MARTIN, J., delivered the opinion of the court, in which OLIVER, D.J., joined. BOGGS, C.J. (pp. 380-88), delivered a separate dissenting opinion.
OPINION
BOYCE F. MARTIN, JR., Circuit Judge.
On July 22, 2005, the district court granted Carol Ege’s petition for a condi[367]*367tional writ of habeas corpus on grounds that (1) admission of bite-mark evidence at Ege’s state trial violated her right under the Due Process Clause to a fair trial, and (2) the performance of Ege’s state trial counsel was unconstitutionally deficient and caused her actual prejudice. The State appeals the district court judgment on both grounds, and argues additionally that Ege’s habeas petition is time-barred under the one-year limitations period of 28 U.S.C. § 2244(d)(1). For the following reasons, we AFFIRM in part and REVERSE in part the judgment of the district court.
I
This is a troubling case. The crime is horrific. The initial investigation was deficient. Defendant was not charged until nine years after the murder. There are others who are logical suspects. No one saw defendant at the scene the evening of the murder. No physical evidence links defendant to the crime except testimony that a mark on the victim’s cheek is a bite mark that is highly consistent with defendant’s dentition.
People v. Ege, No. 173448, 1996 WL 33369075, at *1 n. 1 (Mich.Ct.App. Sept., 17, 1996). Such was the description of Carol Ege’s case by the Michigan Court of Appeals, which heard her direct appeal following a jury trial and conviction for first-degree murder for the killing of Cindy Thompson.
Ege and Thompson had both been romantically involved with Mark Davis, whose child Thompson allegedly was carrying. Davis testified that he found Thompson in her upstairs bedroom some time before 5:00 a.m. on February 22, 1984, bludgeoned and stabbed to death, her organs laying beside her. There was no sign of forced entry at Thompson’s home, and the back door was found unlocked. The phone cords had been cut. Thompson was last seen alive on the evening of February 21, sometime between 8:45 and 9:15 p.m. The initial police investigation, concluded in April 1984, yielded no definitive evidence. Eight years later, however, the investigation was reopened as a result of persons coming forward with evidence allegedly incriminating Ege. During the course of this reopened investigation, in 1992-1993, evidence that had been collected at the murder scene in February 1984 was submitted to the Michigan state crime lab for the first time. None of the evidence submitted to the crime lab connected Ege to the crime. The lab results yielded fingerprints of Davis and Thompson and hairs of Thompson and others, but no similar trace evidence connected to Ege. Thompson’s body was exhumed in 1993, apparently to investigate a mark on her left cheek visible in photographs taken at the murder scene. The initial autopsy report had concluded that the mark was livor mortis.1 Ege was tried for murder following the 1992-1993 investigation.
At trial, the prosecution attempted to show that Ege was obsessed with Davis and was therefore furiously jealous of Thompson and the child Thompson was carrying. The prosecution presented witnesses who testified that Ege and Thompson had argued several years prior to Thompson’s death, when Ege entered Thompson’s house to destroy a watch case and T-shirts that Thompson had bought for Davis. Further evidence was presented that Ege and Thompson engaged in a physical struggle at Thompson’s sister’s [368]*368house, when Thompson was five months pregnant. Witnesses also testified that Ege had attempted to hire two different men to kill Thompson, and that about one week before Thompson’s death, Ege had asked her roommate, Carol Parker, to provide her with an alibi in exchange for free rent. Finally, several witnesses testified that Ege had expressed to them a desire to see Thompson killed. One witness testified that after Thompson became pregnant, Ege said to her, “Cindy [Thompson] was not going to have the baby; that she didn’t know how or why, and she didn’t want to get me involved, but that she wasn’t going to have the baby.” Another witness testified that Ege told her “she could stomp the baby out of her, slit her throat, rip her up in little pieces and think nothing of it.” Yet another witness testified that Ege told him she wanted Thompson “really hurt bad, either beat her up bad or kill her.”
Ege denied virtually all of the allegations made by prosecution witnesses, and much of their testimony was called into serious question on cross-examination, either through impeachment or showing of bias. The defense’s theory of the case was that Ege could not have been at the crime scene on the evening of the murder because she was at home all evening, and that although there was perhaps some evidence pointing to her, a more compelling circumstantial case could in fact be made against several of the prosecution’s witnesses, including Davis. Davis admitted that he had been drinking most of the day and night prior to Thompson’s murder, and that by the time he decided to go to Thompson’s house on the morning of February 22, he had consumed approximately five bottles of wine. Davis’s presence at Thompson’s house coincided approximately with the time she' died. His alibi that he was drinking at a friend’s house up until the time that he found Thompson’s body was largely undermined by the friend’s subsequent testimony that he and Davis were not in fact together that night. Also on cross-examination, Davis testified that he never believed that Ege had killed Thompson, and affirmed that Ege had in fact been home all night.
