
179 P.3d 153 (2007)
The PEOPLE of the State of Colorado, Plaintiff-Appellee,
v.
Trevon Deon WASHINGTON, a/k/a Venda Johnson Jr., Defendant-Appellant.
No. 03CA1895.
Colorado Court of Appeals, Div. I.
May 31, 2007.
Certiorari Granted December 18, 2007.
*156 John W. Suthers, Attorney General, Matthew S. Holman, First Assistant Attorney General, Denver, Colorado, for Plaintiff-Appellee.
The Viorst Law Offices, P.C., Anthony Viorst, Denver, Colorado, for Defendant-Appellant.
Opinion by Judge J. JONES.
Defendant, Trevon Deon Washington, appeals the trial court's judgment of conviction entered on jury verdicts finding him guilty of three counts of first degree murder after deliberation; four counts of aggravated robbery; and one count each of attempted first degree murder, second degree kidnapping, aggravated first degree sexual assault, conspiracy to commit first degree murder, and accessory to a crime. We affirm.

I. Background
On September 10, 1998, defendant, Randy Canister, and Dante Owens went to an apartment where the four victims, DH, PS, NP, and MN, resided. A few weeks earlier, DH and PS had gone to California to purchase cocaine, which they brought back to Colorado. The cocaine was to be split between Canister and DH; however, there was testimony that DH withheld some of the cocaine from Canister as payment for transporting the drugs.
After sitting and talking for about an hour, defendant, Canister, and Owens got up and began walking toward the door. DH got up with them and was walking in front of Canister. Before reaching the door, defendant pulled out a gun and said, "We're not leaving without taking all of this shit."
Canister forced DH to go back to a bedroom, while defendant ordered the others to sit in the living room. Defendant then gave the gun to Owens, told Owens to hold the gun on PS, NP, and MN, and went into the bedroom. Defendant returned a short time later and asked PS, NP, and MN, "Where's the shit?" They responded by shaking their heads.
Defendant took the gun back from Owens and told PS to undress and sit on the couch. Defendant and the other assailants then forced MN to perform oral sex on PS (MN's stepbrother), perform oral sex on Owens, have sexual intercourse with Owens, and perform oral sex on defendant in various rooms in the house.
When MN returned to the living room after performing oral sex on defendant, DH, PS, and NP were lying on the floor, face *157 down, with their hands and feet tied together. Defendant made MN lie on the floor and tied her. Defendant asked who had tied NP, Owens said he had, and defendant re-tied NP.
Defendant put socks in MN's and NP's mouths. Socks were also placed in DH's and PS's mouths. One of the assailants played a song on the stereo, turned up the volume loud, and programmed the stereo to play the song repeatedly.
Canister told DH, "California comes back on you ten times worse," and shot DH in the head. DH was shot a second time in the head. PS and NP were also shot in the head more than one time. MN testified that she saw defendant shoot PS in the head. She tried to scoot under a table to protect herself but defendant shot her in the back four times. Owens then shot her in the head.
Defendant, Canister, and Owens ransacked the apartment. They left with a bag.
DH, PS, and NP died at the scene. An autopsy of DH showed that he had puncture wounds on his neck and chest. PS also had bruises and contusions that were inflicted before he died. MN survived, but was rendered a paraplegic.
MN identified defendant, Canister, and Owens as the assailants.
In September 1998, the People charged defendant with (1) three counts of first degree murder (after deliberation), in violation of § 18-3-102(1)(a), C.R.S.2006; (2) three counts of first degree murder (felony murder), in violation of § 18-3-102(1)(b), C.R.S. 2006; (3) one count of attempted first degree murder, in violation of § 18-2-101(4), C.R.S. 2006; (4) one count of second degree kidnapping, in violation of § 18-3-302(1), C.R.S. 2006; (5) one count of aggravated first degree sexual assault, in violation of § 18-3-402(1)(a), C.R.S.2006; (6) four counts of aggravated robbery, in violation of § 18-4-302(1)(a), C.R.S.2006; (7) one count of conspiracy to commit first degree murder, in violation of § 18-2-201(5), C.R.S.2006; and (8) one count of accessory to a crime, in violation of § 18-8-105(1) and (3), C.R.S. 2006.
After the prosecution indicated its intent to seek the death penalty, defendant filed a motion with the court pursuant to §§ 18-1.3-1102 and 18-1.3-1103, C.R.S.2006, to preclude such punishment because he was mildly mentally retarded. After holding an evidentiary hearing, the court concluded that defendant was not eligible for the death penalty because he was mildly mentally retarded.
On July 24, 2003, following a trial that lasted three weeks, a jury convicted defendant of all counts. On the People's motion, the trial court dismissed the three convictions for first degree murder (felony murder) prior to sentencing because they were redundant of the convictions for first degree murder (after deliberation). See People v. Glover, 893 P.2d 1311, 1314 (Colo.1995).
On August 22, 2003, the court sentenced defendant to serve consecutive life sentences in the Department of Corrections, without the possibility of parole, on the three first degree murder (after deliberation) convictions and consecutive sentences for various terms of years on the remaining convictions.

