815 S.W.2d 166, 174-75 (Tenn.1991).
Our earlier review of the TCCA’s assessment concerning whether Black is mentally retarded under Atkins does not compel a similar result concerning his competency to stand trial because Atkins explicitly held that “[mjentally retarded persons frequently know the difference between right and wrong” and can be competent to stand trial. See Atkins v. Virginia, 536 U.S. 304, 318, 122 S.Ct. 2242, 153 L.Ed.2d 335 (2002). The district court determined, and Black does not offer any evidence to the contrary, that Black’s competency argument relies primarily on evidence from his post-conviction proceed*103ings. “None of these experts state an opinion as to whether Petitioner met the standard for competence at the time of trial.” Black v. Bell, 181 F.Supp.2d 832, 843 (M.D.Tenn.2001). The district court thus correctly determined that Black’s evidence did not amount to “the clear and convincing proof required for this Court to disregard the state court’s findings.” Id. And the state court’s decision was not “contrary to, [nor did it] involve[ ] an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States.” 28 U.S.C. § 2254(d)(1).
Black further argues that the procedures used by the state trial court to determine whether he was competent were inadequate under the Due Process Clause. Due process in a competency hearing requires “that only the most basic procedural safeguards be observed.” Medina v. California, 505 U.S. 437, 453, 112 S.Ct. 2572, 120 L.Ed.2d 353 (1992) (internal quotation marks omitted). The court allowed both Black and the prosecution to present their expert testimony at Black’s competency hearing. Then, rather than base its determination on either of these experts, the court appointed its own independent expert to evaluate Black. The court further afforded Black a reevaluation at his attorneys’ request after the voir dire. Black has not pointed to any required process that he was denied. The process that was undertaken in Black’s state-court competency hearing was therefore not contrary to, nor did it involve an unreasonable application of, the process that was required to determine Black’s competence. In rejecting Black’s challenge to the state court’s determination of his competency to stand trial, we specifically note that we make no determination regarding his claim of incompetence to be executed, which the district court dismissed without prejudice because the claim was not yet ripe. Black, 181 F.Supp.2d at 882-83.
D. Ineffective assistance of counsel regarding mitigation evidence
Black next challenges the state court’s rejection of his claim that his trial attorneys were ineffective in investigating and presenting mitigation evidence at the penalty phase of his trial. He contends that his attorneys failed to investigate his social history and failed to hire a psychiatrist regarding his mental-health issues.
To establish the ineffective assistance of trial counsel, Black must show that his counsel’s performance (1) was deficient (i.e., that it was objectively unreasonable under prevailing professional norms), and (2) prejudiced the defense. See Strickland v. Washington, 466 U.S. 668, 687-88, 104 S.Ct 2052, 80 L.Ed.2d 674 (1984). “[A] court must indulge a strong presumption that counsel’s conduct falls within the wide range of reasonable professional assistance; that is, the defendant must overcome the presumption that, under the circumstances, the challenged action might be considered sound trial strategy.” Id. at 689, 104 S.Ct. 2052 (internal quotation marks omitted).
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. “A reasonable probability -is a probability sufficient to undermine confidence in the outcome.” Id. The Strickland prejudice component “focuses on the question whether counsel’s deficient performance renders the result of the trial unreliable or the proceeding fundamentally unfair.” Lockhart v. Fretwell, 506 U.S. 364, 372, 113 S.Ct. 838, 122 L.Ed.2d 180 (1993).
Defense counsel’s failure to reasonably investigate a defendant’s back*104ground and present mitigating evidence to the jury at sentencing can constitute ineffective assistance. Wiggins v. Smith, 539 U.S. 510, 522-23, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003). In assessing the reasonableness of an attorney’s mitigation investigation, the court considers “not only the quantum of evidence already known to counsel,” but also whether that evidence should have led “a reasonable attorney to investigate further.” Id. at 527, 123 S.Ct. 2527.
Counsel has a duty to conduct an independent investigation regarding mitigating evidence regardless of the defendant’s reluctance to investigate and disclose such evidence. Harries v. Bell, 417 F.3d 631, 638 (6th Cir.2005). Because of this obligation, counsel cannot rely solely on information provided by the defendant and his family in determining the extent of a proper mitigation investigation. Rompilla v. Beard, 545 U.S. 374, 388-89, 125 S.Ct. 2456, 162 L.Ed.2d 360 (2005). But a “reasonably diligent counsel may draw a line when they have good reason to think further investigation would be a waste.” Id. at 383, 125 S.Ct. 2456.
