KELLY, Circuit Judge.

A Minnesota jury found Charles Yang guilty of twelve counts of murder. After appealing the verdict to the Minnesota Supreme Court, Charles Yang filed a habeas corpus petition pursuant to 28 U.S.C. § 2254, alleging violations of his Sixth Amendment Confrontation Clause rights during his trial. The district court1 denied the petition with prejudice and on the merits. With jurisdiction under 28 U.S.C. § 2253, we affirm.

I. Background

On February 3, 2005, a pool hall fight between the largely Hmong gang "Menace of Destruction" ("MOD") and a group of Tibetan men resulted in two men killed and four wounded. The sequence of events is set out in greater detail in the district court opinion, but the following describes the facts as relevant here. Earlier that day, MOD members made hostile comments to some of the Tibetans in the parking lot of a pool hall in Columbia Heights, Minnesota. That night, at least one of the Tibetans confronted one of the MOD members in the pool hall. A fight began inside the hall, but both groups soon ran out the back door and into the alley nearby. The district court found that at least twelve and possibly twenty gun shots were fired. Once the gunfire started, police officers came quickly to the pool hall, and some stopped a car that was leaving the area. MOD member Sai Vang was driving the car, with petitioner Yang in the passenger seat and Yang's brother Grogan Yang (also an MOD member) in the back seat. Police found two guns under the driver's seat and a .357 Magnum Smith and Wesson under Yang's seat, with six empty bullet shells. Yang acknowledged that he, too, was a member of the MOD gang and had been at the pool hall that night. A subsequent search of Yang's home uncovered .357 ammunition in his bedroom.

Yang was charged with aiding and abetting first-degree premeditated murder (two counts); aiding and abetting first-degree premeditated murder for the benefit of a gang (two counts); aiding and abetting attempted first-degree murder (four counts); and aiding and abetting attempted first-degree murder for the benefit of a gang (four counts). At trial, three witnesses testified against Yang based on conversations with him while in the Anoka County Jail. Other prosecution witnesses included Vang (the driver of Yang's car) and Xee Lor, both of whom were also MOD members and were also charged with twelve felony counts. Vang's and Lor's plea agreements allowed them to plead guilty to lesser offenses, and they accordingly expected shorter sentences than if they had gone to trial. The plea agreements also required them to testify at Yang's trial.

The Minnesota trial judge prohibited defense counsel from cross-examining codefendants Vang and Lor about the number of months by which their sentences would be reduced based on their plea agreements; he permitted cross-examination into the percentage of reduction, if the parties could agree on percentages to use. No such agreement was reached. Although the district court denied Yang's federal habeas petition, the court granted a certificate of appealability on the issue of whether Yang's rights under the Confrontation Clause were violated by the limit on his counsel's ability to cross-examine Vang and Lor regarding the extent to which their sentences might be reduced in exchange for their testimony against Yang.

II. Discussion

In reviewing a habeas petition, we first evaluate whether the state court ruling at issue was contrary to, or an unreasonable application of, clearly established law as reflected by the holdings, not the dicta, of Supreme Court decisions at the time of the relevant state court decision. 28 U.S.C. § 2254(d)(1); see also Williams v. Taylor, 529 U.S. 362, 412, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). In this context, "contrary to" means that the state court arrived at a conclusion opposite to that reached by the Supreme Court on a question of law. Id. at 405, 120 S.Ct. 1495. A ruling is an "unreasonable application of" Supreme Court precedent if the state court identifies the correct governing legal principle but unreasonably — rather than simply erroneously or incorrectly — applies that principle to the facts of the prisoner's case. Id. at 409, 413, 120 S.Ct. 1495. "In other words, the state court's application might be erroneous in our independent judgment without being `objectively unreasonable.'" Clemons v. Luebbers, 381 F.3d 744, 750 (8th Cir.2004) (quoting Wiggins v. Smith, 539 U.S. 510, 521, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003)). We presume that the state court's factual determination is correct unless Yang rebuts it with clear and convincing evidence. 28 U.S.C. § 2254(e)(1).

