Paul Scrimo appeals from a judgment of the United States District Court for the Eastern District of New York (Donnelly, J.), denying his petition for a writ of habeas corpus pursuant to 28 U.S.C. §2254. We conclude that the trial court’s exclusion of three defense witnesses violated Scrimo’s constitutional right to present a complete defense. Accordingly, we reverse and remand the judgment of the district court with direction to grant the writ. Judge NEWMAN concurs in a separate opinion. DENNIS JACOBS, C.J. The petitioner, Paul Scrimo, was convicted by a jury of murdering Ruth Williams, chiefly on the testimony of the only person who was in the room with them when she was killed: John Kane. Scrimo petitioned for a writ of habeas corpus challenging his state court conviction for murder on the ground that he was deprived of the constitutional right to a meaningful opportunity to present a complete defense when the trial court excluded, as collateral, evidence relevant to establishing that the State’s main witness was the murderer. Scrimo also argues that he received ineffective assistance from his trial counsel. He appeals now the denial of the writ by the United States District Court for the Eastern District of New York (Donnelly, J.). We conclude that the State trial court’s exclusion of evidence violated Scrimo’s constitutional right to present a complete defense. Accordingly, we reverse without reaching Scrimo’s ineffective assistance of counsel claim.] BACKGROUND Ruth Williams was strangled to death in her Farmingdale apartment in the early morning of April 12, 2000. Two people were with her: Scrimo and Kane. Kane testified it was Scrimo who killed her. Scrimo’s defense, as laid out for the jury by counsel, was that Kane was the killer rather than Scrimo, that Kane sold drugs, that Williams was a customer, and that Kane choked her because of a dispute about a drug transaction. The DNA under the victim’s fingernails pointed toward Kane. Kane testified that she gripped his flesh while she gave him oral (unconsummated) sex. The prosecution surmised that Scrimo had a motive to kill her because the deceased rejected his advances and said that his wife was fat and ugly. I. At trial, the State elicited the following testimony from Kane. On Tuesday nights, Scrimo and Kane played darts at a bar in Farmingdale called Falcon’s Nest. On Tuesday, April 11, 2000, they and others played darts and drank at Falcon’s Nest until midnight, then walked to another bar, Granny O’Shea’s, where they saw Ruth Williams and drank some more before they all went to yet another bar called Y.L. Childs. Kane had a prior sexual relationship with Williams, who flirted with Kane and kissed him at the bars they visited that night. Kane and Scrimo left Y.L. Childs at around 4:00 a.m.; Williams had left some time before. Kane proposed that he and Scrimo go to Williams’s apartment for a drink, but when they arrived, they discovered that Williams was out of beer, so Scrimo left the apartment and went to a 7-Eleven for beer and cigarettes.1 While Scrimo was out, Williams performed oral sex on Kane, but not to completion. He “asked her to stop because [Kane] knew Scrimo would be coming back soon.” Trial Tr. 1432. Williams ran her fingers through his hair and across his buttocks. (The grope reported by Kane conveniently accounted for DNA beneath Williams’s fingernail, while the interruption implicitly explained why none of Kane’s DNA was elsewhere.) After the oral sex ended and Scrimo came back, the three of them sat in the kitchen drinking beer until at some point Scrimo stood up “and said that, you know, I’m not going to take this. I’m out of here,” and started to walk away. Id. at 1435. Kane stood up to persuade Scrimo to stay, but Williams said, “[f]uck him. Let him go home to his fat ugly wife.” Id. Scrimo then knocked Williams to the floor, strangled her, wrapped a wire around her neck, and pulled up on it. Kane interceded by grabbing Scrimo by the shoulders, but “[h]e was like a rock.” Id. at 1436. After Williams was dead, Scrimo wiped down the chairs and table with a napkin, instructed Kane to turn off the music and grab the beer, and left with Kane. The night of the murder, and when they met to play darts the next week, Scrimo told him to keep his mouth shut. Other witnesses offered little corroboration of the foregoing account of Kane: Francine Quinn identified Kane and Scrimo at Y.L. Childs and testified that, as she was walking home from the bar, she heard and saw Williams arguing loudly outside her home with a man fitting Scrimo’s description. However, Quinn was unable to pick Scrimo out of a lineup. When she testified at trial and before the grand jury, Quinn was unable to recollect whether she left Y.L. Childs before or after Scrimo and Kane. Police officers testified that both Scrimo and Kane provided false stories in the course of the investigation: Scrimo admitted that he knew Williams and saw her on the night of the murder, but denied going to Williams’s home with her, while Kane said that he knew nothing about the crime before telling the police the story he gave at trial. Police Officer Stark testified that she responded to a disturbance at Scrimo’s home on October 18, 2000, months after Scrimo’s release on bond. Stark testified that when she arrived, Scrimo came out, put his hands in the air, and said, “Paul Scrimo. I didn’t do it. John Kane did. I was never in that apartment.” Id. at 1407. Scrimo also told Stark that: while all three of them were at Y.L. Childs, Williams whispered in Scrimo’s ear that “she wanted drugs from Kane,” “Kane is a drug dealer,” and “[h]e doesn’t give away drugs for free,” id. at 1408; on the night of the murder, the three walked towards Williams’s apartment when the bar closed, but Scrimo never went inside; he went instead to the 7-Eleven to buy beer and cigarettes for Kane and Williams; he gave Kane the beer and cigarettes in an alleyway, and went home; and the reason Scrimo did not mention Kane to the police earlier was “because of the drugs,” id. at 1409. A Nassau County detective testified that Kane’s fingerprints were found on a compact disc in the victim’s apartment, and Scrimo’s fingerprints were not found on any materials. A forensic pathologist testified that Williams’s cause of death was strangulation and that her blood alcohol content was 0.26 percent at time of death — extremely high. Williams had no toxological indication of drug abuse and had not used cocaine in the 48 hours before death. Another Nassau County detective testified that he examined the black plastic cord that was wrapped around Williams’s neck, as well as a Leatherman cutting tool that was in Scrimo’s possession when he was arrested. The detective concluded that a black plastic fragment on the interior