The prosecution’s expert witness, Dr. Alan Warnick, opined that the mark found on Thompson’s cheek, which the original autopsy report had concluded was liver mortis, was actually a bite mark. Dr. Warnick was unable to examine the actual injury, because Thompson’s body was too badly decomposed upon exhumation nine years after the murder. Thus, Dr. War-nick relied on photographs of the mark which had been taken at the time of the initial autopsy, in 1984. Dr. Warnick compared dentitions of several suspects raised by the defense and found that none of them could have made the bite mark. He also checked Ege’s dentition and concluded that it was highly consistent with the bite mark. Dr. Warnick was asked by the prosecution, “Let’s say you have the Detroit Metropolitan Area, three, three and a half million people. Would anybody else within that kind of number match like she did?” He responded, “No, in my expert opinion, nobody else would match up.” Ege’s defense counsel did not object to Dr. Warnick’s testimony, but rather called two expert witnesses in rebuttal. The first, a pathology professor at Wayne State University, concluded that the mark on Thompson’s cheek was liver mortis, and not a bite mark. The second, a dentist and medical doctor, provided similar testimony, and added that even if it were a bite mark, the pattern did not align with Ege’s dentition.
A jury found Ege guilty of first-degree murder. On January 28, 1994 she was sentenced to life imprisonment without the possibility of parole. Ege’s direct appeal [369]*369was rejected by the Michigan Court of Appeals on September 17, 1997. Ege’s conviction became final on March 30, 1998, ninety days after the Michigan Supreme Court denied her application for leave to appeal.
On July 28, 1999, almost sixteen months after her conviction became final, Ege filed a motion for post-conviction relief in Michigan circuit court. She argued that her due process right to a fair trial was violated by the admission of Dr. Warnick’s bite mark testimony, both because the evidence itself was scientifically and probabilistically unsound and because Dr. Warnick had a demonstrated record of unreliability. Ege also raised an ineffective assistance of counsel claim, on grounds that her trial attorney had failed to object to the introduction of the bite mark evidence, as well as to the introduction of evidence concerning Ege’s prior sexual history. The circuit court concluded on January 11, 2000, that Ege’s due process evidentiary challenge to the prosecution’s bite mark evidence, particularly the testimony concerning the mathematical probability of an alternate random match, “lacked a proper foundation” and should have been excluded had an objection been raised. However, the circuit court denied relief because (a) trial counsel had failed to object to the evidence, and (b) the opportunity to present evidence challenging Dr. Warnick’s methodology removed any prejudice resulting from receipt of the inadmissible evidence. The court weighed the improper evidence against the strength of the untainted evidence and found that a new trial was not required. As to Ege’s ineffective assistance of counsel claim, the circuit court denied relief as well, finding that trial counsel’s performance was not substandard. The circuit court denied a motion for reconsideration on February 15, 2000. The Michigan Court of Appeals denied Ege’s appeal as to the post-conviction motion on August 24, 2000, and the Michigan Supreme Court did likewise on April 30, 2001.
On August 13, 2001, Ege presented in federal district court the following claims in a petition for writ of habeas corpus:
I. Petitioner was denied a fundamentally fair trial in violation of due process of law through the admission of an erroneous expert opinion that there was a “3.1 million to one chance” that a bite mark on the victim’s body was made by anyone other than the petitioner, where this opinion was without scientific foundation and where subsequent cases have shown this particular expert to be completely unreliable with a series of demonstrably erroneous bite mark identifications in capital cases.
II. Petitioner was denied the effective assistance of trial counsel where counsel failed to object to a series of obviously inadmissible and inflammatory prosecu-torial questions posed to the testifying defendant about her sexual history, and her history of multiple abortions, and where counsel failed to demand a Davis-Frye hearing as to expert testimony given by Dr. Warnick and denied the effective assistance of appellate counsel where counsel, who represented petitioner both at trial and on appeal, failed to raise the issue of his own ineffectiveness at trial on appeal.
III. Petitioner’s constitutional rights were violated where she was confronted by the prosecution at trial with questions regarding her sexual history and the fact that she had two abortions.