If Yang's Sixth Amendment rights were violated as a result of the Minnesota court's decision, he must also demonstrate that the error was prejudicial, meaning that it had a "substantial and injurious effect or influence in determining the jury's verdict." Brecht v. Abrahamson, 507 U.S. 619, 623, 113 S.Ct. 1710, 123 L.Ed.2d 353 (1993) (quotation omitted). "A `substantial and injurious effect' occurs when the court finds itself in `grave doubt' about the effect of the error on the jury's verdict." Toua Hong Chang v. Minnesota, 521 F.3d 828, 832 (8th Cir.2008) (quoting O'Neal v. McAninch, 513 U.S. 432, 435, 115 S.Ct. 992, 130 L.Ed.2d 947 (1995)). "`Grave doubt' exists where the issue of harmlessness is `so evenly balanced that [the court] feels [itself] in virtual equipoise as to the harmlessness of the error.'" Id.

A. Contrary to or Unreasonable Application of Clearly Established Law

A defendant has the right under the Sixth Amendment's Confrontation Clause to elicit enough facts about a witness' "possible biases, prejudices, or ulterior motives" to let the jury assess witness credibility. Davis v. Alaska, 415 U.S. 308, 316, 94 S.Ct. 1105, 39 L.Ed.2d 347 (1974). "[T]he exposure of a witness' motivation in testifying is a proper and important feature of the constitutionally protected right of cross-examination." Id. at 316-17, 94 S.Ct. 1105. "[A] criminal defendant states a violation of the Confrontation Clause by showing that he was prohibited in engaging in otherwise appropriate cross-examination designed to show a prototypical form of bias on the part of the witness, and thereby `to expose to the jury the facts from which jurors ... could appropriately draw inferences relating to the reliability of the witness.'" Delaware v. Van Arsdall, 475 U.S. 673, 680, 106 S.Ct. 1431, 89 L.Ed.2d 674 (1986) (quoting Davis, 415 U.S. at 318, 94 S.Ct. 1105). Even so, this right is not unlimited: a defendant is guaranteed "an opportunity for effective cross-examination, not cross-examination that is effective in whatever way, and to whatever extent, the defense might wish." Delaware v. Fensterer, 474 U.S. 15, 20, 106 S.Ct. 292, 88 L.Ed.2d 15 (1985). The trial judge "retain[s] wide latitude insofar as the Confrontation Clause is concerned to impose reasonable limits on such cross-examination based on concerns about, among other things, harassment, prejudice, confusion of the issues, the witness' safety, or interrogation that is repetitive or only marginally relevant." Van Arsdall, 475 U.S. at 679, 106 S.Ct. 1431. We take these considerations into account when assessing Yang's claim that the state court violated his Sixth Amendment rights.

In affirming Yang's verdict, the Minnesota Supreme Court relied on two Minnesota decisions regarding two codefendants that applied this line of cases. In State v. Greenleaf, 591 N.W.2d 488 (Minn.1999) and State v. DeVerney, 592 N.W.2d 837 (Minn.1999), the Court considered the impact on defendants' Sixth Amendment rights when the trial court limited the extent to which their codefendant Martin was cross-examined about his plea agreement. Martin's plea agreement provided that he was required to testify truthfully at Greenleaf's and DeVerney's trials and that he would receive a sentence ranging from 163 to 244.5 months. Greenleaf, 591 N.W.2d at 502. The trial judge did not allow Greenleaf's counsel to question Martin about the exact number of months by which his sentence could be reduced, but the judge "did not prohibit Greenleaf from cross-examining Martin regarding every other aspect of the plea agreement, including the percentages by which Martin's sentence could be reduced." Id. Mindful of Fensterer's admonition that "the Confrontation Clause guarantees only `an opportunity for effective cross-examination,'" the Minnesota Supreme Court found that the trial judge was correct to be "concerned that a recitation of the number of months of confinement Martin could serve might mislead the jury regarding the number of months another defendant, if convicted, might be confined." Id. (quoting Fensterer, 474 U.S. at 20, 106 S.Ct. 292). Since "[i]t is for the court to sentence, and not the jury," the trial court had "properly prevented the jury from speculating about possible sentences." Id. The Court reached the same conclusion in codefendant DeVerney's appeal. DeVerney, 592 N.W.2d at 845.