handle of the Leatherman did not originate from the cord tied around Williams’s neck. He believed the cord was cut with a one-directional shearing instrument, that the Leatherman was a shearing instrument of such a kind, but that he could not say that the cord was actually cut with the Leatherman. A firearm and tool-marks examiner testified that the Leatherman could have made the cut, but that he could not “say definitively” that it did. Id. at 935. A forensic expert testified that several items collected from the crime scene contained DNA consistent with Williams’s profile; that two cigarette butts contained DNA consistent with Kane’s profile; that DNA beneath one of Williams’s fingernails was consistent with the DNA of Williams and Kane; that neither Kane nor Scrimo could be excluded from DNA on a beer bottle; and that Kane could not be excluded from being the major donor of the DNA under the fingernail. The prosecution introduced evidence to support the assertion that Scrimo was “trying to get lucky”, id. at 1782, including testimony that Scrimo “thought [Williams] was good looking,” id. at 1142, that Williams had been dancing “all over” Scrimo and kissing him at the bars, id. at 444, 501-02, and that Scrimo was given a condom on the way to her apartment. The prosecution’s remaining witnesses shed no further light on whether Kane or Scrimo was the killer. II. Scrimo’s defense consisted mainly of an opening, a closing, attempts to cross-examine the State’s witnesses, and unsuccessful efforts to offer his own witnesses. In his opening argument, defense counsel described Kane as a barfly “selling cocaine,” id. at 338, and stated that the evidence would show that it was Kane, not Scrimo, who murdered Williams. The defense attempted to show by cross-examination that Kane was a drug dealer and that Williams used drugs and bought them from Kane, but the court sustained objections. The defense argued that the questions were relevant to Kane’s “drug relationship” with Williams and that “there will be evidence that there was a drug transaction going on that night.” Id. at 463. The court characterized the questions merely as an attack on Kane’s credibility and ruled that Kane’s alleged drug dealing was a collateral matter. Scrimo’s counsel argued that the fact of Kane’s drug dealing was not collateral and that the questions were not intended to attack credibility. For example, when defense counsel cross-examined Penny Shouse, one of the State’s witnesses, the trial court sustained objections to questions about cocaine use by Shouse and Williams and about their purchases from Kane. This led to a confused exchange: the court, assuming the questions were intended to impeach Shouse’s credibility, permitted questions regarding Shouse’s drug use only on the day she was testifying about and on the day of her testimony. Defense counsel tried to clarify that the issue was whether Williams used drugs and whether Kane sold them, not mere credibility: It’s not just this witness’s credibility. It’s not just Mr. Kane’s credibility….It is Mr. Kane — this witness was put on, who, among other things, and along with other witnesses, to establish the relationship of the various parties to each other…. I believe I should be allowed to inquire into her knowledge of Kane being a drug dealer…. I have evidence that this witness was a [partier] not only that got drugs from Kane…, but she partied, she used cocaine with the victim who also got drugs from [Kane]. Trial Tr. 460-61. The court was convinced that Scrimo’s counsel was trying “to impeach the credibility of a witness who hasn’t testified yet,” and disallowed the questions. Id. at 461. Scrimo’s counsel tried again: [I]t’s just not credibility. I’m entitled through witnesses that have been produced by the People to establish what they know about the relationship between the victim and somebody who claims he was right there and then cleaned up after an alleged murder that he claims happened the way he claims it happened. Id. at 462. The trial judge wondered, “[w]hat do you mean by the word ‘relationship?’” Id. at 462-63. Defense counsel explained, I mean, drug relationship. First of all, Kane in his statement [to the police] said he had a prior sexual relationship with the victim. He had a sexual encounter that — the night of the victim’s murder. I believe there will be evidence that there was a drug transaction going on that night. Id. at 463. The State’s objection was sustained and drug-related questions were limited to the day of the murder and the day of Shouse’s testimony. Id. When the court later sustained more objections to questions about drug use, defense counsel argued “it’s a question of the relationship between her and the witness and also the relationship between her and the victim.” Id. at 472. Later again, defending the relevance of the line of cross-examination, defense counsel pleaded, “the relationship between [Shouse] and Ruth Williams…she knew that Ruth Williams got cocaine from John Kane in that time frame, and her-the relationship between the victim and Kane is crucial.” Id. at 473. The trial judge adhered to his ruling: “I do not see any relevance whatsoever with respect to whether Ruth Williams partied — as you put it — with this witness.” Id. at 475. When Francine Quinn testified on direct examination, she stated that John Kane was a customer at Downtown Bar and Grill, where she worked as a bartender. On cross-examination, the court sustained objections to defense counsel’s questions going to whether Kane had “ever been barred from the Downtown for selling drugs,” id. at 566, and whether Quinn was present “when there was an incident involving a woman who grabbed money from John Kane claiming that he had shorted her on a drug sale,” id. at 567. The prosecutor pressed his objection, adding, “I want [defense counsel] sanctioned.” Id. at 568. In sustaining the State’s objection, the trial judge suggested to defense counsel how he could proceed with his line of questioning once Kane was called as a witness: “[y]ou can certainly ask Mr. Kane on the specific dates with respect to any cocaine transaction you want. If he denies it, I said you can bring in anybody you want under subpoena or bring them in.” Id. at 569. But when the time came for Kane’s cross-examination, the court asked for a good faith basis for certain questions the defense intended to ask about Kane’s drug dealing. Defense counsel gave reasons for his belief that Kane had sold drugs to several persons, including Stephanie Domaradzki, Charles Ball, and Jennifer Hartman, and represented that when Hartman protested to Kane in 1997 that drugs he sold her were diluted, and “tried to take some of her money back from a hundred dollars in change [Kane] had in the bar in the Falcon’s Nest, he started