The State moved to dismiss the habeas petition on summary judgment, arguing that it was time-barred under the one-year statute of limitations established by 28 U.S.C. § 2244(d)(1). The district court denied the State’s motion because it was [370]*370satisfied that “discovery of non-record facts relating to the reliability of the state’s witness did not occur and could not have occurred until after the expiration of the habeas filing deadline, even as tolled by [Ege’s] state post-conviction motion.” D. Ct. Op., July 22, 2005, at 15 (quoting the court’s June 4, 2002 opinion). In particular, the district court found that it was “some time after April 1999” when Ege’s counsel was first made aware of a> letter from the Wayne County (Michigan) prosecutor’s office concerning the unreliability of Dr. Warnick as an expert witness in two previous murder trials. D. Ct. Op., June 4, 2002, at 4. The letter indicated that “the Office of the Wayne County Prosecuting Attorney will not approve warrants where the main evidence as to the identity of a potential defendant is the opinion of Dr. Warnick that he/she is the source of the bite marks.” Only after receiving this letter, and researching Dr. Warnick’s record of testimony in other Michigan counties (including the one in which Ege was tried, Oakland County), did Ege’s counsel pursue her July 1999 state collateral appeal. Because this factual predicate for Ege’s claim could not have been discovered until April 1999, even “through the exercise of due diligence,” the district court concluded that Ege’s section 2244(d)(1) clock only began to run as of April 1999. The clock was then tolled after approximately four months, as of the filing of her July 1999 petition for state collateral relief. See 28 U.S.C. § 2244(d)(2). As a result of this tolling, the district court did not consider Ege’s August 2001 habeas claim, filed approximately four months after her avenues for state post-conviction relief had been exhausted, to be time-barred under 28 U.S.C. § 2244(d)(1).
In a separate, subsequent opinion, the district court reached the merits of Ege’s habeas petition, concluding that “the evidence, already found by the State trial judge to be improperly admitted, had a substantial and injurious effect or influence in determining the jury’s verdict.” D. Ct. Op., July 22, 2005, at 36 (quoting Brecht v. Abrahamson, 507 U.S. 619, 638, 113 S.Ct. 1710, 123 L.Ed.2d 353 (1993)). The district judge further noted:
There can be no question that the bite mark evidence together with Dr. War-nick’s 3.5-million-to-one odds making was powerful evidence against the petitioner. It also contradicted her claim that other logical suspects committed the crime. The evidence plainly was material in the sense of a crucial, critical highly significant factor. There was evidence presented at the trial that the petitioner harbored intense animosity against the victim and expressed a desire to see her killed. That evidence was also challenged and many of the witnesses who gave that testimony were impeached. Some even were the logical suspects themselves, as the State court of appeals observed. However, without the bite mark and opinion testimony, the nature of the State’s proofs would have been altogether different and a weaker case necessarily would have resulted with no physical evidence connecting the petitioner to the crime. Dr. Warnick’s evidence was unreliable and grossly misleading. The evidence was so extremely unfair that its admission violates fundamental concepts of justice.
Id. at 36-37 (internal citations and quotations omitted).
The district court also granted Ege’s ineffective assistance of counsel claim, finding a “reasonable probability” that “but for the defective performance [of counsel], which resulted in the receipt of the bite mark evidence and the statistical probability testimony, the result of the proceeding would have been different.” Id. at 38 (citing Strickland v. Washington, [371]*371466 U.S. 668, 694, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984)). As to Ege’s third claim and those portions of her second claim relating to the admission of evidence at trial of her prior sexual history, the district court denied relief. Ege does not appeal these denials.
The State appeals the district court’s July 22, 2005 ruling on the merits of counts I and II of Ege’s habeas petition, as well as the district court’s June 4, 2002 ruling that Ege’s state post-conviction petition was not time-barred.
II
This Court reviews a district court’s decision regarding a writ of habeas corpus de novo. Wolfe v. Brigano, 232 F.3d 499, 501 (6th Cir.2000). Factual findings made by the district court are reviewed for clear error unless the factual determinations are made based on state court documents. Bugh v. Mitchell, 329 F.3d 496, 500 (6th Cir.2003). In such cases, the factual findings are reviewed de novo. Id.
Under the Antiterrorism and Effective Death Penalty Act of 1996 (“AED-PA”), a federal court may not grant habeas relief unless the state court’s adjudication of the claim either:
(1) resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States; or
(2) resulted in a decision that was based upon an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.
28 U.S.C. § 2254(d). Under the “unreasonable application” prong of this section, “a federal habeas court may not issue the writ simply because that court concludes in its independent judgment that the state-court decision applied [a Supreme Court case] incorrectly.” Price v. Vincent, 538 U.S. 634, 123 S.Ct. 1848, 155 L.Ed.2d 877 (2003). Rather, “[i]n order for a federal court to find a state court’s application ‘unreasonable,’ the state court’s decision must have been more than incorrect or erroneous[;][it] must have been ‘objectively unreasonable.’” Wiggins v. Smith, 539 U.S. 510, 520, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003). As this Court has stated, “a federal habeas court must ask whether the state court’s application of clearly established federal law was objectively reasonable. If the federal court finds that, viewed objectively, the state court has correctly identified the governing legal principle from the Supreme Court’s decisions but unreasonably applied that principle to the facts of the prisoner’s case, it may grant the writ.” Millender v. Adams, 376 F.3d 520, 523 (6th Cir.2004).
