OPINION
COATS, Judge.
Following a jury trial, Jay Huf was convicted of burglary in the first degree, AS 11.46.300(a)(1), and sexual assault in the first degree, AS 11.41.410(a)(1). Trial Judge Charles Cranston found that Huf was subject to presumptive sentencing because there was clear and convincing evidence that Huf “possessed or used a firearm ... during the commission of the offense _” Former AS 12.55.125(e)(1)
. Huf appeals his conviction, and also argues that Judge Cranston erred in not having the jury decide whether he possessed or used a firearm for purposes of applying the presumptive sentencing provisions. Huf also argues that if we hold that determination of whether he possessed or used a firearm is a question for the court, then the court erred in not requiring the state to prove that fact by a standard of beyond a reasonable doubt. We affirm Huf s conviction. We also conclude that the question of whether Huf “possessed or used a firearm during the commission of the offense” was properly a question for the court. However, we conclude that the court should have required the prosecution to prove that fact by the standard of beyond a reasonable doubt. We consequently vacate Huf’s sentence and remand to the trial court for redetermination of that issue.
Huf argues that his conviction should be reversed because Judge Cranston, over objection by defense counsel, allowed the prosecutor to argue the mathematical probability that hairs found in a cap which was left at the scene of the sexual assault were hairs of the defendant. A certain amount of factual background is necessary to understand our ruling on this issue. It is not contested that the person who committed the sexual assault on the victim, P.M., left a stocking cap in the room where the assault took place. The assault took place in P.M.’s bedroom. At trial, the state presented the testimony of Michael P. Malone, an F.B.I. agent, who had analyzed the hairs found on various items of evidence and compared them to known hair samples taken from Huf. Agent Malone testified that pubic hairs found on the stocking cap left by P.M.’s assailant matched Huf’s pubic hairs in twenty characteristics. He stated it would be “highly unlikely” for the hair of two different people to have the same twenty characteristics in exactly the same arrangement. He explained that during the last seven years he had performed about 10,000 separate examinations of the hair of about 10,000 different people. In that time there were only two occasions in which the hair from two different people was so similar it could not be distinguished. Agent Malone also testified that when he compared the head hairs found on the knit cap with the known head hairs from Huf, they microscopically matched. He testified that head hair and pubic hair are “two independent events.” Because head hairs are “totally different — separate from pubic hairs,” the chances of finding somebody else with both the same head hairs and the same pubic hairs would be “extremely remote ... almost non-existent.”
During closing argument, the state used Agent Malone’s testimony to argue that there was a one in 5,000 chance that á person would have pubic hairs like Huf’s. The state also argued that, because head and pubic hairs were independent, there was a separate one in 5,000 chance that the head hair of another person would have the same characteristics as Huf’s head hair. Huf objected to the prosecution’s argument. However, Judge Cranston overruled Huf’s objection, and the state was allowed to argue that the likelihood of anyone having both the same head hair and pubic hair as Huf’s was “one in 5,000 times one in 5,000.”
We agree with Huf that it was misleading to argue from Agent Malone’s testimony that the evidence presented at trial established that the chance of anyone hav
ing the same head hair and pubic hair as Huf was “one in 5,000 times one in 5,000.” However, we also conclude that it is clear that this argument “did not appreciably affect the jury’s verdict,...”
Love v. State,
457 P.2d 622, 632 (Alaska 1969).
Huf has cited séveral cases in which courts have condemned misleading statistical arguments. The leading cases appear to be
United States v. Massey,
594 F.2d 676 (8th Cir.1979) and
People v. Collins,
68 Cal.2d 319, 66 Cal.Rptr. 497, 438 P.2d 33 (1968). However, in those cases the statistical evidence clearly was a major part of the prosecution’s proof and may have had a major impact on the outcome of the trial. That is not true in the instant case. Although it appears that the prosecutor’s argument may have greatly overstated whatever the true probability was that a person in the general population would have head hair and pubic hair which matched both the head hair and pubic hair of Jay Huf, the probability was “extremely remote ... almost non-existent,” based on the testimony of Agent Malone. Thus, based on Malone’s testimony at trial, the prosecutor had an extremely strong argument even without the overstatement.
