HIGGINBOTHAM, Circuit Judge:

A Texas jury convicted Robert Ladd of capital murder and sentenced him to death for the rape and murder of Vicki Ann Garner. Ladd sought habeas relief in federal district court, claiming that he is mentally retarded1 and therefore categorically ineligible for the death penalty under Atkins v. Virginia.2 Following an evidentiary hearing, the district court denied habeas relief, but granted a Certificate of Appealability ("COA"). We AFFIRM.

I

A

In 1978, Robert Ladd was convicted of murdering a woman and her two children, and then setting her house on fire. After serving 16 years of a 40 year prison sentence, Ladd was released from prison. On September 25, 1996, Vicki Ann Garner was found dead in her home. Garner had been raped and strangled to death. In addition, her home was robbed and then set on fire.

A police investigation quickly connected Ladd to Garner's murder.3 Ladd's DNA was found on Garner, his hand print was found in Garner's kitchen, and Ladd had sold a TV set that had been taken from Garner's residence in exchange for crack cocaine.4

Soon thereafter, Ladd was indicted for capital murder, as the murder occurred during the commission of burglary, robbery, sexual assault, and arson. On August 23, 1997, a Texas state jury convicted Ladd of capital murder, and, on August 27, 1997, the jury imposed the death penalty. A direct appeal then followed, which was denied on October 6, 1999.5 Ladd's petition for a writ of certiorari was then denied on April 17, 2000.

Ladd filed his first state petition for habeas relief, asserting an ineffective assistance of counsel claim, alleging that Ladd's counsel was ineffective for failing to raise evidence of mental retardation during the punishment phase. The state district court held an evidentiary hearing, where Ladd presented testimony of his trial counsel, but did not present a psychiatric expert. The State presented its psychologist and psychiatrist who had both testified at trial that Ladd presented a future danger. These experts generally opined that they would discount Ladd's prior IQ score of 67, explaining that they did not know enough about the administration of the test and that such a result was inconsistent with his later academic achievement. But, neither expert had tested Ladd's IQ, nor otherwise examined him for mental retardation; indeed, their testimony centered on their conclusion that the additional information obtained about Ladd would not have changed their expert opinions regarding his future dangerousness. The state trial court then issued its findings of fact and conclusions of law, wherein it concluded:

The Texas Court of Criminal Appeals ("CCA") then denied Ladd's petition for state habeas relief on December 15, 1999.7

Ladd filed his first application for federal habeas relief on January 18, 2001. Ladd again raised the claim that he received ineffective assistance by counsel because his attorney had not raised evidence of Ladd's mental retardation during the punishment phase. The district court rejected this claim on October 24, 2001. We affirmed, concluding that "the Texas court was well-within the bounds of AEDPA reasonableness in concluding that Ladd suffered no prejudice."8

Following the Supreme Court's decision in Atkins v. Virginia,9 Ladd filed his second petition for state habeas relief on April 7, 2003, arguing that he was categorically excluded from the death penalty because of mental retardation. In support of this claim, Ladd attached several exhibits to his state petition, including: (i) documentation from Ladd's childhood institutionalization in the Gatesville State School, where his IQ had been tested at 67; (ii) psychiatric notes from this institutionalization wherein the psychiatrist noted that Ladd is "rather obviously retarded" and had "mental retardation, mild to moderate"; (iii) institutionalization records showing that Ladd was functioning below his grade level in basic academic skills and had social development problems; and, (iv) documentation that as a child Ladd was prescribed Mellaril, an anti-psychotic medication, to control his impulsive behavior. Arguing that he had set forth a prima facie Atkins claim, Ladd requested an evidentiary hearing to refute any evidence the State might offer and to develop fully his claim. Without an evidentiary hearing, or any opportunity to develop fully his Atkins claim, the CCA dismissed the petition on the merits ten days later on April 17, 2003, explaining that he failed to plead sufficient facts to permit a successive writ under Texas state law.10

Ladd sought authorization from this Court to file a second application for habeas relief in the district court. We authorized the successive writ, and on June 20, 2003, Ladd filed the application for habeas corpus at issue.