Ill
A. The Limitations Period under 28 U.S.C. § 2244(d)(1)
“A 1-year period of limitation shall apply to an application for a writ of habeas corpus by a person in custody pursuant to the judgment of a State court.” 28 U.S.C. § 2244(d)(1). The limitation period runs “from the latest of’ several possible occurrences, including
(A) the date on which the judgment became final by the conclusion of direct review or the expiration of the time for seeking such review; ... or (D) the date on which the factual predicate of the claim or claims presented could have been discovered through the exercise of due diligence.
Id. (emphasis added). Furthermore, the one-year limitation period is tolled for the “time during which a properly filed application for State post-conviction or other [372]*372collateral review with respect to the pertinent judgment or claim is pending.” 28 U.S.C. § 2244(d)(2).
If the district court was correct that the factual predicate — namely, that Dr. War-nick was a “sham” scientist — for Ege’s due process habeas claims could not have been discovered until “some time after April 1999,” then the § 2241(d)(1) limitations period would not begin to run from the date on which her conviction became final (March 30, 1998), but rather from Ege’s discovery of the letter in April 1999. The limitations period would then have been tolled in July 1999, approximately four months after it began to run, upon Ege’s proper filing of a claim for state post-conviction relief. Running of the statute would have recommenced on April 30, 2001, when the Michigan Supreme Court denied leave to appeal Ege’s denial of post-conviction relief. Ege’s federal habeas petition was then filed on August 13, 2001, approximately four months after this denial. Thus, if the district court was correct in its factual finding, then Ege’s federal claims are not time-barred, because they were submitted well within the one-year limitations period — four months initially, plus four months after tolling had ended.
In support of the district court’s factual finding, Ege draws our attention to a letter, dated June 19, 1995, which was signed by the Chief of Operations of the Wayne County Prosecutor’s Office.2 The letter concerns two cases in which Dr. Warnick provided expert testimony regarding the identity of persons suspected of leaving bite marks on murder victims. In noting that Dr. Warnick’s testimony was totally unreliable — in one case, because DNA evidence later excluded the defendant as a possible suspect; in the other, because a second expert undermined Warnick’s probability determination — the Wayne County Prosecutor’s Office concluded that it “will not approve warrants where the main evidence as to the identity of a potential defendant is the opinion of Dr. Warnick that he/she is the source of the bite marks.” Ege notes that while the letter dates from 1995, it was not a public document, and thus she could not have known that Dr. Warnick had been thrown into disrepute until her receipt of the letter in 1999. Ege further argues that prior to April 1999 there existed no published or unpublished Michigan appellate decisions relating to Dr. Warnick, and thus the “fact that defense counsel learned of the [Wayne County] letter at all can only be characterized as fortuitous.”3 Appellee’s Br. at 54-55. In fact, two other cases in which Dr. Warnick’s bite mark testimony was questioned were only published around the same time that Ege’s counsel received the letter. See Amolsch v. Warnick, No. 203198, 1999 WL 33446484 (Mich.Ct.App. Apr.27, 1999); People v. Wright, No. 179564, 1999 WL 33446496 (Mich.Ct.App. Apr.23, 1999).
The State’s strongest argument in support of the § 2244(d)(1) time bar is that nothing in the Wayne County prosecutor’s letter provides a new factual basis for Ege’s claim that Dr. Warnick’s 3.5 million-to-one probability determination was clearly objectionable at trial. The State argues that bite mark evidence, while admissible in Michigan (unlike in some other states), is nevertheless controversial. Accordingly, the State contends, Dr. Warnick’s testimony could easily have been flagged by Ege’s counsel at trial, and the “new” fact that [373]*373Dr. Warnick was no longer being relied on by other Michigan county prosecutors was irrelevant. See Souter v. Jones, 395 F.3d 577, 587 (6th Cir.2005) (noting that evidence “merely cumulative to the evidence already presented by the defense at trial” cannot form the newly discovered factual predicate). This would appear to jibe with the district court’s finding, in assessing Ege’s ineffective assistance of counsel claim, that “[t]he flaw in Dr. Warnick’s statistical opinion should have been obvious and its admissibility readily assailable.” D. Ct. Op., July 22, 2005, at 28.
We must analyze Ege’s two habeas claims separately with regard to the State’s argument and the section 2244(d)(1) bar. On the one hand, the strength of Ege’s free-standing ineffective assistance claim&emdash;that her counsel blundered in not objecting to Dr. Warnick’s bite mark evidence and that the state trial court’s failure to recognize the impact of this was an unreasonable application of clearly established federal law&emdash;clearly does not rest on Ege’s counsel only having been made aware of the Wayne County letter in 1999. If it “should have been obvious” to trial counsel to object to Dr. Warnick’s testimony, and trial counsel did not have the benefit of the Wayne County letter, then so too should it have been obvious to Ege (or to her appellate counsel) that she should promptly file for habe-as relief under Strickland. In other words, as styled by the district court, it would seem that Ege’s otherwise meritorious ineffective assistance claim in no way rests on the April 1999 discovery of the Wayne County prosecutor’s letter. The letter, which only points to the unreliability of Warnick, cannot logically constitute a “factual predicate” for Ege’s free-standing ineffective assistance claim. Her ineffective assistance claim is therefore barred under 28 U.S.C. 2244(d)(1), and we reverse the district court as to this point.
