Peterson, Justice. Rodney Noel was granted habeas relief from his conviction for murdering nine-month-old Terrell Williams (“Terrell”). The habeas court held that Noel’s appellate counsel provided ineffective assistance for two related reasons: (1) counsel failed to challenge the trial court’s denial of Noel’s right to impeach his intimate partner and Terrell’s mother, Crystal Williams (“Williams”), using three prior violent acts by her, and (2) counsel failed to assert Noel’s right to use these acts as proof that Williams, not Noel, killed Terrell. The State appeals. We disagree with the habeas court that appellate counsel’s performance was constitutionally ineffective. Noel’s claim regarding alleged impeachment error fails because it was not preserved at trial and so could not have been successfully raised on appeal. And Noel has not shown that any deficiency of appellate counsel regarding proof of third-party guilt was prejudicial. We therefore reverse. 1. Background (a) Noel is accused of murdering Terrell Williams. According to trial testimony, in March 2007, Noel, Terrell, and Williams traveled to Atlanta from Chicago for the weekend, staying at a hotel. Shortly before this, there was an incident where Williams threw Terrell into his car seat, but when Terrell left Chicago, he appeared to be healthy. Early in the weekend he had a hurt lip, which Noel and Williams attributed to Terrell’s car seat tipping over on the hotel floor while he was not strapped in. A doctor specializing in child protection testified that she found this explanation suspicious, but could not rule out the possibility that this injury was accidental. Hotel housekeeper Laverne[1] Pickett testified that the following Monday afternoon, she was cleaning the room next to Noel’s. She heard a baby crying and a man repeatedly saying “shut up,” then a thump, after which the noise stopped. She knocked on the door, and Noel answered. She looked past him into the room and saw Terrell in a car seat. Noel attempted to cast doubt on Pickett’s testimony. He testified that she never came to his door. He presented a copy of the time-card reflecting when Pickett clocked in and out for work, and that card indicated that Pickett may have left for the day before she claimed to have encountered Noel. However, the hotel’s record keeper explained that the card did not necessarily show that Pickett had departed, and confirmed that Pickett was assigned to clean Noel’s room and others on the floor that day and that Pickett initialed a form indicating that she cleaned that room. Noel also called his defense investigator, who testified that he spoke with Pickett. The investigator testified that Pickett told him Noel was dressed (which conflicted with another witness’s testimony from the same timeframe) and that Pickett told the investigator she did not, in fact, hear a thump. In addition, Noel presented evidence that a different housekeeper reported hearing “unnatural” baby cries near Noel’s room, but no other sounds, and that this housekeeper denied that Pickett ever mentioned what she saw when she went to the room. Separately from Pickett’s testimony, a hotel maintenance engineer testified that he saw Noel naked in the room’s doorway (a paramedic also described Noel as undressed), panicking and shouting for help while crouching over Terrell. The engineer called 911 and instructed Noel in CPR. Police officers and paramedics arrived. Paramedics did not find anything in Terrell’s mouth, although he had “a white substance” around it. When they asked Noel what happened, all he said in response was that Terrell “had some ice cream earlier.” Terrell had no pulse or breath, and his eyes were fixed and dilated. Terrell was placed on life support at the hospital and soon died. Williams told a hospital social worker, and testified at trial, that she never believed Noel hurt Terrell. According to the social worker, Williams “initially smiled and giggled often” while accompanying Terrell on his way to the hospital. Williams denied doing so. Noel’s cousin also testified that she spoke by phone with Williams while Williams was at the hospital, and Williams seemed unconcerned about Terrell but very anxious about Noel. Hospital records did note that Williams cried “profusely” when she learned that Terrell sustained severe brain damage. It was undisputed at trial that only Noel was in the room with Terrell immediately before Terrell began manifesting a medical emergency. Williams told police that she had put Terrell in his car seat so he could sleep, gone downstairs to do laundry, and upon returning, found Terrell