We have also considered the fact that the prosecution’s case was strong even without the evidence that the head hair and pubic hair on the stocking cap matched the head hair and pubic hair of Jay Huf. The jury heard P.M. identify Jay Huf at trial as the man who raped her. The jury learned from the testimony of Trooper Hagan that the description of her assailant which P.M. gave to the police closely matched that of Jay Huf and that she told the police she believed Jay Huf was her assailant. The jury heard P.M. testify that her assailant wore button-up Levis; button-up Levis were found during the March 6, 1981, search of Huf’s home. P.M. testified her assailant had a penlite flashlight; a penlite flashlight was discovered at Huf’s home. P.M. testified that her assailant wore a black and white striped hat; the hat which was left behind at P.M.’s home matched the hat tassel with rare fibers later found during the search of Huf’s residence. P.M. testified that her assailant threatened her with a gun; revolver ammunition was found at Huf’s home. P.M. testified that her assailant bound her with duct tape; duct tape was found during the search at Huf’s residence.
On March 6, 1981, Huf was informed by police that he was a suspect in the case. Jay Huf then left the area and was not seen again for almost a year. Huf’s employer testified that Huf left his job of five years on March 6, 1981. Jay Huf’s brother testified that he did not know where Huf had gone after the defendant left the Kenai area on March 6, 1981. On February 19, 1982, Huf was arrested in Anchorage, where he was working under a false name. Huf’s defense was limited to two witnesses, Jan Huf (his sister) and Deborah Wise. Their testimony indicated that Huf was drinking on the morning of March 6, 1981. Their testimony was consistent with that of P.M.’s and did little if anything to undermine the state’s case.
We also note that prior to counsels’ final argument, the court cautioned the jury:
It now becomes the time, ladies and gentlemen of the jury, for argument by counsel. Once again, although you’ve been told this by the court, arguments of counsel are not evidence.
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OPINION
COATS, Judge.
Following a jury trial, Jay Huf was convicted of burglary in the first degree, AS 11.46.300(a)(1), and sexual assault in the first degree, AS 11.41.410(a)(1). Trial Judge Charles Cranston found that Huf was subject to presumptive sentencing because there was clear and convincing evidence that Huf “possessed or used a firearm ... during the commission of the offense _” Former AS 12.55.125(e)(1)
. Huf appeals his conviction, and also argues that Judge Cranston erred in not having the jury decide whether he possessed or used a firearm for purposes of applying the presumptive sentencing provisions. Huf also argues that if we hold that determination of whether he possessed or used a firearm is a question for the court, then the court erred in not requiring the state to prove that fact by a standard of beyond a reasonable doubt. We affirm Huf s conviction. We also conclude that the question of whether Huf “possessed or used a firearm during the commission of the offense” was properly a question for the court. However, we conclude that the court should have required the prosecution to prove that fact by the standard of beyond a reasonable doubt. We consequently vacate Huf’s sentence and remand to the trial court for redetermination of that issue.
Huf argues that his conviction should be reversed because Judge Cranston, over objection by defense counsel, allowed the prosecutor to argue the mathematical probability that hairs found in a cap which was left at the scene of the sexual assault were hairs of the defendant. A certain amount of factual background is necessary to understand our ruling on this issue. It is not contested that the person who committed the sexual assault on the victim, P.M., left a stocking cap in the room where the assault took place. The assault took place in P.M.’s bedroom. At trial, the state presented the testimony of Michael P. Malone, an F.B.I. agent, who had analyzed the hairs found on various items of evidence and compared them to known hair samples taken from Huf. Agent Malone testified that pubic hairs found on the stocking cap left by P.M.’s assailant matched Huf’s pubic hairs in twenty characteristics. He stated it would be “highly unlikely” for the hair of two different people to have the same twenty characteristics in exactly the same arrangement. He explained that during the last seven years he had performed about 10,000 separate examinations of the hair of about 10,000 different people. In that time there were only two occasions in which the hair from two different people was so similar it could not be distinguished. Agent Malone also testified that when he compared the head hairs found on the knit cap with the known head hairs from Huf, they microscopically matched. He testified that head hair and pubic hair are “two independent events.” Because head hairs are “totally different — separate from pubic hairs,” the chances of finding somebody else with both the same head hairs and the same pubic hairs would be “extremely remote ... almost non-existent.”
During closing argument, the state used Agent Malone’s testimony to argue that there was a one in 5,000 chance that á person would have pubic hairs like Huf’s. The state also argued that, because head and pubic hairs were independent, there was a separate one in 5,000 chance that the head hair of another person would have the same characteristics as Huf’s head hair. Huf objected to the prosecution’s argument. However, Judge Cranston overruled Huf’s objection, and the state was allowed to argue that the likelihood of anyone having both the same head hair and pubic hair as Huf’s was “one in 5,000 times one in 5,000.”