On the other hand, the strength of Ege’s due process claim does not rest solely on her trial counsel’s inadequate performance. Rather, it rests on the adequacy of the physical evidence presented against her at trial. While it should have been obvious to Ege’s trial attorney that the manner in which this physical evidence was presented was objectionable (i.e., that Dr. Warnick’s probability determination was entirely without foundation), we cannot say that it should have been similarly obvious to Ege that the substance of the physical evidence&emdash;at least as presented by Dr. Warnick&emdash;was complete bunk. Thus, it is reasonable to assume that Ege did not fully appreciate the strength of her due process claim until she found out, entirely fortuitously, that the man who provided critical, physical trial testimony against her was now considered to be a charlatan by a sister office of the very state prosecutors who had chosen to put him on the witness stand. This is especially true because Ege’s due process claim was “hybrid” in nature&emdash;that is, Ege identified both Dr. Warnick’s probability determination in her particular case, as well as his general record of unreliability, as flaws denying her right to a fair trial.
Furthermore, the district court’s conclusion that the Wayne County letter provided the factual predicate for Ege’s claims, and thus tolled the running of section 2244(d)(1), was a factual finding that this Court reviews for clear error. Bugh, 329 F.3d at 500. And while the district court’s misapplication of section 2244(d)(1) with respect to Ege’s free-standing ineffective assistance claim constitutes clear error, the same cannot be said for Ege’s due process claim. Ege could not be expected to know, in advance, how strong or weak [374]*374that claim might be.4 Prior to receipt of the Wayne County letter, she likely felt that she did not have a basis for pursuing her due process claim, as she was yet unaware of the extent to which Dr. War-nick’s reputation had been thrown into disrepute. It was therefore not clear error for the district court to find that the Wayne County letter provided Ege with the factual predicate for her due process habeas claim. Accordingly, we agree with the district court that Ege’s due process claim is not time-barred by 28 U.S.C. § 2244(d)(1), and thus will consider it on the merits.
B. Ege’s Due Process Claim
Ege asserts she was deprived of her due process right to a fair trial because of the trial court’s improper admission of Dr. Warnick’s bite-mark testimony, which she claims was both substantively and probabilistically unsound. Both parties, as well as the district court, have correctly highlighted the critical portion of Dr. War-nick’s trial testimony:
Q: Now, Doctor, with regard to your testimony, you indicated that it’s highly consistent with the dentition of Defendant Carol Ege; is that correct?
A: Yes.
Q: Okay. With regard to — let me ask you a question. Let’s say you have the Detroit Metropolitan Area, three, three and a half million people. Would anybody else within that kind of number match like she did?
A: No, in my expert opinion, nobody else would match up.
Tr. Vol. VIII, at 42. Also critical is the judgment of the state court which considered Ege’s claims on collateral review:
This Court agrees that the testimony regarding the probability that the bite matched the defendant lacked a proper foundation. Expert forensic testimony regarding identification of the defendant based upon a statistical analysis requires a proper foundation. To make a statistical evaluation it is necessary to know the frequency of a particular characteristic in the population. The probability of any combination of known characteristics is equal to the product of the frequency of each. In this case there was no evidence offered to support the expert’s conclusion regarding the probability that the defendant made the mark. In other words, the expert did not testify that he had identified particular features of the bite mark that had a knoum rate of occurrence. Neither did the expert did [sic] testify that he had multiplied these values to reach his conclusion.
People v. Ege, Oakland Circuit Case No. 93-125655-FC, January 11, 2000, at 5 (internal citation omitted) (emphasis added). Thus, the state habeas court found it highly. problematic not that the prosecution had used Dr. Warnick to introduce bite mark evidence in the first place, but that Warnick had tied his observations to a statement about probabilities that was wholly without foundation. We agree. The prosecution failed to lay any foundation whatsoever, either for Dr. Warnick’s [375]*375connection of the bite mark to Ege’s dentition in general, or for Warnick’s assertion that the two were connected by a probability of 3.5 million to one.
But the state habeas court then ruled that any possible prejudice that could have resulted from improper admission of Dr. Warnick’s testimony was negated by the fact that Ege had been permitted to present her own experts in opposition to Dr. Warnick, both of whom rejected Warnick’s conclusion that the mark on Thompson’s cheek was a bite mark and not simply livor mortis. Id. at 6. Furthermore, the state habeas court noted that
this was not a case, where the guilt or innocence of the defendant hinged on an unchallenged and suspect expert opinion. Numerous independent witnesses testified to the efforts which the defendant made to secure help in killing the victim, to the steps which she took in one attempt to kill the victim, and to her statements before the murder which accurately predicted the manner in which the victim was ultimately murdered.