to choke her.” Id. at 1453-54. The court allowed Scrimo to ask Kane about these incidents — selling drugs and choking Hartman. On cross-examination, Kane denied selling drugs during the years prior to the murder, denied ever selling drugs to Domaradzki, Ball, and Hartman, and denied choking Hartman. When the State rested, the court solicited an offer of proof as to the admissibility of testimony from three witnesses the defense intended to call: Domaradzki, Ball, and Hartman (the “Witnesses”). Defense counsel stated that Ball would testify that he purchased drugs from Kane. The trial court ruled that this testimony went to Kane’s character for truthfulness and impeachment of his testimony, and was thus inadmissible extrinsic evidence of a collateral matter. Defense counsel again argued that “there should be testimony allowed with respect to prior drug sales by this witness, in view of his involvement in this crime and the relationship with the victim,” id. at 1629, that Ball’s testimony would “establish [Kane's] relationship to the victim in this case and that involves drug sales,” id. at 1630, and that one of the Witnesses would “testify about drug sales [Kane made] directly to the victim,” id. at 1631. The court allowed testimony only as to Kane’s reputation for truthfulness, and foreclosed questions about drug sales or any other specific acts that Kane had denied on the stand. Next, defense counsel offered that Hartman would testify that she purchased drugs from Kane, but did not mention the choking incident. The court stated that Hartman’s testimony also contradicted Kane’s testimony and was inadmissible for the same reasons as Ball’s testimony. Finally, defense counsel offered that Domaradzki would testify to the victim’s drug purchases from Kane. The court asked what the purchases have to do with the crime, and defense counsel explained: [Kane] is not just a witness to a crime. This is a person who was present who was certainly, at the very least, and based upon physical evidence, a participant in this matter based on his own testimony, who at the very least should have been charged with a felony of accessory after the fact, facilitation of murder, and, also, the relationship between the victim and the witness is crucial to the issue here, the issues before this jury. It’s a question of who did it. He’s not just a witness. What I see — what he saw happening, he was part and parcel of this and his relationship to the victim is crucial in this case. Id. at 1637 (emphasis added). Despite the court’s earlier assurance that defense counsel could “bring in anybody you want under subpoena or bring them in,” id. at 569, the trial court ultimately denied the request to call Hartman and Domaradzki as witnesses, and would allow Ball to testify only to Kane’s general reputation for truthfulness. The defense called none of the Witnesses, and rested. Defense counsel’s closing argued that Kane was a drug dealer, that his account of the events of the evening of April 11 made no sense, that the physical evidence at the scene of the crime pointed to Kane, and that the key question in the case involved Kane’s relationship to Williams. Scrimo was convicted of second degree murder on June 18, 2002. He was sentenced to 25 years to life. He has been in prison for 17 years. III. Scrimo’s appeal to the Appellate Division raised many claims, including that the exclusion of the Witnesses’ testimony violated his constitutional rights and that he received ineffective assistance of counsel (though not for the reasons set forth in Scrimo’s Section 2254 petition). The Appellate Division denied the appeal in an order dated November 10, 2009. The order did not rule on whether the preclusion of the Witnesses’ testimony violated Scrimo’s right to present a complete defense, except to state: “[t]he defendant’s remaining contentions are without merit.” People v. Scrimo, 67 A.D.3d 825, 826 (2d Dept. 2009). Scrimo’s application for leave to appeal to the New York Court of Appeals made the same arguments he made to the Appellate Division; leave to appeal was denied on March 29, 2010, People v. Scrimo, 14 N.Y.3d 805 (2010), and reconsideration was denied on July 30, 2010, People v. Scrimo, 15 N.Y.3d 778 (2010). Scrimo’s petition for a writ of habeas corpus repeated the arguments he made in the state appellate court. Judge Donnelly denied the petition, as well as a certificate of appealability, on September 29, 2017.2 Scrimo v. Lee, No. 11-cv-4171, 2017 WL 4381658 (E.D.N.Y. Sept. 29, 2017). The district court held that “the trial court did not abuse its discretion in precluding counsel from calling certain witnesses, because the subject — narcotics use — was collateral and not clearly linked to the April 12, 2000 murder.” Id. at *8. The court observed that “counsel was permitted to and did explore the subject of the victim’s drug use, her relationship to Kane, and whether Kane sold drugs” during cross-examination. Id. Finally, the court held that any constitutional error was harmless in light of the other evidence of Scrimo’s guilt. Id. A panel of this Court granted a Certificate of Appealability on the following issues: (1) whether Appellant was deprived of the constitutional right to “a meaningful opportunity to present a complete defense” when the trial court, relying on a rule barring collateral evidence, excluded evidence about John Kane’s bad acts (selling drugs, and a crime with a similar modus operandi) that was relevant to establishing that Kane was the real murderer, see Holmes v. South Carolina, 547 U.S. 319, 324 (2006); (2) whether, under Strickland v. Washington, 466 U.S. 668 (1984), defense counsel rendered ineffective assistance by failing to argue (i) that this evidence was admissible to prove that Kane had the motive and opportunity to commit the murder,…(ii) that excluding the evidence violated Appellant’s right to present a complete defense; (iii) that the trial court should have required the prosecution to admit Appellant’s October 18, 2000 statement to Officer Stark in toto (including any exculpatory aspects) or not at all. Dkt. no. 23. This appeal followed. DISCUSSION We review the denial of a Section 2254 habeas petition de novo. Washington v. Schriver, 255 F.3d 45, 52 (2d Cir. 2001). Because the claim that Scrimo was denied his constitutional right to present a complete defense was denied on the merits, our authority to review the decision is limited. Under the Antiterrorism and Effective Death Penalty Act (“AEDPA”), Scrimo is entitled to relief only 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. 