We agree with Huf that it was misleading to argue from Agent Malone’s testimony that the evidence presented at trial established that the chance of anyone hav
ing the same head hair and pubic hair as Huf was “one in 5,000 times one in 5,000.” However, we also conclude that it is clear that this argument “did not appreciably affect the jury’s verdict,...”
Love v. State,
457 P.2d 622, 632 (Alaska 1969).
Huf has cited séveral cases in which courts have condemned misleading statistical arguments. The leading cases appear to be
United States v. Massey,
594 F.2d 676 (8th Cir.1979) and
People v. Collins,
68 Cal.2d 319, 66 Cal.Rptr. 497, 438 P.2d 33 (1968). However, in those cases the statistical evidence clearly was a major part of the prosecution’s proof and may have had a major impact on the outcome of the trial. That is not true in the instant case. Although it appears that the prosecutor’s argument may have greatly overstated whatever the true probability was that a person in the general population would have head hair and pubic hair which matched both the head hair and pubic hair of Jay Huf, the probability was “extremely remote ... almost non-existent,” based on the testimony of Agent Malone. Thus, based on Malone’s testimony at trial, the prosecutor had an extremely strong argument even without the overstatement.
We have also considered the fact that the prosecution’s case was strong even without the evidence that the head hair and pubic hair on the stocking cap matched the head hair and pubic hair of Jay Huf. The jury heard P.M. identify Jay Huf at trial as the man who raped her. The jury learned from the testimony of Trooper Hagan that the description of her assailant which P.M. gave to the police closely matched that of Jay Huf and that she told the police she believed Jay Huf was her assailant. The jury heard P.M. testify that her assailant wore button-up Levis; button-up Levis were found during the March 6, 1981, search of Huf’s home. P.M. testified her assailant had a penlite flashlight; a penlite flashlight was discovered at Huf’s home. P.M. testified that her assailant wore a black and white striped hat; the hat which was left behind at P.M.’s home matched the hat tassel with rare fibers later found during the search of Huf’s residence. P.M. testified that her assailant threatened her with a gun; revolver ammunition was found at Huf’s home. P.M. testified that her assailant bound her with duct tape; duct tape was found during the search at Huf’s residence.
On March 6, 1981, Huf was informed by police that he was a suspect in the case. Jay Huf then left the area and was not seen again for almost a year. Huf’s employer testified that Huf left his job of five years on March 6, 1981. Jay Huf’s brother testified that he did not know where Huf had gone after the defendant left the Kenai area on March 6, 1981. On February 19, 1982, Huf was arrested in Anchorage, where he was working under a false name. Huf’s defense was limited to two witnesses, Jan Huf (his sister) and Deborah Wise. Their testimony indicated that Huf was drinking on the morning of March 6, 1981. Their testimony was consistent with that of P.M.’s and did little if anything to undermine the state’s case.
We also note that prior to counsels’ final argument, the court cautioned the jury:
It now becomes the time, ladies and gentlemen of the jury, for argument by counsel. Once again, although you’ve been told this by the court, arguments of counsel are not evidence. And are intended to be helpful to you. Once again, the evidence is that which is in the form of exhibits that have been admitted, as well as testimony from the witness stand except that which has been stricken. And you should view counsels’ arguments in that light.
Following final arguments, the court also read this cautionary instruction as part of its instructions to the jury:
Arguments, statements, and remarks of counsel are intended to help you in understanding the evidence and applying the law, but are not evidence. If any argument, statement or remark has no basis in the evidence, then you should disregard that argument, statement or remark.
Given these instructions and the evidence which the jury heard during the course of trial, it appears unlikely that the state’s argument concerning mathematical probability had any appreciable effect on the jury’s verdict. We conclude that allowing the argument was harmless error.
Huf’s next argument turns on the interpretation and the constitutionality of former AS 12.55.125(c) which established sentences for class A felonies. That provision reads as follows:
(c) A defendant convicted of a class A felony may be sentenced to a definite term of imprisonment of not more than 20 years, and shall be sentenced to the following presumptive terms, subject to adjustment as provided in AS 12.55.155-12.55.175;
(1) if the offense is a first felony conviction, other than for manslaughter, and
the defendant possessed or used a firearm
or caused serious physical injury during the commission of the offense, six years;
(2) if the offense is a second felony conviction, 10 years;
(3) if the offense is a third felony conviction, 15 years. [Emphasis added.]