Id. at 10. Following Michigan Supreme Court precedent, see People v. Mateo, 453 Mich. 203, 551 N.W.2d 891, 896 (1996), the state habeas court inquired into the nature of the evidentiary error and “assesse[d] its effect in light of the weight and strength of the untainted evidence.” The court concluded that “[t]he untainted evidence in this case overwhelmingly pointed to the guilt of [Ege].” People v. Ege, No. 93-125655-FC, at 6.
The lack of prejudice notwithstanding, the state habeas court also ruled that Ege’s claim was barred by Michigan’s contemporaneous objection rule, because her trial counsel failed to object to admission of Dr. Warnick’s testimony at any point in the proceedings.
(1) The State Habeas Court’s Application of “Prejudice” under Chambers
Any review of habeas due process claims based on improper admission of evidence must be cognizant of the Supreme Court’s mandate that “it is not the province of a federal habeas court to reexamine state-court determinations on state-law questions.” Estelle v. McGuire, 502 U.S. 62, 68, 112 S.Ct. 475, 116 L.Ed.2d 385 (1991). Under this very deferential standard, due process is violated, and thus habeas relief warranted, only if an eviden-tiary ruling is “so egregious that it results in a denial of fundamental fairness.” Bugh, 329 F.3d at 512 (6th Cir.2003). “Whether the admission of prejudicial evidence constitutes a denial of fundamental fairness turns upon whether the evidence is material in the sense of a crucial, critical highly significant factor.” Brown v. O’Dea, 227 F.3d 642, 645 (6th Cir.2000).
These principles have their roots in the Supreme Court decision of Chambers v. Mississippi, 410 U.S. 284, 302-03, 93 S.Ct. 1038, 35 L.Ed.2d 297 (1973), which held that trial errors cannot “defeat the ends of justice” or otherwise deprive a defendant of her right to a fair trial. In Chambers, the Court was looking at a state trial court’s improper exclusion of certain evidence that would potentially have assisted the defendant, but its tenets are equally applicable to situations involving a state trial court’s improper admission of certain evidence injurious to the defendant. The ultimate question is therefore whether the state habeas court, in finding that admission of Dr. Warnick’s testimony was not prejudicial to the ultimate outcome of Ege’s case, unreasonably applied Chambers.5
[376]*376In the instant case, hindsight assessment of the impact of Dr. Warnick’s testimony requires two intertwined assessments of the evidence against Ege: the first, taken in the context of defense counsel’s rebuttal experts, and the second, taken in the context of the prosecution’s other evidence, all of which was only circumstantial. As to the first assessment, the effectiveness of Ege’s rebuttal experts must be viewed in comparison to the substance of the rebutted testimony. We agree with the district court that “Dr. Warnick’s opinion that the petitioner was the only person in the entire Detroit metropolitan area who could have made the mark on the corpse carried an aura of mathematical precision pointing overwhelmingly to the statistical probability of guilt, when the evidence deserved no such credence.” D. Ct. Op., July 22, 2005, at 35. Bite mark evidence may by its very nature be overly prejudicial and unreliable,6 but it may nevertheless be admitted under Michigan evidence law, and we do not question the Michigan courts’ judgment with respect to admission of the bite mark evidence standing alone. See People v. Marsh, 177 Mich.App. 161, 441 N.W.2d 33 (1989). However, Dr. Warnick’s statement that among the 3.5 million residents of the Detroit metropolitan area, Ege’s teeth, and only Ege’s teeth, could have made the mark on Thompson’s cheek, was without doubt highly prejudicial. It strains credulity to think that a jury hearing Dr. Warnick’s testimony would not immediately place Ege at the scene of Thompson’s violent murder, if only her teeth, and not those of 3,499,999 other Detroit residents, were linked to a bite mark on Thompson’s cheek. Such “testimony expressing opinions or conclusions in terms of statistical probabilities can make the uncertain seem all but proven, and suggest, by quantification, satisfaction of the requirement that guilt be established ‘beyond a reasonable [377]*377doubt.’ ” People v. Carlson, 267 N.W.2d 170, 176 (Minn.1978); see also generally Lawrence H. Tribe, Trial by Mathematics, 84 HaRV. L.Rev. 1329 (1971). Furthermore, the injurious effect of Dr. Warnick’s probability testimony was not in any way diffused by the experts put on by Ege’s counsel. Both of these experts opined that the mark on Thompson’s cheek was livor mortis, and not a bite mark, but neither directly refuted Dr. Warniek’s methods in coming to his 3.5 million-to-1 probability determination. Thus, even if a majority of jurors did not believe Dr. Warnick’s testimony that the mark was a bite mark, the minority who did would have been inclined to think that such a mark could only have come from Ege.
