specially concurring.
¶ 721 concur in the result and join much of the analysis. I write separately, however, because I cannot agree with the majority’s analysis on the issue relating to admission of the ex-wife’s testimony nor with its failure to dispose of two other issues that were raised and briefed. I also join in the majority exposition of the Apprendi issue and the discussion of Arizona’s capital sentencing regime. See opinion at ¶¶ 40-44. But I do so in light of the more detailed explanation in State v. Ring, 200 Ariz. 267, 25 P.3d 1139 (Ariz.2001). The majority view of the issue is set forth in Ring and need not be repeated here. See also State v. Gould, 23 P.3d 801 (Kan.2001).
A. The ex-wife’s testimony
¶ 73 The court finds no error in admitting the testimony of Harrod’s ex-wife because that testimony “was based on what Harrod had told her or done in her presence.” Opinion at ¶28. But nothing had been done in the ex-wife’s presence; she was not a percipient witness and had never been at or near the scene.
¶ 74 What happened was this: the defense tried to establish the ex-wife’s bias against Harrod by showing she divorced him. To rehabilitate its witness, the state asked her why she left her husband. She said she divorced him because she could not live with a “murderer.” What she was obviously saying was that she could not live with someone who told her he had killed and who she therefore thought was a murderer. The statement was not offered for the truth that Harrod was a murderer and was not a statement of opinion as to Harrod’s guilt; it merely described her state of mind, explaining why the ex-wife divorced Harrod. The door had been opened and the reason for the divorce had been made relevant when the defense tried to show bias by raising the issue of the divorce. I therefore concur in the court’s conclusion that there was no error in admitting the ex-wife’s testimony.
*322¶ 75 Hopefully, the majority agrees that a lay opinion of a defendant’s guilt is inadmissible. We do not allow opinion evidence of guilt, even when it is offered by experts. State v. Moran, 151 Ariz. 378, 383, 728 P.2d 248, 253 (1986); State v. Lindsey, 149 Ariz. 472, 474, 720 P.2d 73, 75 (1986); Fuenning v. Superior Court, 139 Ariz. 590, 605, 680 P.2d 121, 136 (1983). There is even less reason to allow lay opinion of guilt. If Harrod’s ex-wife had been at the scene and had first-hand knowledge, she could have testified to the facts she knew, but any statement of her belief that Harrod was guilty of the charge would not have been admissible. See State v. Williams, 133 Ariz. 220, 228, 650 P.2d 1202, 1210 (1982) (“generally a witness may not indicate his belief in defendant’s guilt”); State v. Lummus, 190 Ariz. 569, 571-72, 950 P.2d 1190, 1192-93 (App.1998).
B. Residual doubt
¶ 76 Harrod claims that residual doubt of his guilt should be considered as a mitigating factor. The state argued that Harrod has no right to present residual doubt evidence. The trial judge permitted such evidence but rejected any mitigation in this case, stating that, given all of the circumstances, he had no residual doubt.
¶ 77 Harrod claims that the trial judge erred in failing to find residual doubt. The majority shrinks to a plurality on this issue and agrees with the trial judge that there is no “lingering doubt” about Harrod’s guilt. Opinion at ¶ 39. So do I. But the court then refuses to decide whether residual doubt can ever be a mitigating factor. Opinion at ¶¶ 38-39 and note 7. I believe it is time to make it clear to the bench and bar that residual doubt is a mitigating factor. With so much recent evidence that wrongful convictions occur, this seems a strange time to have to argue the issue. See Barry Scheck, Peter Neufeld, & Jim Dwyer, Actual Innocence 219-20 (2000) (giving several examples of death row inmates recently exonerated by DNA evidence). Unfortunately, the court’s failure to grapple with the issue leaves the question unresolved in Arizona.