Based on Greenleaf and DeVerney, the trial judge ruled that Yang could not ask Vang and Lor about the specific number of months by which their sentences might be reduced. Although Yang was permitted to ask them about the percentage reduction, there was no such percentage explicitly included in their plea agreements, nor could defense and prosecution counsel agree on one. Tr. 795-804, No. 11-177, ECF No. 5 Ex. 4. Yang was thus unable to elicit information that would quantify Vang's and Lor's anticipated sentence reductions. He was, however, allowed to ask Vang about the charges that had been brought against him; those to which he ultimately pled guilty; and whether he was satisfied with the plea agreement. Id. at 1777-79. On direct exam, Lor testified, unprompted, that he had taken a "32 years plea agreement" with the state; when asked whether he agreed "to plead guilty to a lower count of murder ... to take advantage of less time in jail" and whether he "believed [the plea agreement] was a good deal" for him, he answered in the affirmative. Id. at 1843. On cross-examination, Yang asked Lor whether, as part of his plea agreement, Lor would be able to serve his sentence for the charges arising from the pool hall incident concurrently with a sentence for unrelated charges; Lor again said yes. Id. at 1888. Lor was also cross-examined as to the charges he originally faced and those to which he pled guilty in the plea agreement. Id. at 1893. The Minnesota Supreme Court held that the trial court did not err in limiting cross-examination: "the jury had sufficient information about [Yang's] codefendants' plea agreements to assess their credibility," since "[t]he jury knew that the codefendants received considerably less jail time in exchange for their testimony." State v. Yang, 774 N.W.2d 539, 553 (Minn. 2009).

In evaluating the Confrontation Clause implications, we are concerned that "the accused should [be] able to contrast the original punishment faced by the witness with the more lenient punishment contemplated by the plea agreement." United States v. Walley, 567 F.3d 354, 360 (8th Cir.2009). This contrast, however, need not be in the form of a particular number attached to the sentencing benefit received by a testifying codefendant. In Walley, we evaluated on direct appeal the claim that the district court improperly limited the defendant's ability to cross-examine a cooperating witness, Brandon Pender, about the possible sentence he was facing. During direct examination, Pender admitted that he was testifying pursuant to a plea agreement with the government and that he hoped to receive a reduced sentence as a result of his testimony. The district court did not allow cross-examination about the forty-year maximum sentence Pender faced or the five-year mandatory minimum sentence he could avoid only if the government filed a substantial-assistance motion. Instead, the district court allowed inquiry into whether Pender was "facing the possibility of a significant sentence in this case." Id. at 359. Given the information the jury had about Pender's cooperation plea agreement, we were "not persuaded that evidence of Pender facing a `five-year sentence' rather than a `significant sentence' would have given the jury a `significantly different impression' of Pender's credibility." Id. at 360 (citing Van Arsdall, 475 U.S. at 680, 106 S.Ct. 1431).

In this case, the jury knew that Vang and Lor pled guilty to lesser charges and that both hoped for a lower sentence as a result. See Walley, 567 F.3d at 360. Yang argues, however, that the trial judge erred in forestalling specific inquiry into the percentage by which Vang's and Lor's sentences were reduced by virtue of their plea agreements. This, Yang asserts, violated his rights under the Confrontation Clause. Although the agreements did not include percentages, Yang contends that the trial judge could have estimated a percentage based on the sentences they potentially faced from the original charges. We find that this was not a realistic possibility. Under Minnesota law, a premeditated first-degree murder conviction meant a mandatory life sentence, which is inherently not a fixed number of months. Minn.Stat. Ann. § 609.185(a)(1) (2004). Calculating the sentences that Vang and Lor anticipated absent a plea agreement would be complicated by the fact that they faced multiple counts of murder, at least one of which was charged as a crime committed for the benefit of a gang and thus subject to different sentence calculations. See Minn.Stat. Ann. §§ 609.15(1), 609.229 (2004). More importantly, however, Vang and Lor had not been sentenced at the time they testified, so estimating their percentage reduction would have been little more than a guess. It is also unclear how defense counsel would have elicited this information from Vang and Lor themselves. In this case, permitting cross-examination based on conjecture likely risked confusing the jury, without giving the jury a "`significantly different impression'" of the witnesses' credibility. See United States v. Baldenegro-Valdez, 703 F.3d 1117, 1123-24 (8th Cir.2013) (quoting Van Arsdall, 475 U.S. at 680, 106 S.Ct. 1431). We find that the Minnesota Supreme Court's determination that Yang's Confrontation Clause rights were not violated was not an unreasonable application of Supreme Court precedent.