28 U.S.C. §2254(d)(1).3 We “look through” the state appellate courts’ “unexplained decision[s] to the last related state-court decision that does provide a relevant rationale,” and determine whether that rationale was contrary to, or represented an unreasonable application of, clearly established federal law. Wilson v. Sellers, 138 S. Ct. 1188, 1192 (2018) (emphasis added). We therefore consider the rulings and explanations of the trial judge. A state court acts “contrary to” clearly established federal law if it (1) “arrives at a conclusion opposite to that reached by [the Supreme Court] on a question of law,” or (2) “decides a case differently than [the Supreme Court] has on a set of materially indistinguishable facts.” Williams v. Taylor, 529 U.S. 362, 413 (2000). “An unreasonable application of” federal law occurs if the state court’s “application of clearly established federal law was objectively unreasonable,” Jones v. Stinson, 229 F.3d 112, 119 (2d Cir. 2000) (quoting Williams, 529 U.S. at 409), or if it “fails to extend a principle of clearly established law ‘to situations which that principle should have, in reason, governed,’” Tueros v. Greiner, 343 F.3d 587, 591 (2d Cir. 2003) (quoting Kennaugh v. Miller, 289 F.3d 36, 45 (2d Cir. 2002)). The trial court’s decision need not teeter on “judicial incompetence” to warrant relief under Section 2254(d). Francis S. v. Stone, 221 F.3d 100, 111 (2d Cir. 2000). * * * We conclude that Scrimo’s claim is based on clearly established constitutional law (Part I). We also conclude that the trial court unreasonably applied this clearly established law because the exclusion of the Witnesses’ testimony was inconsistent with state evidentiary rules (Part II.A) and because the error, which excluded evidence that would have introduced reasonable doubt, was not harmless (Part II.B). I. We conclude that Scrimo’s constitutional claim is based on clearly established federal law as determined by the Supreme Court, and that the claim was fairly presented to the trial court. The Supreme Court has clearly and repeatedly held that a criminal defendant is entitled by the Constitution to a meaningful opportunity to present a complete defense, including the opportunity to call witnesses to aid in that defense: “[f]ew rights are more fundamental than that of an accused to present witnesses in his own defense.” Chambers v. Mississippi, 410 U.S. 284, 302 (1973); see also Crane v. Kentucky, 476 U.S. 683, 690 (1986) (“[T]he Constitution guarantees criminal defendants a meaningful opportunity to present a complete defense.”) (internal quotation marks omitted)); California v. Trombetta, 467 U.S. 479, 486 n.6 (1984) (“[C]riminal defendants are entitled to call witnesses on their own behalf and to cross-examine witnesses who have testified on the government’s behalf.”). As we have observed, “[t]he right to call witnesses in order to present a meaningful defense at a criminal trial is a fundamental constitutional right secured by both the Compulsory Process Clause of the Sixth Amendment and the Due Process Clause of the Fourteenth Amendment.” Schriver, 255 F.3d at 56. At the same time, a criminal defendant’s right to present evidence is not boundless; it may be limited by evidentiary and procedural rules “designed to assure both fairness and reliability in the ascertainment of guilt and innocence,” Chambers, 410 U.S. at 302, so long as such rules are not “arbitrary or disproportionate to the purposes they are designed to serve,” Rock v. Arkansas, 483 U.S. 44, 56 (1987). “The accused does not have an unfettered right to offer testimony that is incompetent, privileged, or otherwise inadmissible under standard rules of evidence.” Taylor v. Illinois, 484 U.S. 400, 410 (1988). In light of these principles, Scrimo’s petition is well grounded in clearly established federal law as determined by the Supreme Court. The Constitution protects a criminal defendant’s right to present evidence in his defense, including evidence tending to establish third-party culpability. We therefore proceed to consider whether the state court was adequately apprised that the Witnesses’ testimony was relevant to Scrimo’s defense and whether its decision was “contrary to” or “an unreasonable application of” this clearly established law. A court does not unreasonably apply federal law in “failing to guess a theory of relevance that was not argued” at trial. Fuller v. Gorczyk, 273 F.3d 212, 222 (2d Cir. 2001); see also Corby v. Artus, 699 F.3d 159, 168 (2d Cir. 2012) (“The state trial judge was not required to read between the lines of counsel’s motion to divine a previously unasserted legal theory.”). Here, the defense theory and its relation to the testimony proffered was sufficiently clear. The opening statement of the defense laid out the theory of the defense in unmistakable terms: Kane was a drug dealer with an ongoing relationship with the victim, who was also customer of his, and all the forensic evidence pointed to Kane being the murderer: Whether she was after [Kane] for sex or for drugs is a question you’re going to have to ask yourselves. And there may be evidence about that. But, the question is, what does he do? He’s there. They can prove he’s there. They know he’s got a prior relationship…. So, what does he do? He says, the only way out, I’m going to lay it on [Scrimo] — I’m going to lay it on the defendant. Trial Tr. 340. The issue is, who killed this poor woman? And there is only one thing I can tell you about that, every piece of evidence, scientific evidence, which you can’t fudge, points to Kane…. His prints are there. His DNA is all over the place…. [S]ubsequent DNA tests showed it was Kane’s DNA that was found under, not on — you heard it was on the fingernail. It wasn’t on the victim’s fingernail. It was scrapings from underneath her nail. Where somebody being strangled would struggle and you would get scrapings. Id. at 341. Who was there? Kane. Whose fingerprints are in the apartment? Kane’s. Whose DNA is on all other locations in the apartment? Kane. Who is the major [DNA] contributor to this beer bottle? Kane. Kane. Kane. Kane. Kane. Kane. Id. at 341-42. I think when you’re through, you will find that if there’s proof beyond a reasonable doubt, it’s proof that Kane committed this murder, not this defendant. Id. at 342. Later, when proffering a basis for calling the Witnesses to testify, defense counsel emphasized that they would testify about Kane’s prior drug dealing, and argued that “there should be testimony allowed with respect to prior drug sales by this witness, in view of his involvement in this crime and the relationship with the victim.” Id. at 1629. Thus, Ball’s testimony would “establish [Kane's] relationship to the victim in this case and that involves drug sales,” id. at 1630, and another of the Witnesses would “testify about drug sales [Kane made] directly to the victim,” id. at 1631. Then, having just previewed the Witnesses’ role in supporting the theory of Kane’s