II. Drawing the Jury Panel from a Fair cross-section of the Community
In the course of jury selection, defendant filed a motion to dismiss the jury pool on the grounds it was constituted in violation of the Colorado Uniform Jury Selection and Service Act, § 13-71-101, et seq., C.R.S.2006, the Sixth and Fourteenth Amendments to the United States Constitution, and the Colorado Constitution (presumably, art. II, § 16). The essence of defendant's motion was that the State's method of constituting jury panels for Arapahoe County systematically excluded a disproportionate number of African-Americans and Hispanics, such that his jury was not selected from a fair cross-section of the community.
The trial court conducted a hearing on defendant's motion after the trial. Defendant presented evidence showing how the State creates jury panels for Arapahoe County, and expert testimony as to the degree of underrepresentation of African-Americans and Hispanics on jury panels in Arapahoe County, as well as the likelihood that the *158 degree of such underrepresentation is attributable to chance.
The trial court denied defendant's motion, finding that defendant had failed to demonstrate systematic exclusion of African-Americans and Hispanics to a constitutionally significant degree, and that any underrepresentation was justified by the State's compelling interests in not overusing prospective jurors from Aurora, Colorado (who are eligible for municipal court jury service as well as county and district court jury service) and creating jury panels in an economically efficient manner.
Defendant contends that the trial court erred in denying his motion. We disagree.

A. Standard of Review
We review a trial court's factual findings concerning a fair cross-section claim for clear error, but review its legal determination whether a defendant established a violation of the fair cross-section requirement de novo. See United States v. Orange, 447 F.3d 792, 797 (10th Cir.2006); State v. Gibbs, 254 Conn. 578, 758 A.2d 327, 337 (2000); State v. Paz, 118 Idaho 542, 798 P.2d 1, 7 (1990), overruled in part on other grounds by State v. Card, 121 Idaho 425, 825 P.2d 1081 (1991). Here, defendant does not challenge any of the trial court's factual findings. He challenges only the trial court's legal conclusion that he failed to demonstrate a constitutional violation. Hence, our review is de novo.

B. Creation of Jury Panels for Arapahoe County
The Office of the State Court Administrator of the Colorado State Judicial Branch creates "jury wheels"  essentially, master lists of eligible potential jurors  for every county in the state. It culls driver's license and voting records to determine eligible jurors statewide, randomly assigns each such person a number, and then sorts the eligible jurors by county. See §§ 13-71-105, 13-71-107, 13-71-108(1), C.R.S.2006.
The State Court Administrator also creates a jury wheel for the City of Aurora. It does so, in large part, by selecting potential jurors from the Arapahoe County jury wheel who reside in Aurora. (Aurora is mostly, but not entirely, located in Arapahoe County.) Prior to March 2003, potential jurors chosen for the Aurora jury wheel were removed from the Arapahoe County jury wheel. In March 2003, however, that practice ceased, and prospective jurors residing in Aurora remained in both jury wheels, and therefore remained eligible and available for jury service in Aurora Municipal Court and in Arapahoe County county and district courts.
Each week, eligible potential jurors are drawn at random from the master county jury wheel to form the jury panel for that week. To reduce the likelihood that persons will be selected for jury service with disproportionately high frequency, the State Court Administrator, acting pursuant to statute, assigns each prospective juror a "service rank," which gives weight to prior jury service during a five-year period, with more recent service weighted more heavily. See § 13-71-108(2), C.R.S.2006. Those prospective jurors with lower service ranks are selected for jury panels before those with higher service ranks.