¶ 78 Residual doubt is not grounds for a new trial. Despite rhetoric about a thirteenth juror, so long as a verdict is supported by properly admitted evidence, a trial judge may not overturn it and grant a new trial, even if he or she has doubts about the jury’s finding. See Hutcherson v. City of Phoenix, 192 Ariz. 51, 55, 961 P.2d 449, 453 (1998); Anderson v. Nissei ASB Machine Co., Ltd., 197 Ariz. 168, 173, 3 P.3d 1088, 1093 (App.1999); Cano v. Neill, 12 Ariz.App. 562, 569, 473 P.2d 487, 494 (1970). But it is one thing to say that a verdict will not be disturbed just because the judge disagrees with it and quite another to say that a judge should sentence a defendant to death even though the judge believes the jury might have made a mistake. Recent events have shown quite clearly that there have been all too many instances in which juries have found a defendant guilty and the convictions have been affirmed, only to have it later determined that the defendant was actually not the perpetrator. See Death Penalty Information Center, Innocence: Freed From Death Row, at http://www.deathpenaltyinfo.org/Innocentlist.html (last visited July 11, 2001) (listing death row exonerations from 1973-2001).1
¶ 79 As the Innocence Project at Cardozo School of Law has established, juries and judges do make mistakes, the results of which can be tragic. See Scheck et al., supra.2 Arizona is not immune. See, e.g., State v. Youngblood, 173 Ariz. 502, 844 P.2d 1152 (1993). Youngblood, though not a capital case, involved a serious crime in which the police failed to properly preserve potentially exculpatory evidence. Nevertheless, Young-blood was found guilty beyond a reasonable *323doubt, and his conviction was ultimately upheld by this court on a 3 to 2 vote.3 Years later, advances in science permitted testing of what evidence remained. Those tests revealed that Youngblood, who served some seven years in prison, was not the perpetrator. The convictions were vacated in 2000. See Thomas Stauffer & Jim Erickson, DNA Test Clears Tucsonan Convicted in Molestation, Arizona Daily Star, Aug. 9, 2000, at A1 (county attorney “sorry” that Youngblood was “incarcerated for an offense for which he was not guilty”). If Youngblood’s had been a capital case, it is possible he would have been executed despite the uncertainty about his guilt.
¶80 The saga of John Knapp provides another example of a near-execution. Knapp was originally convicted and sentenced to death for murdering his minor daughters via arson. State v. Knapp, 114 Ariz. 531, 562 P.2d 704 (1977). While incarcerated, Knapp once came within forty-eight hours of execution and was scheduled for execution a total of five times. See Death Penalty Symposium, Prisoners Released From Death Rows Since 1970 Because Of Doubts About Their Guilt, 13 T.M. Cooley L.Rev. 907, 948 (1996). He was released in 1987 after newly developed tests showed that the children could have set the fire playing with matches. Id. Knapp was eventually rearrested in 1990 and retried in 1991; the jury deadlocked, and, through a plea bargain, Knapp pleaded no contest to second-degree murder, gaining a sentence of time served and avoiding a fourth trial. Id. He was released in 1992. In light of the evidence and proceedings in the case, we do not know if Knapp was guilty; we do know that his execution would have been a miscarriage of justice.
¶ 81 What harm is done by showing mercy because there is a possibility of the defendant’s innocence? Why need we run the risk of executing someone who may actually be innocent? Such a risk does not exist in most cases, but we can hypothecate many instances in which it would. Take, for instance, a case in which important evidence has been lost or misplaced, the circumstantial evidence is not strong, and the defendant’s guilt is established for the most part by the testimony of one or two eyewitnesses. See Erica Beecher-Monas, Blinded By Science: How Judges Avoid the Science in Scientific Evidence, 71 Temp. L.Rev. 55, 93 (1998) (“Studies of proven cases of wrongful conviction indicate that eyewitness errors constitute the largest single factor in wrongful convictions”); see also Scheck et al„ supra, at 16-18, 32-34. Sometimes convictions are procured on the basis of testimony from a witness who is biased or who, like a “snitch” or a co-defendant who has made a deal with the state, has some reason to lay blame on the defendant. See e.g. State v. Carriger, 143 Ariz. 142, 692 P.2d 991 (1984) (affirming death sentence of defendant convicted on testimony of witness seeking immunity for an earlier burglary attempt). Carriger was sentenced to death in 1978, won a new trial in 1998, and was freed through a plea agreement with a sentence of time served. Richard Ruelas, Time Opens Cell Door: Convicted Killer Now A Free Man, Arizona Republic, Jan. 24, 1999, at Bl.4
¶ 82 Two of our eases intimate if not hold that residual doubt is a mitigating circumstance. See State v. Spears, 184 Ariz. 277, 295, 908 P.2d 1062, 1080 (1996); State v. Atwood, 171 Ariz. 576, 653, 832 P.2d 593, 670 *324(1992). The majority’s language raises doubt where perhaps none exists.