guilt, defense counsel emphasized that he was not seeking to call the Witnesses “merely to attack” Kane’s credibility, id. at 1630, but to show that he was the killer: [Kane] is not just a witness to a crime. This is a person who was present who was certainly, at the very least, and based upon physical evidence, a participant in this matter based on his own testimony…and, also, the relationship between the victim and the witness is crucial to the issue here, the issues before this jury. It’s a question of who did it. He’s not just a witness. What I see — what he saw happening, he was part and parcel of this and his relationship to the victim is crucial in this case. Id. at 1637 (emphasis added). The decisive issue was not Kane’s reputation for truthfulness, but whether he murdered Ruth Williams. In light of defense counsel’s opening statements and the arguments made at the proffer, the reasons for offering the Witnesses’ testimony were easy to comprehend. Just as the background assumption throughout a criminal case is that the evidence proffered by the prosecution is offered to advance the narrative of the indictment, here, the trial court should have understood that the evidence proffered by the defense was offered to advance the narrative set out in the opening statement. And defense counsel’s proffer — if less than perfect in places — did not leave the trial court to “guess a theory of relevance that was not argued.”4 Fuller, 273 F.3d at 222. The argument that the Witnesses’ testimony would present “a question of who did it” by elaborating Kane’s “relationship to the victim” was clearly before the court. Trial Tr. 1637. Accordingly, we easily conclude that the trial court was sufficiently apprised of the role of the Witnesses in Scrimo’s defense such that the constitutional implications of their exclusion were clear. We now turn to the question of whether the exclusion of the Witnesses’ testimony was “contrary to” or an “unreasonable application of” the law establishing Scrimo’s right to present a defense. II. The trial court did not act “contrary to” clearly established federal law. It did not decide a question of law differently from the Supreme Court, and this case does not “present a set of facts materially indistinguishable from a Supreme Court case.” Hawkins v. Costello, 460 F.3d 238, 244 (2d Cir. 2006). Instead, we consider under AEDPA whether “the state court’s application of clearly established federal law was objectively unreasonable,” Jones, 229 F.3d at 119, or if it “fail[ed] to extend a principle of clearly established law to situations which that principle should have, in reason, governed,” Tueros, 343 F.3d at 591 (internal quotation marks omitted). “Of course, ‘habeas corpus relief does not lie for errors of state law,’ and that necessarily includes erroneous evidentiary rulings.” Hawkins, 460 F.3d at 244 (quoting Lewis v. Jeffers, 497 U.S. 764, 780 (1990)). However, when a trial court’s evidentiary exclusions take on constitutional dimensions, as they do here, “we must examine the stated reasons for the exclusion and ‘inquire into possible state evidentiary law errors’ that may have deprived the petitioner of a fair trial.” Schriver, 255 F.3d at 57 (quoting Jones, 229 F.3d at 120). “[I]f the evidentiary ruling was correct pursuant to a state evidentiary rule, our inquiry is more limited. We consider whether the evidentiary rule is arbitrary or disproportionate to the purposes it is designed to serve.” Hawkins, 460 F.3d at 244 (cleaned up). On the other hand, “[i]f potentially exculpatory evidence was erroneously excluded, we must look to whether the omitted evidence evaluated in the context of the entire record creates a reasonable doubt that did not otherwise exist.” Id. (cleaned up); see also Wade v. Mantello, 333 F.3d 51, 59 (2d Cir. 2003) (confirming that “[t]his test applies post-AEDPA”). Evidentiary errors at trial are subject to “lenient harmless error review” on a habeas petition, Jones, 229 F.3d at 120, and only a “substantial and injurious effect or influence in determining the jury’s verdict” merits habeas relief. Brecht v. Abrahamson, 507 U.S. 619, 638 (1993) (internal quotation marks omitted). The creation of reasonable doubt satisfies the “substantial and injurious” standard. Jones, 229 F.3d at 120. We first consider whether the exclusion of the Witnesses’ testimony was consistent with state evidentiary rules that were stated by the trial court, and we conclude that it was not (Part II.A). We therefore do not reach the question whether those rules are themselves arbitrary or disproportionate. We then consider whether the error was harmless and whether the excluded evidence would have introduced reasonable doubt (Part II.B). We conclude that the error was not harmless and that the excluded evidence would have introduced reasonable doubt. A. The trial court excluded the Witnesses’ testimony, which would have contradicted Kane’s prior testimony, on the ground that it was extrinsic evidence on a collateral matter. For example, as to Ball, the court quoted a case it believed was “right on point”: “the testimony of the proposed witness would have been collateral to the question of the defendant’s guilt and was sought to be introduced merely to impeach the credibility of [a] prosecution witness.” Trial Tr. 1629 (quoting People v. Johnson, 143 A.D.2d 847, 848 (2d Dep’t 1988) (alteration in transcript)). But Johnson involved a witness the defendant sought to call to “demonstrate the bias or interest of a key prosecution witness.” 143 A.D. 2d at 847. Scrimo, on the other hand, argued that the Witnesses’ testimony was not collateral because it was not being offered “merely to attack…Mr. Kane’s credibility but to establish his relationship to the victim in this case and that involves drug sales.” Trial Tr. 1630. Counsel emphasized that Kane was “not just a witness to a crime,” that “the relationship between the victim and [Kane] is crucial,” and (indisputably) that “[i]t’s a question of who did it.”5 Id. at 1637. Scrimo’s defense was that Kane was a drug dealer who strangled the victim over a drug deal. The jury could have inferred non-payment, or payment in kind (oral sex) that failed to give satisfaction. The proposed testimony from the three Witnesses related to Kane’s prior drug transactions: one of those transactions involved the victim; another of those transactions ended with him choking his female customer. The Witnesses’ testimony was the opposite of collateral — it went to the obvious and decisive question of whether Kane committed the murder rather than Scrimo. True, as the trial court emphasized, the Witnesses’ testimony would have contradicted Kane’s testimony. But “a fact is not a collateral matter if it could be shown in evidence for any purpose independent of the contradiction [of a witness's testimony].” Rosario v. Kuhlman, 839 F.2d 918, 926 (2d Cir. 1988) (quoting People v. Schwartzman, 24 N.Y.2d 241, 246 (1969)). Nor was the testimony being offered solely to contradict Kane: it was offered to affirmatively support the defense’s theory of third-party culpability. Because that theory was not by any means collateral to the question of Scrimo’s guilt, it was error to exclude the Witnesses’ testimony for that reason. B. The last question is whether the trial court’s error was harmless. It falls into two parts: whether the Witnesses’ testimony could have been excluded on other grounds (Part II.B.1) and whether the testimony would have introduced reasonable doubt where none otherwise existed (Part II.B.2). 