At the close of his trial, Huf asked for instructions which would have required the jury to find beyond a reasonable doubt that he “possessed or used a firearm during the commission” of the sexual assault. Huf argued that whether he possessed or used a firearm was a factual question for the jury. Judge Cranston ruled that the question was one for the court at sentencing and refused to give Huf’s proposed instructions. Following Huf’s conviction, Judge Cranston found by clear and convincing evidence that Huf “possessed or used a firearm ... during the commission of the offense” and thus sentenced Huf to a presumptive term under the provisions of former AS 12.55.125(c)(1).
Huf argues on appeal that the issue of whether he used or possessed a firearm during the commission of the offense was properly a matter for jury determination and claims that later raising this issue in the sentencing proceeding violated the double jeopardy clause of the Alaska Constitution, article 1, section 9, and the double jeopardy clause of the fifth amendment to the United States Constitution.
The first question for our consideration is a matter of statutory interpretation. Did the legislature intend to have the fact of the possession or use of a firearm during the commission of an offense determined by the jury at trial or by the court at sentencing? Former AS 12.55.125(c)(1) appears to be a sentencing provision. It is placed in the statutes with the other sentencing provisions and former AS 12.55.-125(c) states that the penalties set forth in the statute are to be applied to “a defendant
convicted
of a class A felony.” (Emphasis added.) Sentencing matters have traditionally been matters for the court. We conclude that the legislature intended the question of whether the defendant possessed or used a firearm during the commission of a sexual assault to be a sentencing matter for determination by the court.
The next question is whether the statute is constitutional. Huf argues that he was entitled to a jury determination of the question of whether he used or possessed a firearm during the commission of the sexual assault. The issue is whether the legislature can enact a statutory scheme in which the question of whether Huf used or possessed a firearm is a matter to be determined by the trial judge.
Although Huf attempts to frame his argument more as a double jeopardy issue, generally the question of whether the defendant has been unconstitutionally deprived of his right to a jury trial is a matter of substantive due process. In general, substantive due process requires “proof beyond a reasonable doubt of every fact necessary to constitute the crime with which [the defendant] is charged.”
In re Winship,
397 U.S. 358, 364, 90 S.Ct. 1068, 1073, 25 L.Ed.2d 368, 375 (1970). However, we believe that in
Patterson v. New York,
432 U.S. 197, 210-11, 97 S.Ct. 2319, 2327, 53 L.Ed.2d 281, 292-93 (1977), the United
States Supreme Court, while holding firm to the proposition that the constitution requires the prosecution to shoulder the traditional burden of proving the guilt of the accused beyond a reasonable doubt, also indicated that state legislatures have considerable authority to define crimes.
See Walker v. State,
674 P.2d 825, 827-829 (Alaska App.1983).
In
State v. Kleber,
2 Kan.App.2d 115, 575 P.2d 900, 904 (Kan.App.1978), the court ruled on an argument similar to that which Huf advances in this case. Kleber was sentenced under a provision of the Kansas code which imposed a mandatory minimum sentence for certain crimes where the defendant used a firearm in the commission of the offense. Kleber argued that the statute was unconstitutional because the determination that he used a firearm was decided not by a jury in his trial but by a judge at a sentencing proceeding. The court upheld the provision. The court distinguished cases where other courts held that the question of whether the defendant used a firearm during the offense was a question for the jury:
The cases relied upon by defendant are not controlling since they concern statutes from other jurisdictions wherein an additional enhanced sentence may be imposed upon a defendant who commits a crime with a firearm. Such statutes frequently provide that one who commits a felony with a firearm may receive a separate sentence for the use of the firearm in addition to whatever sentence may be imposed for the felony. In construing such statutes, it has been held that the question as to whether a firearm was used must be determined by the trier of fact before the additional sentence may be imposed. It has been said that such statutes define a new class of crimes by adding a new element, use of a firearm, and the existence of the new element requires an additional finding of fact.
Id.
(citations omitted). The court went on to point out that the Kansas statute was a true sentencing provision and did not create a different offense:
We believe K.S.A.1977 Supp. 21-4618 is distinguishable from those statutes of other jurisdictions construed in the cases cited by defendant. K.S.A.1977 Supp. 21-4618, when read in conjunction with K.S.A.1977 Supp. 22-3717(8), has the effect of imposing a mandatory minimum sentence for all Article 34 crimes in which the defendant used a firearm in the commission of the crime. We have construed K.S.A.1977 Supp. 21-4618 as precluding the suspension of sentence where defendant has been found guilty of an Article 34 crime with the use of a firearm. While K.S.A.1977 Supp. 21-4618 limits the range of authorized dispositions available to the trial court in some instances, it does not create a new class of crimes, add a new element to the statutory definition of already existing crimes, or provide for an additional sentence. Use of a firearm under the statute is not made an element of the offense charged, and is only pertinent to the authorized disposition the court may consider in the event of a conviction.