¶ 83 Vice Chief Justice Jones discusses the question of residual doubt in his concurring opinion and concludes that “it would seem advisable that the judge be allowed to consider such doubt.” Jones concurrence at ¶ 67. He believes, however, that “residual doubt, as discussed in the cases, and mitigation evidence as referenced in A.R.S. § 13-703(G), are two quite different things.” Jones concurrence at ¶ 70. Thus, he concludes, residual doubt “does not fall within the permissible scope of A.R.S. § 13-703(G),” so that the question “is best addressed to the legislature.” Id. at ¶ 71.
¶ 84 But in my view, the legislature has already addressed the question. The statute does not limit the mitigating circumstances just to those concerning “the defendant’s character, propensities or record and any of the circumstances of the offense,” as Vice Chief Justice Jones argues. Id. at ¶ 69. Instead, A.R.S. § 13-703(G) defines mitigating factors as “any factors ... which are relevant ... including any aspect of the defendant’s character____” (Emphasis added.) Thus, the statute does not limit mitigation to evidence of the defendant’s character and the circumstances of the offense but only provides examples for the operative, all-inclusive command to consider any factors relevant to sentencing. The trial judge’s doubt about guilt is certainly relevant in determining whether to sentence to life or death.
¶ 85 In addition, the Eighth Amendment to the United States Constitution requires that the sentencer be permitted to consider any relevant information in deciding on the imposition of death. See Buchanan v. Angelone, 522 U.S. 269, 276, 118 S.Ct. 757, 761, 139 L.Ed.2d 702 (1998) (“In the selection phase, our cases have established that the sentencer may not be precluded from considering, and may not refuse to consider, any constitutionally relevant mitigating evidence.”) (citations omitted). One would assume that even in the maze of death- penalty jurisprudence, considerations of possible actual innocence are relevant to sentencing.
¶ 86 Given this court’s responsibility for overseeing capital cases, it is time to resolve the residual doubt issue. I therefore cannot agree with the court’s policy of avoidance. Residual doubt, properly defined, should be considered a substantial mitigating circumstance, and the court should say so. Having been left in no doubt by the facts of this case, however, I concur in the majority’s disposition.
C. Polygraph testing
¶ 87 Harrod claims the trial judge erred, at the aggravation/mitigation hearing, by not permitting him to introduce evidence that he had passed a polygraph examination in which he denied participation in the crime.5 Har-rod claims the polygraph results should have been admissible under A.R.S. § 13-703(G) and also because they were relevant to any residual doubt the trial judge may have had regarding his guilt. The state objected on the grounds that the results were per se unreliable, that Harrod had no constitutional right to present residual doubt evidence, and thus had no corresponding right to present polygraph evidence in support of residual doubt. The trial judge rejected the evidence and refused to consider it, but he stated he was aware of it and that even if he had considered it, he would not have found any residual doubt.
¶ 88 We first held polygraph examination results inadmissible because they were per se unreliable in State v. Valdez, 91 Ariz. 274, 280, 371 P.2d 894, 898 (1962). Indeed, the Frye test, which we follow in this state, originated in a dispute about the unreliability *325of polygraph evidence. See Frye v. United States, 293 F. 1013 (D.C.Cir.1923). Much has happened in the eighty years since Frye. As a result, we have found that such evidence is reliable enough to be considered by courts if the parties so stipulate. See State v. Ikirt, 160 Ariz. 113, 115, 770 P.2d 1159, 1161 (1987). Even more has changed since Ikirt.