1. The State advances alternative grounds for supporting the trial court’s erroneous ruling that would render that error harmless. The State argues that the Witnesses’ testimony was properly excluded because the risk of prejudice outweighed its probative value. That is a ruling that the trial court did not make. In any event, the argument is defective. New York courts review the admissibility of third-party culpability evidence “under the general balancing analysis that governs the admissibility of all evidence.” People v. Primo, 96 N.Y.2d 351, 356 (2001). Such evidence may thus be excluded “if its probative value is outweighed by the prospect of trial delay, undue prejudice to the opposing party, confusing the issues or misleading the jury.” Id. at 355. However, third-party culpability evidence presents “particularly acute” “countervailing risks of delay, prejudice and confusion,” id. at 356; so its admission “may not rest on mere suspicion or surmise,” id. at 357. Accordingly, evidence of third-party guilt is routinely excluded unless evidence connects the third party to the crime. That depends in part on whether (as here) the third party was on the scene. In People v. Schulz, the New York Court of Appeals upheld a trial court’s exclusion of a photograph of a third party (named Guilfoyle) that the defendant sought to introduce in order to argue that he (not Schulz) committed the robbery. 4 N.Y.3d 521, 526 (2005). Although newspapers reported that Guilfoyle had committed other robberies around the same time, exclusion of the photograph was warranted because the defendant offered “no evidence which shows a modus operandi, a witness who saw Guilfoyle at the scene or even a connection between the getaway car and Guilfoyle.” Id. at 528. On the other hand, in People v. DiPippo, the Court of Appeals vacated a conviction and reversed the trial court’s exclusion of evidence of third-party culpability, even though no direct proof linked the third party to the crime scene, because a jailhouse informant submitted an affidavit implicating the third party, who had also been accused of committing the same crime in a strikingly similar manner. 27 N.Y.3d 127, 139-41 (2016). The Court of Appeals acknowledged that “proof directly linking the third party to the crime scene” is powerfully probative, but concluded that “proof connecting a third party to the crime may [also] establish the probative value of the proffered evidence.” Id. at 136 (emphasis in original). And in People v. Negron, the Court of Appeals vacated a conviction involving a shooting when the excluded evidence would have shown that a third party who “closely matched the description of defendant [and] lived in the same building” “was arrested the day after the incident” for possessing a weapon, even though the weapon “had not been used to commit [the] offense and [was] found on the roof of an adjacent building.” 26 N.Y.3d 262, 265 (2015). In that case, the evidence could not “be classified as ‘[r]emote’ or ‘disconnected’ from the crime at issue.” Id. at 269. At the risk of being obvious, Kane was on the scene and connected to the crime, the only question being whether he did it. Turning first to the testimony that Kane dealt drugs, the defense proffer for the purpose of cross-examining Kane gave an early account to the trial judge as to the Witnesses’ testimony. Defense counsel represented that Ball would testify to at least one purchase of cocaine from Kane in August 1998 at the Falcon’s Nest (one of the bars Kane and Scrimo visited the night of the murder); that Domaradzki would testify to “multiple purchases from Mr. Kane including purchases just prior to the murder at which time she shared cocaine purchased from Mr. Kane with the victim,” Trial Tr. 1455; and that Hartman would testify to cocaine purchased in 1997. The State objected that the alleged acts were “too remote in time,” id. at 1454; see also id. at 1450-53 (making similar arguments regarding remoteness and citing cases). But after a lengthy colloquy, the court rejected the State’s remoteness arguments and allowed defense counsel to cross-examine Kane with respect to all of the alleged drug purchases. Kane denied all of them. Later, when the defense sought to call the Witnesses to testify, counsel again proffered that each of the Witnesses would testify to drug purchases from Kane, that one of the Witnesses (presumably Domaradzki) would “testify about drug sales directly to the victim,” id. 1631, and that Domaradzki would testify to “purchases with the victim from Mr. Kane on or about” the date of the murder, id. at 1637.6 The State objected, and the court excluded all of this testimony, flatly precluding defense counsel “from saying anything about drugs.” Id. at 1634. The court thus acknowledged the obvious relevance and probative value of Kane’s drug dealing, including drug sales in 1997 and 1998, by allowing defense counsel to cross-examine him about it. Yet the court granted the State’s objection to calling the Witnesses to testify to those very facts, not on the basis that the testimony’s risk of delay, prejudice, and confusion would outweigh its probative value, but because it was impermissible extrinsic evidence on a collateral matter. As discussed above, that ruling was error as a matter of law. In light of Scrimo’s defense that Kane was a drug dealer who killed Williams over a drug deal gone bad, the probative value of testimony that Kane was a drug dealer overwhelms any risk of delay, prejudice, and confusion; a ruling otherwise would be error and an abuse of discretion. The risk of prejudice is virtually nil in light of defense counsel’s cross-examination of Kane regarding the same topics; the risk of confusion is likewise non-existent. The risk of delay is no more than the normal interval for testimony on a simple matter; the State can hardly contend that it would have expended much time cross-examining on a matter it contended was of no moment to Scrimo’s guilt. And, as set forth above, the trial court had already acknowledged