unresponsive. She testified that Noel told her Terrell had choked while Noel was sleeping. Noel told a paramedic he was in the shower when he heard Terrell choking and got out to help. But he later told a detective that when Williams went downstairs, he dozed off and awoke to the sound of Terrell choking. He then shook Terrell and tried to do CPR, put water on him in the shower,[2] and held him in front of the air conditioner. Asked by a detective to demonstrate how he shook Terrell, Noel gave “a very physical shake.” Noel testified that after none of this worked, he called for help. Noel soon told the detective, though, that the detective had misunderstood him and gave a different demonstration, indicating that he only lightly shook the car seat. At trial, Noel testified that he “jostled” either Terrell or the car seat holding him. At trial, medical experts disagreed about the cause and timing of Terrell’s medical event. It was undisputed that Terrell suffered a fatal “severe brain injury” including bleeding and swelling. The only expert who testified about choking denied that choking could have caused Terrell’s injuries. According to three State experts, Terrell’s head injuries were consistent with having been violently shaken shortly before manifesting a medical emergency. However, the medical examiner attributed Terrell’s death only to non-accidental traumatic head injuries generally, and could not make a determination about shaking as the specific cause. The defense’s expert testified that Terrell’s head injuries were consistent with being hit by a hand or fixed object – not with being shaken – and could have been inflicted up to 24 hours before Terrell became nonresponsive. He testified that Terrell’s head injuries may not have been immediately visible or quickly incapacitating. Terrell also had some bruising on his buttocks and thigh, according to the defense expert and a State expert. (Additionally, while the medical examiner attributed the buttocks shading to a natural skin mark, he did note buttock abrasions and thigh bruising.) The defense expert indicated that the buttock bruising was from blunt force and could have been caused by squeezing or by being struck with a linear object, like a belt. The medical examiner also stated that a belt could have caused the thigh bruising. Two of Williams’s belts were found in the hotel room, and Noel denied having any belts of his own with him. Another State expert disavowed being able to tell when this non-head bruising — which she did not personally see when examining Terrell — was caused. (b) Noel tries to introduce Williams’s three violent acts. During the trial, Noel blamed Williams for Terrell’s injuries and tried to present evidence of three prior violent acts Williams had committed in Illinois. In 2004, she struck a fellow high school student with a padlock and pleaded guilty to battery, receiving a one-year sentence. In 2007, she was charged with domestic battery for pushing her adult aunt to the ground; it is not clear whether this resulted in a conviction. In 2008 — between Noel’s 2007 indictment and his 2009 trial in this case — Williams pleaded guilty to domestic battery with bodily harm, which Noel characterizes as the stabbing of an ex-boyfriend, and she was sentenced to 18 months of probation. The State moved in limine to exclude evidence of these acts. Noel’s counsel initially said that “the applicable statute” as to admissibility was former OCGA § 24-9-84.1, under which he claimed “any evidence” of crimes punishable by one year or more “can be introduced into the trial,” and “what we’re talking about here is impeachment material relevant to a State’s witness.”[3] He continued that he wanted “to introduce certified copies of these documents into evidence to impeach [Williams] in the event she did not acknowledge the conduct.” But counsel then stated, “I’m not offering this information to impeach her. I’m going to be asking her questions about the offenses for the purposes of showing her propensity for violence and inability to control her anger,” adding that “nothing could be more germane” to his defense. Following a lengthy exchange, counsel concluded by disavowing any intention of impeaching Williams: “. . . I’m not seeking to impeach her. That’s not the goal here. That’s not what I need to do. I’m only asking the questions to establish her propensity for violence and inability to control her anger, which is absolutely relevant to the facts in this case.” The trial court asked whether this was “just a question of relevance.” Counsel agreed that it was, as he was just trying to