¶ 89 We must first look at the provisions of our rules and statutes. Under A.R.S. § 13-703(C), a defendant may offer “[a]ny information relevant to any mitigating circumstances included in subsection G of this section,” regardless of its admissibility at trial. Given that questions about the extent of a defendant’s participation in the crime are certainly relevant as circumstances of the offense, and noting that the statute does not require reliability or compliance with the rules of evidence but permits the offer of “any information,” it would seem that the question is solved by our statutes. But even if we were to read a reliability requirement into the offer of mitigating evidence, I conclude that the court should receive and consider such evidence when dealing with the literal decision of life or death.
¶ 90 As a matter of common knowledge, polygraph evidence has developed to the point that it is used in industry’s determination of hiring or firing, in law enforcement, by national security agencies such as the Central Intelligence Agency, the armed services’ intelligence agencies, and the Federal Bureau of Investigation. John J. Canham, Jr., Military Rule of Evidence 707: A Bright-Line Rule That Needs to be Dimmed, 140 Mil. L. Rev. 65, 84-85 (1993); 1 Am.Jur. Trials § 38, at 481 (1965); Rhonda Bodfield Sander, Predator law to get high-court hearing, Arizona Daily Star, Mar. 25, 2001, at A1 (Department of Corrections uses polygraph results in sexual predator program); Wire Reports, 500 at FBI to get lie-detector tests in security move to thwart spying, Arizona Daily Star, Mar. 25, 2001, at Al (FBI to screen employees with polygraph tests). When important decisions in industry and government are made with the help of polygraph tests, it seems strange to refuse any use of such information to determine whether to impose a life or death sentence.
¶ 91 To perpetuate such a ban is to say that the leaders of government, law enforcement, and industry are all wrong in deciding what to consider in making important decisions. But polygraph testing techniques have improved to the point that we cannot realistically make that claim. There is no need here to make a detailed examination of the improvements in polygraph testing. The interested reader will find the subject well developed in the recent case of United States v. Crumby, 895 F.Supp. 1354 (D.Ariz.1995). I will do no more here than attempt to summarize District Judge Strand’s thorough and thoughtful Daubert analysis6:
¶ 92 In Crumby, the accused sought to admit polygraph test results indicating he truthfully stated that he did not commit the crimes he was charged with. In addressing the question of admissibility and its limits, the trial judge listed some pragmatic reasons for abandoning the rule of per se inadmissibility, finding as follows: polygraphy has faced extensive scientific testing; numerous peer-reviewed scholarly articles have dealt with the reliability and validity of polygraph evidence; known error rates for polygraphy are remarkably low, accuracy being about ninety-five percent when used to show truthfulness; polygraph evidence has gained widespread acceptance; and, because the modern science of polygraphy has existed for about twenty-five years and has found use in business and law enforcement, polygraph expert testimony can be based on research unrelated to the litigation. Thus, polygraphy was reliable enough to admit for limited purposes. See id. at 1358-61.
¶ 93 Given these considerations, Judge Strand found that fears of polygraph evidence abuse do not apply when the defendant seeks to introduce such evidence for the limited purpose of bolstering his version of the *326events to prove innocence. He also found that judicial resources will not be unduly-consumed as courts become more familiar with the use of polygraph evidence and that there is little reason to deny a criminal defendant the use of highly probative evidence on such grounds. Id. at 1362. Finally, any “aura of infallibility” argument could not survive the common use of stipulated polygraph evidence, the value of vigorous cross-examination, and the protection provided by proper limiting instructions to the jury. Id.
¶ 94 Though the judge admitted the polygraph evidence, he was careful to limit its use. The defendant would not be permitted to testify to either the questions asked in the examination or his answers. If the polygra-pher is qualified as an expert, and a foundation laid to meet Rule 608(a), Ariz.R.Evid. (evidence of truthful character admissible to support credibility of a witness whose credibility has been attacked), the polygrapher may give an opinion as to the truthful character of the defendant. Even then, the substance of the questions and their answers must not be published to the jury. Moreover, to properly admit polygraph evidence, the defendant must provide adequate notice to the government, and opposing parties must be given a reasonable opportunity to have their own examiners administer a materially similar test.
¶ 95 Thus, concluded Judge Strand, “[s]o long as the Defendant’s credibility and his statements concerning his participation in the robbery are impeached, the polygraph evidence will be admissible” to support his version of the facts. Id. at 1364. If this type of testimony is admissible in a jury trial, we should not preclude a trial judge required to determine who shall live and who shall die from even considering it for whatever weight it may have in a particular case.