C. Applicable Law

1. The Fair cross-section Requirement
The Sixth Amendment to the United States Constitution guarantees every defendant "the right to a speedy public trial by an impartial jury. . . ." See also Colo. Const. art. II, § 16. This guarantee "contemplates a jury drawn from a fair cross section of the community. . . . `[I]t is part of the established tradition in the use of juries as instruments of public justice that the jury be a body truly representative of the community.'" Taylor v. Louisiana, 419 U.S. 522, 527, 95 S.Ct. 692, 696, 42 L.Ed.2d 690 (1975) (quoting in part Smith v. Texas, 311 U.S. 128, 130, 61 S.Ct. 164, 165, 85 L.Ed. 84 (1940)); see also § 13-71-104(2), C.R.S.2006 ("All trial and grand jurors shall be selected at random from a fair cross section of the population of the area served by the court."); People v. Rubanowitz, 688 P.2d 231, 241 (Colo.1984); People v. Sepeda, 196 Colo. 13, 18, 581 P.2d 723, 727 (1978). The fair cross-section requirement seeks to avoid "the possibility that the composition of juries would be arbitrarily skewed *159 in such a way as to deny criminal defendants the benefit of the common-sense judgment of the community" as well as the "appearance of unfairness" that would result from excluding "large groups of individuals not on the basis of their inability to serve as jurors, but on the basis of some immutable characteristic such as race, gender, or ethnic background. . . ." Lockhart v. McCree, 476 U.S. 162, 175, 106 S.Ct. 1758, 1766, 90 L.Ed.2d 137 (1986).
There are, however, substantial limits on the fair cross-section requirement. It does not guarantee that juries be "of any particular composition." Taylor, supra, 419 U.S. at 538, 95 S.Ct. at 702; see also Holland v. Illinois, 493 U.S. 474, 480, 110 S.Ct. 803, 807, 107 L.Ed.2d 905 (1990); Sepeda, supra, 196 Colo. at 18, 581 P.2d at 727 ("There is no requirement . . . that each petit jury reflect the exact ethnic proportion of the population to which the defendant belongs."). All that is required is that "the jury wheels, pools of names, panels, or venires from which juries are drawn must not systematically exclude distinctive groups in the community and thereby fail to be reasonably representative thereof." Taylor, supra, 419 U.S. at 538, 95 S.Ct. at 702.

2. Proving a Fair cross-section Claim
In order to establish a prima facie violation of the fair-cross-section requirement, the defendant must show (1) that the group alleged to be excluded is a "distinctive" group in the community; (2) that the representation of this group in venires from which juries are selected is not fair and reasonable in relation to the number of such persons in the community; and (3) that this underrepresentation is due to systematic exclusion of the group in the jury-selection process.
Duren v. Missouri, 439 U.S. 357, 364, 99 S.Ct. 664, 668, 58 L.Ed.2d 579 (1979); see also Rubanowitz, supra, 688 P.2d at 241; Sepeda, supra, 196 Colo. at 19, 581 P.2d at 727-28. "[O]nce the defendant has made a prima facie showing of an infringement of his constitutional right to a jury drawn from a fair cross section of the community, it is the State that bears the burden of justifying this infringement by showing attainment of a fair cross section to be incompatible with a significant state interest." Duren, supra, 439 U.S. at 368, 99 S.Ct. at 671.

D. Sufficiency of Defendant's Proof

1. Distinctive Group
There is no dispute that African-Americans and Hispanics constitute "distinctive groups" for purposes of fair cross-section analysis. See United States v. Weaver, 267 F.3d 231, 240 (3d Cir.2001); United States v. Shinault, 147 F.3d 1266, 1271-72 (10th Cir. 1998); cf. Castaneda v. Partida, 430 U.S. 482, 495, 97 S.Ct. 1272, 1280, 51 L.Ed.2d 498 (1977) (holding that Mexican-Americans are a "clearly identifiable class" in the context of an equal protection challenge to grand jury selection); Hernandez v. Texas, 347 U.S. 475, 479-80, 74 S.Ct. 667, 671, 98 L.Ed. 866 (1954) (same, but with respect to jury panels); Fields v. People, 732 P.2d 1145, 1153 (Colo. 1987) (Spanish-surnamed persons constitute a cognizable group for purposes of Sixth Amendment challenge to racial composition of jury); Montoya v. People, 141 Colo. 9, 10-12, 345 P.2d 1062, 1063 (1959) (same as Hernandez, supra). Therefore, defendant satisfied the first prong of his prima facie case.