the relevance of Kane’s alleged drug dealing, which is in any event undeniable in light of Scrimo’s theory of defense. Nor could the Witnesses’ testimony be excluded on the ground that Scrimo’s theory of defense was speculative. This is not a case in which the third party could not be connected to the crime scene, or the crime, see, e.g., Schulz, 4 N.Y.3d at 529: Kane testified that he was the only other person in the room, the only witness to the crime, and an accomplice in the coverup. The probability that Kane killed Williams is at least in balance with the probability that Scrimo did it — with the telling facts that the fingerprints were Kane’s, the DNA under the victim’s fingernail pointed to Kane, and Kane had the far more plausible motive that surfaced at trial. Moreover, Scrimo’s defense was hardly speculative in light of Scrimo’s account of what the victim told him — which the prosecution elicited — that “she wanted drugs from Kane,” “that Kane is a drug dealer,” and that “[h]e doesn’t give away drugs for free.” Trial Tr. 1408. But even if those statements are not enough to render Kane’s defense sufficiently plausible, defense counsel proffered that each of the Witnesses had bought drugs from Kane and that Domaradzki would testify that she (1) bought drugs (2) with the victim (3) around the time of the murder. True, the toxicologist testified that there was no evidence of cocaine use within 48 hours of Williams’s death. But the existence of a dispute between a drug supplier and a drug purchaser, whether arising from non-payment or another cause, does not logically require that the drugs purchased were recently consumed. And though Shouse testified that she had not personally observed Williams using cocaine, that hardly renders Scrimo’s theory of defense speculative. The cases cited by the State do not resemble the arresting circumstance of this case: Kane, who was the chief witness against Scrimo, was the only other person who could have been in the room when the murder was committed, the person with the more plausible motive, and the only person to whom the forensic evidence pointed. No speculation is needed to fix attention on Kane. Turning to the testimony that Kane choked Hartman during the course of the 1997 drug transaction, defense counsel proffered that Hartman would testify that she purchased drugs [from Kane] but that the drugs were cut and when she tried to take some of her money back from a hundred dollars in change he had in the bar in the Falcon’s Nest, he started to choke her. Id. at 1453-54. When the defense attempted to call Hartman, who bought drugs from Kane and was choked by him over a disagreement regarding the sale, defense counsel began to proffer that she would testify that she “purchased previously” and “that the material she purchased was cut and was no good and then there was —,” id. at 1635, but the trial court interrupted to point out that Kane denied the account while he was on the stand and to grant the State’s objection to Hartman as a witness, id. at 1636. Again, the trial court allowed defense counsel to cross-examine Kane with respect to the choking incident, but granted the State’s objection to calling Hartman as a witness on the basis that her testimony was improper extrinsic evidence of a collateral matter. The trial court thus acknowledged the relevance of the incident without considering (or ruling on) whether Hartman’s testimony would cause undue confusion, prejudice, or delay. The State argues that Kane’s chosen method of settling disputed drug transactions — choking — is not a sufficiently unique modus operandi to compel the conclusion that he choked Williams. Appellee Br. 35. But the State is confused. On one hand, modus operandi is a generic term to describe the similarity of behavior. But in some circumstances evidence of modus operandi can be an exception to the state evidentiary rule, named for People v. Molineux, 168 N.Y. 264 (1901), that “[e]vidence of uncharged crimes is inadmissible where its only purpose is to show bad character or propensity towards crime,” People v. Arafet, 13 N.Y.3d 460, 464-65 (2009). It is only when evidence of a third party’s modus operandi across two crimes is used to carve out an exception to the Molineux rule that the proffering party must show that “the similarities were unusual enough to compel the inference that the defendant committed both.” People v. Beam, 57 N.Y.2d 241, 251 (1982). Here, no Molineux argument was made,7 so the prior choking incident is evaluated “under the general balancing analysis that governs the admissibility of all evidence,” Primo, 96 N.Y.2d at 356, keeping in mind that third-party culpability evidence presents “particularly acute” “countervailing risks of delay, prejudice and confusion,” id. The risk of prejudice and confusion from the testimony is minimal since the trial judge already allowed cross-examination on the topic. The risk of delay, again, is insubstantial. The relevance of the testimony is simply obvious, as the court implicitly acknowledged when it allowed cross-examination regarding the incident: Kane’s use of violence — specifically, choking — in connection with contested drug transactions has probative value and supports the defense theory that he strangled Williams over a drug transaction, or the unconsummated effort to pay him with sex. We need to consider, however, whether Hartman’s testimony about the choking incident could be considered evidence of a “[r]emote act[], disconnected and outside of the crime itself,” that the trial court would have discretion to exclude. Schulz, 4 N.Y.3d at 529. To be clear, this case in no way resembles Schulz, where a picture of a man who could not be tied to the crime or to the scene was properly excluded. But our deferential harmless error review requires us to acknowledge that the trial court could have excluded the testimony regarding the choking incident on this ground, and that such a ruling would not have been an abuse of discretion. Accordingly, we conclude that the trial court’s exclusion of the testimony relating to Kane’s drug sales and the victim’s prior drug use could not be justified on alternative grounds, but its exclusion of Hartman’s testimony regarding the prior choking incident could be. 2. The final inquiry is whether the omitted evidence would have introduced reasonable doubt where none otherwise existed. We conclude that it would have. “[I]f the verdict is already of questionable validity, additional evidence of relatively minor importance might be sufficient to create a reasonable doubt.” Jimenez v. Walker, 458 F.3d 130, 147 (2d Cir. 2006) (quoting United States v. Agurs, 427 U.S. 97, 113 (1976)). Here, the State’s case was thin. There were only two candidates for the killer, one of them the defendant, and