As to the second prejudice inquiry, we must assess the relative influence of the prosecution’s WM-bite-mark evidence, all of which was circumstantial and none of which placed Ege at the scene of Thompson’s murder. We recognize that presentation of physical scene-of-the-crime evidence is not a necessary condition to support a guilty verdict. Obviously, many cases are tried on nonphysical circumstantial evidence alone, and in many cases this circumstantial evidence overwhelmingly points toward the defendant’s guilt. And in this case, it is undeniable that some of the circumstantial evidence against Ege- — for example, one witness’s testimony that Ege told her “she could stomp the baby out of [Thompson], slit her throat, rip her up in little pieces and think nothing of it” — was strong on its face, even if the witness was later significantly, if not completely, discredited on cross-examination. This case differs from other circumstantial evidence cases, however, in that it appears the prosecution was not willing to try Ege until it had Dr. Warnick’s bite mark testimony, indicating its desire to have in hand the one piece of physical evidence potentially linking Ege to the crime. After all, nothing in the record suggests that a single one of the “compelling” circumstantial proofs offered by the prosecution at trial in 1993 could not also have been offered nine years earlier in 1984, far closer in time to when the murder was actually committed. We are thus led to believe that while the State may have had a good circumstantial case against Ege in 1984, it was not until 1993, when the State finally obtained expert physical evidence connecting Ege to the murder victim, that it felt comfortable moving forward with Ege’s prosecution. If the prosecution felt that the bite mark evidence was so important, it does not take much of a cognitive leap to believe that the jury viewed it as important as well.
It is not unreasonable to conclude, therefore, that this single piece of physical evidence substantially prejudiced the outcome of Ege’s trial, even in light of other circumstantial evidence against her. Furthermore, any argument by the State that its non-bite-mark evidence against Ege was “overwhelming” simply flies in the face of the findings of its own State Court of Appeals, which noted on direct review how “troubling” Ege’s conviction was, and how many other “logical suspects” still exist. See People v. Ege, No. 173448, 1996 WL 33359075, at *1 n. 1 (Mich.Ct.App. Sept. 17, 1996) (noting also that while the volume of circumstantial evidence concerning Ege’s animosity towards Thompson was considerable, “[t]he credibility of much of this evidence was called into question”). This finding by a state court that Ege’s conviction was “troubling” is quite different from the situation in Brown, in which a state court twice concluded that the evidence against the defendant was “sufficient to justify his conviction,” and thus this Court held it was not objectively unreasonable for the state court to have de[378]*378termined that such evidence “did not rise to the level of a crucial or critical factor in the jury’s decision to convict.” 227 F.3d at 645.
In Ege’s ease, once the state habeas court had concluded that the admission of Dr. Warnick’s testimony was error, it was objectively unreasonable, under the tenets espoused by the Supreme Court in Chambers, for the state court to have concluded that this testimony was not prejudicial. It seems clear to us that the bite-mark evidence was a “crucial, critical highly significant factor,” Brown, 227 F.3d at 645, in the jury’s determination of Ege’s guilt.
(2) Procedural Default&emdash;Trial Counsel’s Failure to Contemporaneously Object
Even though the state habeas court reached the question of whether admission of Dr. Warnick’s testimony unfairly prejudiced her trial (concluding, unreasonably, that it did not), the state court ruled that Ege’s due process complaint could be disposed of prior to reaching this question. Specifically, the state habeas court ruled that because Ege’s trial counsel had failed contemporaneously to object to Dr. War-nick’s testimony, any subsequent federal habeas claims raising the evidentiary issue were barred under of the. doctrine of procedural default.
Ege does not dispute that Michigan’s contemporaneous objection rule is a valid state procedural rule. She therefore must confront a hurdle inherent to our federalist system, namely, that “a habeas petitioner who has failed to meet the State’s procedural requirements for presenting [her] federal claims has deprived the state courts of an opportunity to address those claims in the first instance.” Coleman v. Thompson, 501 U.S. 722, 732, 111 S.Ct. 2546, 115 L.Ed.2d 640 (1991). In such case, a habeas petitioner is required “to demonstrate cause for [her] state-court default of any federal claim, and prejudice therefrom, before the federal habeas court will consider the merits of that claim.” Edwards v. Carpenter, 529 U.S. 446, 451, 120 S.Ct. 1587, 146 L.Ed.2d 518 (2000) (emphasis added). Thus, in order to overcome the State’s procedural default defense, Ege must show both “cause” and “prejudice” for her failure to comply with Michigan’s contemporaneous objection rule. The Supreme Court has acknowledged that “cause” may be established through a showing of counsel’s ineffectiveness in failing properly to preserve a claim for review in state court. Id. “Not just any deficiency in counsel’s performance will do, however; the assistance must have been so ineffective as to violate the Federal Constitution”&emdash;in Ege’s case, her Sixth Amendment right to a fair trial. Id.