B. Prejudice

Even if the jury were left without enough facts to gauge Vang's and Lor's credibility such that Yang's Sixth Amendment rights were violated, Yang must show that the state court's error had a "substantial and injurious effect or influence in determining the jury's verdict." Brecht, 507 U.S. at 623, 113 S.Ct. 1710 (quotation omitted). The Supreme Court in Van Arsdall listed several factors for reviewing courts to use in assessing prejudice: "the importance of the witness' testimony in the prosecution's case, whether the testimony was cumulative, the presence or absence of evidence corroborating or contradicting the testimony of the witness on material points, the extent of cross-examination otherwise permitted, and, of course, the overall strength of the prosecution's case." 475 U.S. at 684, 106 S.Ct. 1431. Since the Minnesota Supreme Court found no Confrontation Clause violation in Yang's case, it did not assess prejudice; the district court therefore did so de novo.2 We agree with the district court that the prosecution's case did not depend so much on Vang's and Lor's testimony that limiting their cross-examination was prejudicial to Yang.

Although their testimony was damaging to Yang, Vang and Lor did not provide enough material information to have a "substantial and injurious effect" on the jury's verdict. Brecht, 507 U.S. at 623, 113 S.Ct. 1710. Vang testified that he only knew Yang had a gun that night when Yang joined him in the car after leaving the pool hall. He did not testify in detail regarding where Yang was during the altercation. Vang's most harmful statement was Yang's admission to him that Yang had fired several shots but did not know if any of them had hit someone. Lor's contribution was less substantive than Vang's. He testified that Yang was in the pool hall when the fight started and in Vang's car when it was stopped by the police. In addition, the credibility of both Vang and Lor was already suspect: Yang was able to show that some aspects of their testimony did not match the accounts they initially gave the police. Likely because of these credibility problems, the prosecution did not rely on either codefendant's testimony significantly during closing argument.

Moreover, the Minnesota Supreme Court relied in part on the trial court's jury instruction that it could not find Yang guilty "based on Vang's accomplice testimony unless it was corroborated by someone other than an accomplice." Yang, 774 N.W.2d at 554. The Court found that Vang's testimony — "[s]pecifically, the events inside the pool hall, and Yang's admission when he entered the car after the shootings" that he had fired a gun several times — was, in fact, corroborated by "numerous witnesses," including three jailhouse informants who had allegedly spoken with Yang while incarcerated with him at the Anoka County Jail. Id. While the informants may have had something to gain from testifying, how much their testimony should be discounted is a credibility determination left to the jury. Vang's statement that Yang had a gun at the pool hall was also corroborated by physical evidence: when the police searched Vang's car, there was a gun under Yang's seat, and police later found bullets of the appropriate size for that gun in Yang's bedroom.

Finally, as the district court acknowledged, Yang was charged with aiding and abetting two murders and four attempted murders. A conviction on these charges did not require the prosecution to prove beyond a reasonable doubt that Yang actually used the gun found under his car seat. "Active participation in an offense is not required"; rather, there must be "`some knowing role in the commission of the crime by a defendant who takes no steps to thwart its completion.'" Yang, 774 N.W.2d at 562 (quoting State v. Ostrem, 535 N.W.2d 916, 924-25 (Minn. 1995)). The Minnesota Supreme Court found, and we agree, that "there was sufficient evidence to prove that [Yang] actively participated in the shootings of the Tibetans, and that he intended his presence to further the commission of these crimes." Id. Even though Vang testified about Yang's admission that he had fired several shots, proving this fact was not necessary for him to be convicted. We find that the limits imposed on Yang's cross-examination of the codefendants did not constitute prejudice.

III. Conclusion

We affirm the district court's denial of Yang's habeas petition on the merits.