the other the State’s chief witness, and each pointed to the other. Both candidates changed their stories to the police on several occasions. The forensic evidence was inconclusive, though it pointed in Kane’s direction. And the sole motive for the murder given by Kane, who was there, was that the victim called Scrimo’s wife fat and ugly. This motive — chivalry — was weak if not risible. The state’s supplemental explanation — that Scrimo committed the murder because he was “trying to get lucky,” and failed — lacks firm evidentiary support. Trial Tr. 1782. If the trial court had allowed the Witnesses to testify, the jury would have heard that Kane was a drug dealer, that the victim was a customer of Kane’s, and that the victim was involved in a drug transaction with Kane around the time of the murder. None of this evidence was before the jury. The Witnesses’ testimony cannot be considered cumulative: on the witness stand, Kane denied selling drugs, and this testimony was in effect unrebutted. The State elicited from the police that Scrimo quoted the victim saying that Kane was a drug dealer from whom she sought drugs, but that was self-serving double-hearsay. The jury had nothing but Scrimo’s word, and was entitled to find — as it apparently did — that the testimony was not credible. Accordingly, independent support for the conclusion that the victim used drugs and that Kane sold drugs to her would have been powerful and needed support for Scrimo’s defense that Kane strangled Williams as the result of a drug deal gone bad. In circumstances in which (as here) the marginal evidence pointing to the defendant over another person is flimsy, and the excluded evidence was the only independent source of facts essential to proving the defense’s theory that the other person committed the crime, we must conclude that the wrongfully excluded testimony would have introduced reasonable doubt where none otherwise existed. We therefore conclude that Scrimo was deprived of his constitutional right to present a complete defense, and that he is entitled to the relief he seeks. CONCLUSION For the foregoing reasons, the judgment of the district court is REVERSED and the case is REMANDED. The district court is instructed to issue a writ of habeas corpus to Scrimo by the twentieth calendar day after the issuance of the mandate unless the State has, by that date, taken concrete and substantial steps to retry Scrimo. Jon O. Newman, Circuit Judge, concurring: With one significant reservation, I join Judge Jacobs’ thorough opinion ruling that Paul Scrimo’s constitutional right to present a complete defense was violated by the state trial judge’s exclusion of evidence pointing to the distinct likelihood that Scrimo’s accuser, John Kane, committed the murder for which Scrimo was convicted. I write to point out that, in addition to the evidence Judge Jacobs deems erroneously excluded, the trial judge also erroneously excluded one of the two most probative items of evidence that Kane murdered the victim,8 his previous act remarkably similar to the act that resulted in the victim’s death. Scrimo’s defense was that Kane, the only person other than Scrimo and the victim who was present in the room where the murder occurred, choked the victim to death because of a dispute about Kane’s sale of narcotics to the victim. The excluded evidence was Jennifer Hartman’s account of an episode three years before the murder in which Kane choked her because of a dispute about Kane’s sale of narcotics to her. Fortunately, Hartman survived the choking episode and was prepared to testify about it at Scrimo’s trial. The trial judge excluded her testimony, mistakenly thinking that it has been offered to impeach Kane’s credibility, rather than to show that he murdered the victim. Judge Jacobs identifies several items of evidence improperly excluded, but when he considers the Hartman choking episode, he states that the state court trial judge “could have excluded” it on the ground that it “could be considered evidence of a ‘remote act, disconnected and outside of the crime itself,’” Maj. Op. at 41 (emphasis in original) (brackets omitted) (quoting People v. Schulz, 4 N.Y.3d 521, 529 (2005)), and that “such a ruling would not have been an abuse of discretion,” id. On the contrary, the evidence was not remote; properly admitted, it would have been devastating for Kane and critical for Scrimo; and its exclusion as “remote” would have far exceeded the trial judge’s discretion. Judge Jacobs acknowledges that Hartman’s excluded testimony “has probative value and supports the defense theory that [Kane] strangled [the victim] over a drug transaction.” Maj. Op. at 40-41. Its obvious probative value arises because it shows the modus operandi of Kane’s conduct when one of his female customers has a dispute with him over a narcotics transaction. Schulz, which Judge Jacobs acknowledges does not resemble Scrimo’s case, rejected a complaint about excluding evidence because the defendant there “offers no evidence which shows a modus operandi.” 4 N.Y.3d at 528. In the pending case, Scrimo offered very similar evidence of modus operandi. Of course, a trial judge can consider the time interval between a prior similar act and the act at issue, and, at some point, a long interval would likely be a permissible ground for exclusion, but the probative force of the prior act derives primarily from the degree of similarity to the act at issue. With Kane’s prior act so similar to the act at issue, an interval of three years would not have been a permissible basis for exclusion of exculpatory evidence, even if the trial judge had relied on it.9 “[T]he standard of admissibility when a criminal defendant offers similar acts evidence as a shield need not be as restrictive as when a prosecutor uses such evidence as a sword.” United States v. Aboumoussallem, 726 F. 2d 906, 911-12 (2d Cir. 1984) (considering Fed. R. Evid. 404(b)).10 The egregiousness of the trial judge’s constitutional error was enhanced by his reneging on an assurance he gave defense counsel. First, the judge explained to defense counsel, “You can certainly ask Mr. Kane on the specific dates with respect to any cocaine transaction you want. If he denies it, I said you can bring in anybody you want.” Tr. 569. Then, when defense counsel cross-examined Kane about the Hartman episode, Kane denied that it had occurred. But when defense counsel then proffered Hartman as a witness, the trial judge excluded her testimony as “collateral,” Trial Tr. 1643, mistakenly thinking it was offered only to impeach Kane’s credibility. The erroneous exclusion of Hartman’s testimony of Kane’s prior choking of a female narcotics customer adds significantly to the grounds Judge Jacobs documents for issuance of a writ of habeas corpus.