The district court correctly noted that as a general rule, trial counsel’s strategic decisions on how the trial is to be conducted are afforded great deference. See Strickland, 466 U.S. at 689, 104 S.Ct. 2052 (holding that “a court must indulge a strong presumption that counsel’s conduct falls within the wide range of reasonable professional assistance”); see also Wiggins v. Smith, 539 U.S. 510, 521, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003) (declining to articulate “specific guidelines” for trial counsel conduct, and instead emphasizing that “the proper measure of attorney performance remains simply reasonableness under prevailing professional norms.”) Nevertheless, the district court was also correct that there must be some limit to this deference:
In this case, it is difficult to conceive of a reason for not objecting to the bite mark evidence and the statistical opinion. As the state court of appeals observed in its opinion on direct appeal, “[t]he defense’s theory as presented in its opening statement was that defendant could not have [379]*379been at the crime scene on the evening of the murder because as [sic] she was at the home all evening,” and “[n]one of the evidence submitted to the crime lab connected defendant to the crime.” Since the bite mark evidence was the only physical evidence connecting the petitioner to the crime scene at the time of the murder, challenging its admissibility likely would have been a sound decision with no adverse consequence. Although bite mark evidence had been used in other Michigan prosecutions, Dr. Warnick never examined the bite wound himself, and the use of a photograph of the wound to make the comparison appears to be novel. Even if defense counsel could not have anticipated the prosecutor’s question soliciting the unsupported statistical evidence, one might expect that lodging a contemporaneous objection and moving to strike the evidence, or perhaps for a mistrial, would be standard operating procedure for a competent defense lawyer. The flaw in Dr. Warnick’s statistical opinion should have been obvious and its admissibility readily assailable.... The basis for objecting to this damaging yet unsubstantiated opinion evidence should have been obvious to defense counsel, and the failure to lodge the objection was substandard performance under prevailing professional norms.
D. Ct. Op., July 22, 2005, at 27-31 (internal citations omitted). We agree with the district court’s resolution of the matter. It is true that Strickland and Wiggins compel a federal habeas court to give a wide berth to trial counsel’s actions, and that in most instances, an attorney’s decision to put on counter-experts rather than object directly to expert testimony is strategically reasonable. But where, as in the instant case, physical evidence is presented linking a defendant to the crime scene, and it is the only physical evidence showing such a link, then defense counsel must object to its admission if no proper foundation has been laid by the presenter. Anything else is objectively unreasonable. Furthermore, the fact that defense counsel chose to introduce counter-experts to Warnick’s testimony does not insulate counsel’s performance. There is no reason counsel could not simultaneously have objected to War-nick’s testimony and attempted to rebut it with experts of his own.
To establish sufficient prejudice to overcome procedural default with an ineffective assistance of counsel claim, a petitioner must show a “reasonable probability” that, but for her counsel’s errors, a different result likely would have occurred. Strickland, 466 U.S. at 694, 104 S.Ct. 2052. A petitioner does not have to establish, however, that counsel’s error “more likely than not altered the outcome of the case.” Id. at 693, 104 S.Ct. 2052. “Reasonable probability” under Strickland, then, is “a probability sufficient to undermine confidence in the outcome.” Id. at 694, 104 S.Ct. 2052. Given our previous discussion of actual prejudice caused by erroneous admission of Dr. Warnick’s testimony, supra, we conclude that the Strickland prejudice standard is met as well. Thus, Ege has met both the nested cause and nested prejudice prongs required to use an ineffective assistance of counsel claim as “cause” for her procedural default.7 Ege’s non-com[380]*380pliance with Michigan’s procedural default rule may therefore be excused.
C. Ege’s Free-Standing Ineffective Assistance of Counsel Claim
In order for a habeas petitioner to succeed on a free-standing ineffective assistance of counsel claim, even if the claim has been used in another guise as “cause” to excuse procedural default, the petitioner must still demonstrate: (i) deficient performance of counsel, and (ii) prejudice, meaning the deficient performance deprived petitioner of a fair proceeding. Strickland v. Washington, 466 U.S. 668, 687, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). If a petitioner can make this showing, and if the state court nevertheless denies her relief, then this Court will consider the state court’s application of Strickland to have been “objectively unreasonable,” and we will grant the writ. As discussed in Part III.A of this opinion, however, we decline to review the merits of Ege’s freestanding ineffective assistance claim on ha-beas because we believe this claim is time-barred under 28 U.S.C. § 2244(d)(1).
rv
For the reasons discussed above, this Court AFFIRMS the district court’s conditional grant of Petitioner Ege’s writ of habeas corpus as to her due process claim, but REVERSES as to her freestanding claim of ineffective assistance of counsel. Our partial reversal thus does nothing to upset the district court’s July 22, 2005 order&emdash;namely, that Ege be released from custody unless the State of Michigan brings her to trial again within seventy days, subject to the exclusions from such period allowed by 18 U.S.C. § 3161.