B

On June 27, 2005, the district court conducted an evidentiary hearing on the application. Ladd presented several witnesses, including: Richard Garnett, a licensed professional counselor;11 Lubertha Cephus, Ladd's mother's first cousin; Russell Pinckard, a death row corrections officer; and, Nelma Thomas, Ladd's sister.

Garnett testified that, in his expert opinion, Ladd was mentally retarded. First, Garnett explained that Ladd had significantly sub-average intellectual functioning.12 Garnett based this conclusion on Ladd receiving an IQ score of 67, when he was tested at age 13 by the Texas Youth Commission.13 Moreover, Garnett explained that the Texas Youth Commission's psychiatrist, Phillip Ash, noted that Ladd appeared mentally retarded.14 In addition, Garnett noted that Ladd had a low birth weight, consistent with fetal alcohol syndrome.15 Garnett did note that Ladd later received an IQ score of 86, but he explained that this score was on a less comprehensive IQ test, the Beta test, that is not as accurate as the previously administered Wechsler test.16 Garnett discounted a more recent Wechsler test IQ score of 60, because there were signs of malingering.17

Second, Garnett testified that Ladd had significant adaptive skills deficits. In particular, Garnett testified that Ladd had deficits with: money concepts, work-related skills, using community resources, communications skills, and social skills.18 In addition, Garnett testified that Ladd's deficits were properly attributed to mental retardation, rather than anti-social personality disorder.19 Although Garnett acknowledged that he could not use any evaluative instruments for measuring the adaptive skills of an incarcerated individual, he explained that he was able to make this assessment based on his clinical judgment and experience.20 Additionally, Garnett discounted Ladd's having obtained a G.E.D., learning to play chess, and having written many letters, by explaining that obtaining a G.E.D. and learning to play chess were not outside the capacity of the mildly mentally retarded.21 As to the letters, Garnett explained that based on his conversations with Ladd he believed that Ladd had received substantial assistance in writing those letters.22

Third, Garnett testified that, given his childhood IQ score of 67 and family reports of adaptive functioning deficits, these deficits developed prior to Ladd turning 18 years old.23

On cross-examination, the State elicited from Garnett that (i) Ladd was a latch-key kid who had been able to take care of himself;24 (ii) by 11 years old, Ladd could handle money;25 (iii) Ladd's failure to make friends during childhood may have been a product of his anti-social personality disorder, and not retardation;26 (iv) Ladd's reading ability tests above the tenth grade level, despite most mentally retarded being unable to read above the seventh grade level;27 (v) Ladd had successfully completed vocational training programs in prison;28 and, (vi) Ladd was successful working in a structured environment when he was not in prison.29

Lubertha Cephus testified that Ladd's mother drank heavily while pregnant with Ladd.30 Ladd's sister, Nelma Thomas, testified that Ladd had problems understanding the concepts of games as a child: she explained that he did not understand the concept of suits in card games and that he did not understand the need to run to first base while playing kickball.31 In addition, Thomas testified that Ladd often failed to dress himself appropriately for the weather when he was twelve to fourteen years old, and that when her mother sent him to the store, he could not remember what he was supposed to purchase.32

The State presented several witnesses, including: Al Matson, the manager of the vocational program at which Ladd worked, Howard Alexander, a prison barber instructor, and Dr. Thomas Allen, a forensic psychologist. Matson explained that he managed the vocational division of the Andrews Center, a community mental health/mental retardation healthcare center.33 Matson testified that Ladd was referred to the Andrews Center from a substance abuse facility,34 and was a capable worker.35 Matson explained that Ladd was placed into some of the more challenging positions, such as line leader and quality control.36 During the course of his employment, Ladd could operate an ultrasonic welding machine, setup electronic weighing scales, and operate a forklift.37 Matson testified that Ladd did not require any special assistance or supervision, and would have been promoted but for his criminal background.38 Although Ladd was initially started at below minimum wage, he received several raises in the course of his work, resulting in above-minimum wage payment.39 These funds were paid into a trust account, but the Andrews Center used trust account for non-mentally retarded workers, as well as the mentally retarded.40 Eventually, Matson explained, Ladd was fired because of problems with absenteeism and confrontations with supervisors.41

Howard Alexander testified that he taught a vocational barber training program in prison.42 The program required at least a seventh grade education,43 and, in Alexander's opinion, could not be completed by anyone with serious learning deficiencies.44 Although Alexander does not remember instructing Ladd, Alexander's records indicate that Ladd completed the state barber exam and was one of Alexander's better students.45