¶ 96 Given the great weight of the evidence in this case and Harrod’s inability to explain any of the incriminating facts, I have no hesitation in agreeing with, much less deferring to, the trial judge’s ruling that even if he had considered the polygraph results he would not have given them any weight or found any residual doubt. But I disagree with the proposition that polygraph results can never be consideréd at all.
CONCLUSION
¶ 97 This court has an obligation to the entire system-victims, judges, prosecutors, defendants, and defense counsel-to set the sentencing standards to be followed in capital cases. The boundaries set by the constitution and A.R.S. § 13-703(C) require consideration of any information that is relevant or anything that may bear on mitigation. If residual doubt is not to be a mitigating circumstance and if polygraph results can play no part in determining residual doubt, the majority should say so. If the majority agrees with the position I have taken, it should say that. The worst course, I submit, is to avoid the issues, even though they have been raised, with the result that no one knows the rules. Games of chance are quite inappropriate to capital cases. The state is currently engaged in an effort to bring more certainty and predictability to capital cases, as well as to bring them to finality more quickly. We do nothing to help and much to hinder this effort by leaving the rules and standards in doubt. The trial judge in this case is one of our most experienced and, deservedly, most respected, and other judges will no doubt follow his lead. There is little consistency to be achieved when one trial judge feels free to consider residual doubt and polygraph results while another may not. It is time to articulate the rules.
CONCURRING: THOMAS A. ZLAKET, Chief Justice.. For a case-by-case examination of sixty-eight death row inmates released because of wrongful convictions, see Death Penalty Symposium, Prisoners Released From Death Rows Since 1970 Because Of Doubts About Their Guilt, 13 T.M. Cooley L.Rev. 907 (1996).
. A 1999 Innocence Project reconstruction of sixty-two United States exoneration cases determined the following factors prevalent in wrongful convictions: mistaken eyewitnesses 84%; in-forman1/“snitch” error 21%; false confessions 24%; defense counsel error 27%; prosecutorial misconduct 42%; police misconduct 50%; tainted or fraudulent science 33%. See Scheck et al, supra, at 246.
. The conviction was reversed by our court of appeals in 1986. See State v. Youngblood, 153 Ariz. 50, 734 P.2d 592 (App.1986). After we denied review, the United States Supreme Court granted certiorari, vacated, and remanded to the court of appeals. See Arizona v. Youngblood, 488 U.S. 51, 109 S.Ct. 333, 102 L.Ed.2d 281 (1988). The court of appeals again reversed, holding that although the United States Constitution does not require that the government preserve evidence that might prove innocence, the protections afforded by the Arizona Constitution's Due Process Clause are greater. See State v. Youngblood, 164 Ariz. 61, 790 P.2d 759 (App.1989). We then granted review, vacated the second court of appeals opinion, and affirmed Youngblood’s conviction, with Chief Justice Feldman and Justice Zlaket concurring in part and dissenting in part. See State v. Youngblood, 173 Ariz. 502, 844 P.2d 1152 (1993).
. It appears, also, that there may be some question as to the great weight we have placed on fingerprint evidence. See Malcolm Ritter, Fingerprints May Face Challenge as Unscientific, Arizona Daily Star, April 8, 2001, at A5.
. The relevant substantive questions posed to Harrod and his responses were:
Q. Were you physically present when Jean Tovrea was killed?
A. No.
Q. Did you shoot Jean Tovrea?
A. No.
Q. Did you enter Jean Tovrea’s home through the kitchen window on April 1, 1988?
A. No.
Q. Did you participate in any way in the killing of Jean Tovrea.
A. No.
Defendant's Motion to Admit Polygraph, filed September 17, 1997, Exhibit A, at 2.
. I am aware, of course, that this court does not follow Daubert. See Logerquist v. McVey, 196 Ariz. 470, 1 P.3d 113 (2000). I do not recommend that we retreat from that position. But evidence found reliable enough to be admitted under Daubert should certainly be admissible under a statute that permits receipt of any information and requires the judge to consider any factors in an offer to which the rules of evidence do not apply.