show that the only other person who could have fatally injured Terrell “is a violent person who can’t control her anger.” The trial court barred the evidence as irrelevant and because “the probative value does not exceed the prejudicial effect.” (c) Noel is convicted, the conviction is affirmed, and he obtains habeas relief. The jury acquitted Noel of malice murder, but found him guilty of three counts of felony murder, predicated on separate counts of aggravated assault, aggravated battery, and first-degree child cruelty, and guilty of the predicate counts as well. On direct appeal, Noel did not challenge the trial court’s ruling as to excluding evidence of Williams’s prior violent acts, and this Court affirmed his convictions. See Noel v. State, 297 Ga. 698 (777 SE2d 449) (2015). Through new counsel, Noel filed a habeas petition challenging his appellate counsel’s failure to raise the admissibility of the contested evidence of Williams’s prior violent acts, both as impeachment under former OCGA § 24-9-84.1 and as proof of third- party guilt. The habeas court concluded that appellate counsel provided ineffective assistance and granted Noel relief. The State now appeals. 2. Analysis A claimant raising ineffective assistance of appellate counsel must demonstrate both that counsel performed deficiently and that this deficiency prejudiced him. See Strickland v. Washington, 466 U.S. 668, 687 (104 SCt 2052, 80 LE2d 674) (1984). Deficiency means that “the identified acts or omissions were outside the wide range of professionally competent assistance.” Id. at 690. It turns on “the objective reasonableness of counsel’s performance, not counsel’s subjective state of mind.” Brown v. State, 302 Ga. 813, 815 (2) (809 SE2d 742) (2018). Prejudice means that “a reasonable probability exists that . . . the outcome of the appeal would have been different.” Gramiak v. Beasley, 304 Ga. 512, 513 (I) (820 SE2d 50) (2018). “We need not address both components of this test” if one is not proven. Watson v. State, 303 Ga. 758, 762 (2) (d) (814 SE2d 396) (2018). Although we review a habeas court’s factual findings only for clear error, we “appl[y] the facts to the law de novo” in analyzing deficiency “and whether any purported deficiency was prejudicial.” Johnson v. Williams, 308 Ga. 791, 794 (2) (843 SE2d 550) (2020). The habeas court erred when it ruled that appellate counsel was constitutionally ineffective. Noel’s claim that the contested evidence was admissible for impeachment was not preserved at trial, so appellate counsel was not deficient for failing to raise it.[4]And any deficiency in failing to raise the evidence’s admissibility as proof of third-party guilt was not prejudicial. (a) Noel’s impeachment claim was not preserved at trial, so his appellate counsel was not deficient in not raising that issue. Noel contends, and the habeas court ruled, that appellate counsel performed deficiently by failing to argue on appeal that the contested evidence should have been admitted under former OCGA § 24-9-84.1. That statute allowed a witness to be impeached with felony convictions, subject to a probative value-prejudice balancing test. See, e.g., Martin v. State, 305 Ga. App. 764, 767 (2) (700 SE2d 871) (2010). This claim was not preserved at trial. “Under the old Evidence Code, to preserve for any sort of review on appeal a claim that the trial court improperly excluded . . . evidence under a particular theory, a defendant had to argue at trial that the evidence was admissible under that theory.” Cross v. State, 309 Ga. 705, 710 (2) (848 SE2d 455) (2020). Noel’s trial counsel ultimately did not seek introduction of the contested evidence for impeachment under former OCGA § 24-9-84.1. Although counsel initially referenced that statute and impeachment, he concluded by saying only that the evidence was admissible to show Williams’s propensity to anger, expressly disavowing an impeachment theory. Noel’s asserted OCGA § 24-9-84.1 error was not preserved, so appellate counsel was not deficient for failing to raise it.