As for demonstrating prejudice under Strickland, Black was required to show that his new evidence differs “in a substantial way — in strength and subject matter— from the evidence actually presented at sentencing.” See Fautenberry v. Mitchell, 515 F.3d 614, 626 (6th Cir.2008) (internal quotation marks omitted). “[T]he failure to present additional mitigating evidence that is merely cumulative of that already presented does not rise to the level of a constitutional violation.” Nields v. Bradshaw, 482 F.3d 442, 454 (6th Cir.2007) (internal quotation marks omitted).
Black claims that the TCCA’s analysis was contrary to Strickland because the court concluded that he was required to establish that “but for his counsel’s deficient performance, the result of his trial would likely have been different.” As Black correctly argues, Strickland requires only a “reasonable probability” that the result would have been different but for his counsel’s deficient performance. He thus argues that the TCCA’s requirement that his attorneys’ deficient performance would “likely” have resulted in a different result, see Black, 1999 WL 195299, at *13, overstated the level of prejudice necessary for relief. The Supreme Court has in fact held that if a state court rejects a defendant’s ineffective-assistance-of-counsel claim based on a preponderance-of-the-evidence standard for prejudice rather than asking whether there was a “reasonable probability that ... the result of the proceeding would have been different,” then that decision would be contrary to clearly established federal law. Williams v. Taylor, 529 U.S. 362, 406, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000) (quoting Strickland, 466 U.S. at 694, 104 S.Ct. 2052).
But the district court emphasized that “[i]n discussing the Strickland prejudice standard, courts frequently use the term ‘likely’ interchangeably with the phrase ‘reasonable probability.’ ” Black, 181 F.Supp.2d at 861 (citing Stanford v. Parker, 266 F.3d 442, 455 (6th Cir.2001)). The court reasoned that, in using the term “likely,” the TCCA “focused on the same analysis as required by the ‘reasonable probability’ standard.” Id. Our review of the record supports the district court’s conclusion.
Moreover, Black’s mitigation argument would fail even de novo review. He summarily argues that, had his trial counsel hired a psychiatrist, the psychiatrist would have easily discovered that he “suffers serious mental illness, has neurological impairments, and severe memory deficits,” which would have led to a diagnosis of *105brain damage. But Black was in fact evaluated by various mental-health experts during the competency evaluation for his trial. Black now presents additional mental-health evidence that was obtained during his post-conviction process that he contends should have been uncovered by his penalty-phase attorneys. But Black’s claim fails because there is no evidence in the record to support the conclusion that Black’s trial attorneys should have been aware at the time of Black’s trial (including the penalty phase) that any further investigation into his social history would have produced more evidence beyond that already obtained by the competency experts. See Wilson v. Parker, 515 F.3d 682, 698 (6th Cir.2008) (assessing the effectiveness of defense counsel’s mitigation efforts by requiring a look at counsel’s conduct “at the time of its occurrence (or when it should have occurred in the case of omissions)” (emphasis added)).
E. Ineffective assistance of counsel regarding the prosecutor’s “reward” argument
Black further claims that his trial counsel performed ineffectively by failing to object to the prosecution’s penalty-phase closing argument that giving Black a life sentence rather than the death penalty would reward him for the additional killings of Latoya and Lakeisha Clay because Black was already subject to a life sentence for the murder of Angela Clay. This claim is based on two Tennessee Supreme Court cases, State v. Smith, 755 S.W.2d 757 (Tenn.1988), and State v. Bigbee, 885 S.W.2d 797 (Tenn.1994), in which the prosecutor made similar arguments to the jury. The TCCA in the present case incorrectly accepted the lower court’s distinction that whereas the defendants in those cases “had previously received life sentences for unrelated murders ..., [Black] was facing the death penalty in the same trial for three related killings. Accordingly, as the [TCCA] noted, the jury [in the present case] could not help but have full knowledge of all three sentences it was considering for the three murders.” Black, 181 F.Supp.2d at 857 (quoting the TCCA’s opinion).