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Therefore, we conclude that the question of defendant’s use of a firearm did not have to be submitted to the jury for determination.
Id.
575 P.2d at 904-05 (footnote added; citations omitted).
We conclude that former AS 12.55.-125(c)(1) does not create a new crime or add an element to the crime of sexual assault. It appears to be similar to the statute in the Kansas case in that it is a true sentencing provision. As a first offender convict
ed of a class A felony, Huf faced a sentence of up to twenty years. Former AS 12.55.125(c)(1) merely limited the judge’s sentencing discretion and required him to impose a presumptive sentence of six years if he found that “the defendant possessed or used a firearm or caused serious physical injury during the commission of the offense.”
We note that the trial judge could impose a sentence greater than a six-year presumptive sentence on a defendant who was convicted of a class A felony even though that defendant had not used a firearm or caused serious physical injury if the facts of the case justified the sentence. We therefore conclude that former AS 12.55.-125(c)(1) is a sentencing provision and that Judge Cranston did not err in not submitting the question of whether Huf used a firearm during the commission of the sexual assault to the jury. His application of former AS 12.55.125(c)(1) to the defendant during sentencing was based on a proper interpretation of the statute. The statute does not violate the due process provisions or the double jeopardy provisions of either the United States or Alaska Constitutions.
The question remains whether Judge Cranston applied the correct burden of proof in determining whether Huf “possessed or used a firearm ... during the commission of the offense.” Judge Cran-ston found this fact by clear and convincing evidence.
Former AS 12.55.125(c) does not indicate what the proper burden of proof should be. Huf argues that under the statutes in effect at the time he was sentenced, the legislature required presumptive sentences only where the defendant had a prior felony conviction which qualified under AS 12.-55.145 or where the defendant was sentenced under former AS 12.55.125(c)(1). Huf points out that under AS 12.55.145(b) and (d), the legislature required a high standard of proof:
(b) When sentence is imposed under this chapter, prior convictions not
expressly admitted
by the defendant
must be proved by authenticated copies of court records
served on the defendant or his counsel at least 10 days before the date set for the imposition of sentence.
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(d) Matters alleged in a notice of denial shall be heard by the court sitting without a jury. If the defendant introduces substantial evidence that he is not the person named in the prior judgment of conviction, that the judgment is not authentic, that the conviction did not occur within the time period specified in (a)(1) of this section, or that a conviction should not be considered a prior felony conviction under (a)(2) of this section,
then the burden is on the state to prove the contrary beyond a reasonable doubt.
[Emphasis added.]
Huf argues that since the legislature .essentially required proof beyond a reasonable doubt to establish prior convictions for presumptive sentencing purposes, by analogy the legislature meant to require proof beyond a reasonable doubt under former AS 12.55.125(c)(1). The state agrees with Huf, but would require Huf to show by substantial evidence that a firearm was not used before the state would have to establish that-Huf possessed or used a firearm by a beyond a reasonable doubt standard. The state’s argument is based on AS 12.55.-145(d).
We conclude, based in part on the state’s confession of error, that Judge Cranston erred in not applying a beyond a reasonable doubt standard to former AS 12.55.125(c).
However, we believe that, by analogy with AS 12.55.145(b) and (d), the
defendant does not have to introduce substantial evidence that he did not possess or use a firearm before this burden of proof is required. We believe that if the defendant does not expressly admit that he possessed or used a firearm during the offense, the prosecution has the burden of proving that fact beyond a reasonable doubt. We believe that the provisions of AS 12.55.145(d) which place a burden of proof on the defendant to show that he was not the person named in a judgment of conviction are related to specific problems which arise from the proof of prior convictions. It does not seem reasonable to us to interpret the revised code to require the prosecution to prove that the defendant possessed a firearm by clear and convincing evidence unless the defendant introduces substantial evidence that he did not possess a firearm, in which case the prosecution must prove that the defendant possessed a firearm by a standard of beyond a reasonable doubt. It seems to us that the prosecution should have the same overall burden of proof, regardless of whether the defendant produces any evidence. Given the state’s concession of error and the analogy with AS 12.55.145(b) and (d), we conclude that the prosecution must prove that Huf possessed a firearm by a standard of beyond a reasonable doubt before the trial judge may presumptively sentence Huf under the provisions of former AS 12.55.125(c)(1). We accordingly vacate Huf s sentence and remand the case for resentencing in conformity with this opinion;
The conviction is AFFIRMED. The sentence is VACATED and the case is REMANDED.