[5] (b) Noel failed to show prejudice from any deficiency by counsel regarding proof of third-party guilt. Noel failed to show prejudice from any deficiency by appellate counsel in failing to raise the contested evidence as proof of third- party guilt. There is no reasonable probability that Noel’s appeal would have had a different outcome had appellate counsel raised the issue. Under the law at the time of Noel’s trial, a defendant could “introduce relevant and admissible testimony tending to show that another person committed the crime for which the defendant is tried.” Klinect v. State, 269 Ga. 570, 573 (3) (501 SE2d 810) (1998); see also Holmes v. South Carolina, 547 U.S. 319, 324 (126 SCt 1727, 164 LE2d 503) (2006) (discussing accused’s federal constitutional right to present a full defense). But for evidence to be admissible on this basis, it had to “raise a reasonable inference of the defendant’s innocence,” and either “show that the other person has recently committed a crime of the same or similar nature” or “directly connect the other person with the corpus delicti.” Klinect, 269 Ga. at 573 (3). We need not decide whether the contested evidence should have been admitted under this test. In order to prevail in habeas corpus proceedings based on ineffective assistance of appellate counsel, Noel must show more than what would be required for admissibility (that the evidence would have raised a reasonable inference of Williams’s guilt, and either show that she committed a crime of the same or similar nature, or directly connect her with the corpus delicti); he also bears the higher burden of showing a reasonable probability that his appeal would have had a different outcome but for counsel’s deficiency. See Gramiak, 304 Ga. at 513 (I). Noel has not succeeded in doing so. The case against Noel was not overwhelming, but neither was it particularly weak. Pickett testified that she heard a man tell a crying baby to “shut up,” then a thump, after which the baby was silent; after this, she saw Noel alone with Terrell. Noel first said he shook Terrell and demonstrated doing so forcefully, then claimed that he only lightly “jostled” either Terrell or the car seat holding him. Noel also changed his story about whether he was sleeping or showering before he noticed Terrell having difficulties. His claim that Terrell choked did not align with any of the medical expert testimony. Noel does not challenge the admissibility of this circumstantial evidence, and it amply supports the jury’s verdict, even considering Noel’s attempts to undercut Pickett’s credibility. Cf. Virger v. State, 305 Ga. 281, 286 (2), 294 (7) (824 SE2d 346) (2019) (deeming evidence of child murder “strong” where child manifested bruising after being with defendant, who was one of two adults present at time of fatal injury, and defendant’s account contradicted medical evidence). But prejudice requires more than just a consideration of the strength of the case against Noel. It requires considering the marginal effect the introduction of the excluded evidence would reasonably have had. See Yi v. State, 267 Ga. 171, 172 (2) (475 SE2d 623) (1996) (“In considering prejudice, the defendant has the burden of showing a reasonable probability that without counsel’s errors the jury would have had a reasonable doubt concerning guilt.”). Here, that effect was not reasonably likely to have been significant. None of the three incidents regarding Williams involved violence against a young child. Noel was allowed to introduce evidence that more directly gave rise to an inference of Williams’s guilt — her throwing Terrell into a car seat only a few days earlier, the possibility that Terrell was beaten by one of Williams’s belts, and Williams’s inappropriate demeanor on the way to and at the hospital. Whatever additional inference — beyond that already arising from the admitted evidence — that might arise from three incidents of violence against adults over a four-year period is simply too tenuous to constitute prejudice in the context of this case. This conclusion is reinforced when we compare the excluded evidence here with the evidence in other cases admitted as raising a reasonable inference of third-party guilt. The other acts in those cases had as a victim either the same person as the charged crime or a similarly vulnerable child. See Gilreath v. State, 298 Ga. 670, 673-674 (2) (784 SE2d 388) (2016); Scott v. State, 281 Ga. 373, 376378 (3) (637 SE2d 652) (2006). This distinction does not necessarily mean that the contested evidence was properly excluded from the trial; again, we express no view on that subject. But it does mean that the inference of Williams’s guilt flowing from that evidence would have been substantially weaker than in Gilreath and Scott, which, in turn, undercuts Noel’s effort to carry his higher burden of showing prejudicial deficiency in appellate counsel’s performance. In the light of the evidence against Noel and the comparatively weak implication of guilt the contested evidence cast on Williams, Noel was not prejudiced by any deficient performance by appellate counsel as to this issue. Judgment reversed. All the Justices concur.