The defendant in Smith was in fact tried for multiple murders in the same trial, just as Black was here. Although the Tennessee Supreme Court in Smith determined that the two separate murders should have been tried separately, it also concluded that the prosecution’s “reward” argument was highly prejudicial specifically because the jury knew about the other murders. Smith, 755 S.W.2d at 767-68. In other words, Smith held that telling the jury that a life sentence will be “no additional punishment” because of the defendant’s life sentence for a different murder is inherently prejudicial to the defendant even where the jury properly knows about the defendant’s life sentence for another murder.
But, like the trial court, the TCCA ultimately did not decide whether counsel’s performance was deficient because it agreed with the trial court that even if defense counsel did make a mistake and “should have objected to the argument,” this error was not prejudicial because “it is unlikely that the objection would have had any effect on the jury’s decision.” Id. Black, however, claims that the prosecutor’s argument was prejudicial because the jury sent a note asking the trial judge whether multiple terms for the murders would be served concurrently or consecutively, and it deliberated for 13 hours, allegedly showing that the jury was considering a life sentence. But, as the TCCA noted, the prosecutor made his “reward” argument about both of Angela’s daughters, yet the jury sentenced Black to death for only Lakeisha’s murder. Moreover, *106Black’s death sentence was supported by six aggravating factors. We therefore agree that Black has not shown a reasonable probability that, but for the prosecutor’s reward argument, the result of his penalty phase would have been different.
F. Instructing the jury regarding Black’s parole eligibility
Finally, Black argues that the trial court violated his due process rights by failing to answer the jury’s questions regarding how long a life sentence actually was in Tennessee, and whether he could be paroled from a life sentence. Black contends that he had a due process right to have the jury receive instructions in response to these questions so that he could rebut the prosecution’s improper argument that a life sentence would reward Black for the murders of Latoya and Lakeisha.
In support of this argument, Black cites Gardner v. Florida, 430 U.S. 349, 97 S.Ct. 1197, 51 L.Ed.2d 393 (1977), Skipper v. South Carolina, 476 U.S. 1, 106 S.Ct. 1669, 90 L.Ed.2d 1 (1986), Simmons v. South Carolina, 512 U.S. 154, 114 S.Ct. 2187, 129 L.Ed.2d 133 (1994), and Shafer v. South Carolina, 532 U.S. 36, 121 S.Ct. 1263, 149 L.Ed.2d 178 (2001). But none of these cases dealt with the type of prosecutorialmisconduct argument that Black raises here. Gardner involved a defendant’s right to rebut information contained in a presentence report. And Skipper concerned a defendant’s right to offer evidence of his good behavior in prison in order to rebut the prosecution’s arguments regarding the defendant’s future dangerousness.
Simmons and Shafer provide the closest analogy to the present case. In Simmons, the Court held that “where a defendant’s future dangerousness is at issue, and state law prohibits the defendant’s release on parole, due process requires that the sentencing jury be informed that the defendant is not eligible for parole.” Black, 181 F.Supp.2d at 870. But if “parole is an option for a defendant sentenced to life imprisonment, ... the Simmons Court emphasized that it will not second-guess the refusal of a State to allow proof, instruction, or argument to the jury on the availability of parole.” State v. Bush, 942 S.W.2d 489, 503 (Tenn.1997) (emphasis in original). And, as the district court explained, “[b]ecause Tennessee is a state in which defendants sentenced to life imprisonment are eligible for parole, ... Simmons does not require that the jury be given information about parole availability.” Black, 181 F.Supp.2d at 870 (citing Bush, 942 S.W.2d at 503).
In fact, Shafer itself explains that Simmons does not apply where, as here, the defendant might be eligible for parole based on the jury’s decision. Shafer, 532 U.S. at 51, 121 S.Ct. 1263 (“Simmons applies where[,] as a legal matter, there is no possibility of parole if the jury decides the appropriate sentence is life in prison.” (emphasis and internal quotation marks omitted)). Moreover, Black does not contend that the prosecutor’s reward argument put his dangerousness at issue. We therefore agree with the district court’s denial of Black’s claim that he had a due process right to have the trial court answer the jury’s questions regarding his parole eligibility and the length of his sentence.
III. CONCLUSION
For all of the reasons set forth above, we AFFIRM the district court’s denial of Black’s habeas petition regarding his non-Atkins claims, VACATE the court’s judgment regarding the denial of Black’s petition concerning his Atkins claim, and REMAND the case for further proceedings consistent with this opinion.