Dr. Thomas Allen, a forensic psychologist,46 testified that in his opinion Ladd was not mentally retarded. First, Dr. Allen explained that he did not trust the IQ score of 67 administered when Ladd was 13, because Ladd had a propensity for "prevarication" and low motivation, and there were no notes as to whether the degree of Ladd's effort on the examination were observed.47 Relatedly, Dr. Allen explained that the IQ score of 86, although only measured by a screening tool, was instructive, as it placed Ladd within the average range of prisoners screened.48 Similar to Garnett, Dr. Allen opined that the recent score of 60 was unreliable because of malingering.49

Second, Dr. Allen testified that Ladd's of possible adaptive deficits were properly explained by Ladd's anti-social personality disorder, because the behavioral observations predominantly focused on aggression and anti-social conduct, not on behavioral deficits typically associated with mental retardation.50

Third, Dr. Allen explained that he administered the Vineland Adaptive Skills Inventory, which he modified to adapt to Ladd.51 Although this inventory has not been normed on prisoners, Dr. Allen explained that Ladd's score placed him well within the middle, or average, range of the population.52 Reviewing Ladd's history, Dr. Allen opined that his adaptive deficits were due to behavioral problems, not mental retardation, including deficits related to functional academics, using community resources, interpersonal skills, and communications skills.53 Finally, Dr. Allen opined that, although possible, it would be very unusual for someone to suffer from both mental retardation and anti-social personality disorder.54

Following the evidentiary hearing, the district court issued a memorandum opinion and order, wherein it concluded that it found the State's expert witness to be more persuasive. Accordingly, the district court denied the application on February 15, 2013, concluding that Ladd had failed to establish by a preponderance of the evidence that he was mentally retarded.55 The district court then granted a COA on March 28, 2013. Ladd timely appeals.

II

We begin with the State's argument that the district court failed to apply proper Antiterrorism and Effective Death Penalty Act of 1996 ("AEDPA") deference to the state court proceedings. The State argues that the state courts were not required to afford Ladd an evidentiary hearing, and accordingly the district court should have afforded AEDPA deference to the state proceedings.

AEDPA mandates deference to state court proceedings. If a "state court has adjudicated a habeas petitioner's claims on the merits, he may receive relief in the federal courts only where the state court decision `resulted in a decision that was contrary to, or involved an unreasonable application of clearly established federal law'" or "`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.'"56 And it is "axiomatic that infirmities in state habeas proceedings do not constitute grounds for federal habeas relief."57 Nonetheless, we have explained that where there is "a significant substantive liberty interest [at stake]," that liberty interest "entitles the petitioner to a set of core procedural due process protections: the opportunity to develop and be heard on his claim that he is ineligible for the death penalty."58 Thus, "when a petitioner makes a prima facie showing of mental retardation, a state court's failure to provide him with an opportunity to develop his claim deprives the state court decision of deference ordinarily due under ... AEDPA."59 This is because where a "state court dismisses a prima facie valid Atkins claim without having afforded the petitioner an adequate opportunity to develop the claim, it has run afoul of the Due Process Clause, and that due process violation constitutes an unreasonable application of clearly established federal law that is sufficient to deprive the state court's decision of AEDPA deference."60 Importantly, this does not require states to "give hearings to all persons with Atkins claims" because "states [are given] discretion to set gateways to full consideration and to define the manner in which habeas petitioners may develop their claims."61

The State rightly points to serious problems regarding the deference due to the CCA's judgment and whether the district court afforded proper deference under AEDPA. This is in no small part directly attributable to the long length of time this case was pending in the district court, during which the landscape of AEDPA deference62 and Atkins claims substantially changed. But we need not reach this, as it is sufficient to say that the district court's rejection of Ladd's Atkins claim following de novo review is, as we explain below, sound, and the district court must be affirmed. Any want of deference to the state court cannot, by definition, have injured the State.

III

We turn to the merits of Ladd's claim of mental retardation. We review the district court's factual findings for clear error and the district court's conclusions of law de novo.63 A finding of fact is "clearly erroneous only if it is implausible in the light of the record considered as a whole."64

In Atkins, the Supreme Court left to the states the formulation and adoption of their own definitions of mental retardation.65 Under Texas law, "mental retardation is a disability characterized by (1) significantly subaverage general intellectual functioning"; "(2) accompanied by related limitations in adaptive functioning; (3) the onset of which occurs prior to the age of 18."66 The CCA defines a significant "subaverage intellectual functioning... as an IQ of about 70 or below."67 Because there is a measurement error of approximately 5 points, "any score could actually represent a score that is five points higher or five points lower than the actual IQ."68 With respect to limitations in adaptive functioning, the CCA has explained that "three adaptive-behavior areas are applicable to determining mental retardation: conceptual skills, social skills, and practical skills."69 Importantly, the subaverage intellectual functioning and significant limitations in adaptive functioning must be linked: "the adaptive limitations must be related to a deficit in intellectual functioning and not a personality disorder."70 A petitioner's failure to establish "any one of these three elements will defeat an Atkins claim."71

The district court concluded that Ladd failed to establish an Atkins claim. First, the district court found "by a preponderance of the evidence that Ladd has significantly sub-average intellectual functioning."72 The district court explained that this conclusion was compelled by (i) Ladd's scoring 67 on a Wechsler IQ test at age 13, and (ii) both parties' experts agreeing that both subsequently administered IQ tests, where Ladd achieved scores of 86 and 60, are less reliable because the higher score of 86 was achieved on a less accurate test instrument and the lower score of 60 was likely the result of malingering.73 Second, the district court found that "Ladd has failed to establish by a preponderance of the evidence that any of his deficits in adaptive functioning are significant."74 The district court explained that although both Ladd's and the State's experts agreed that Ladd "demonstrated deficits in adaptive behavior in functional academics, social skills, work, and communication," the experts disagreed as to whether these deficits were properly attributed to his mental retardation or his anti-social personality disorder.75 The district court considered the experts' testimony as to each adaptive deficits and concluded that the State's expert's testimony was more persuasive. It then concluded that, as to his deficits in functional academics, social skills, and work, Ladd's deficits were properly attributed to his anti-social personality disorder. As to his deficit in adaptive behavior in communications skills, the district court explained that neither expert claimed that a deficiency in this skill could be related to Ladd's anti-social personality disorder. Accordingly, the district court found that this deficit was related to his sub-average intellectual functioning, but, under Texas law, Ladd must possess two deficits in adaptive behavior. In addition, the district court found that to the extent Ladd has deficits in his adaptive behavior, these deficits are not significant limitations. In this regard, the district court found the State's expert's testimony to be more credible and persuasive.

Ladd argues that the district court committed clear error in concluding that he was not mentally retarded. First, Ladd agrees with the district court's finding that Ladd has significantly sub-average intellectual functioning. Second, Ladd argues that the district court clearly erred when it concluded (i) that all but one of Ladd's deficits in adaptive behavior are properly attributed to his anti-social personality disorder, and (ii) that none of Ladd's deficits in adaptive behavior are significant. Ladd argues that it is highly unlikely that Ladd would have subaverage intelligence and not have adaptive deficits. In addition, Ladd argues that the district court erred in requiring Ladd to demonstrate that his adaptive deficits were caused by his low intellectual functioning, and not his anti-social personality disorder.

The district court did not clearly err in finding that Ladd was not mentally retarded. To begin with, as the CCA has noted, the "adaptive behavior criteria are exceedingly subjective[.]"76 The district court held an extensive evidentiary hearing, and, as we noted in Rivera, the district court "having actually presided over the ... evidentiary hearing, is in a better position than this court to judge and weigh credibility of the witnesses who testified on the extent, duration, and causes of [petitioner's] adaptive functioning limitations."77 Here, the parties' experts agreed that Ladd suffered from some degree of deficit in adaptive functioning. The experts sharply disagreed as to whether these deficits were related to Ladd's subaverage intellectual functioning. The district court, having heard and evaluated the testimony of each expert, found the State's expert to be more persuasive. Considering that the district court is in the better position to reach such a conclusion, and that such a conclusion can be supported by the evidence, we find the district court's determination plausible and thus survives clear error review.

IV

For the foregoing reasons, we AFFIRM.