2. Fair and Reasonable Representation

a. Measuring Fair and Reasonable Representation
Demonstrating underrepresentation in this context "is, at least in part, a mathematical exercise, and must be supported by statistical evidence." Weaver, supra, 267 F.3d at 240 (citing Duren, supra, 439 U.S. at 364, 99 S.Ct. at 668). Historically, the courts have, with a few exceptions, applied two statistical measures to assess whether a group's representation in jury panels is "fair and reasonable" in relation to its population in the community: absolute disparity and comparative disparity. See Orange, supra, 447 F.3d at 798; Weaver, supra, 267 F.3d at 241-43; Peter A. Detre, Note, A Proposal for Measuring Underrepresentation in the Composition of the Jury Wheel, 103 Yale L.J.1913, 1917-18 (1994) (Detre).
*160 Absolute disparity refers to the difference between the percentage of a group's representation in jury panels and its percentage of representation in the community. For example, if members of a group comprise 10% of the relevant population (the "community"), but 5% of jury panels, the absolute disparity is 5% (10% (percentage of relevant population)  5% (percentage injury panels)).
Comparative disparity is calculated by dividing the absolute disparity by the percentage of the group in the community and then multiplying by 100 (to create a figure expressed in terms of a percentage). For example, if members of a group comprise 10% of the relevant population but 5% of jury panels, the comparative disparity is 50% ( (5% (absolute disparity) ÷ 10% (percentage of relevant population)) x 100). Orange, supra, 447 F.3d at 798; Detre, supra, 103 Yale L.J. at 1917-18; see also D.H. Kaye, Statistical Analysis in Jury Discrimination Cases, 25 Jurimetrics J. 274, 277-78 (1985) (Kaye).
In effect, comparative disparity imagines how many members of the group in question would be on the wheel if there were full representation, and then calculates the percentage decrease from this figure due to the underrepresentation. Another way to think of the comparative disparity is as the percentage decrease in the probability that someone in the underrepresented group will be selected for the jury wheel due to the underrepresentation.
Detre, supra, 103 Yale L.J. at 1918.
Absolute disparity is by far the most commonly employed measure in this context, with comparative disparity running a rather distant second. Notwithstanding the frequent use of these measures, however, they may, in certain circumstances, have drawbacks, and accordingly have been criticized, to varying degrees, by courts and commentators. See, e.g., Weaver, supra, 267 F.3d at 241-43; Shinault, supra, 147 F.3d at 1273; United States v. Pion, 25 F.3d 18, 23 (1st Cir.1994); David Kairys, Joseph Kadane & John Lehoczky, Jury Representativeness: A Mandate for Multiple Source Lists, 65 Cal. L.Rev. 776, 793-94, 796 (1977) (Kairys); Detre, supra, 103 Yale L.J. at 1921-22, 1927-30.
Absolute disparity is susceptible of criticism on the basis that where the group in question comprises a relatively small percentage of the community, it may understate systematic representative deficiencies, effectively sanctioning wholesale exclusion of distinctive groups. See, e.g., Shinault, supra, 147 F.3d at 1273; Kairys, supra, 65 Cal. L.Rev. at 793-94; Detre, supra, 105 Yale L.J. at 1921. For example, if a group comprises 5% of the relevant population and 0% of the jury pool, the absolute disparity is only 5%, a figure well below what has historically been regarded as sufficient to demonstrate underrepresentation to a constitutionally significant degree, as discussed below.
Conversely, comparative disparity is susceptible of the criticism that it may overstate the disparity where a group is relatively small in the community. See Pion, supra, 25 F.3d at 23; United States v. Hafen, 726 F.2d 21, 24 (1st Cir.1984); Detre, supra, 103 Yale L.J. at 1921-22. For example, if a group comprises 5% of the relevant population and 2% of the jury pool, the comparative disparity is 60%, a figure which may be perceived as relatively high despite the relatively low absolute disparity (3%). For this reason, "[w]hen comparative disparity has been used, it has been emphasized that the significance of the figure is directly proportional to the size of the group relative to the general population, and thus is most useful when dealing with a group that comprises a large percentage of the population." Weaver, supra, 267 F.3d at 242 (citing LaRoche v. Perrin, 718 F.2d 500, 502-03 (1st Cir.1983) (finding prima facie violation where comparative disparity was 68% and group comprised 68% of population), overruled on other grounds by Barber v. Ponte, 772 F.2d 982 (1st Cir. 1985) (en banc)).
Despite these drawbacks and criticisms, however, absolute disparity in particular has continued to enjoy widespread approval and application. In Duren, supra, the Supreme Court relied entirely on an absolute disparity of approximately 35% to conclude that the second prong of the prima facie case had been met. Duren, supra, 439 U.S. at 362-65, 99 S.Ct. at 667-69. Many courts have expressly approved of absolute disparity as an *161 appropriate mode of statistical analysis in fair cross-section cases, though not necessarily as one to be applied to the exclusion of all others. See, e.g., Orange, supra, 447 F.3d at 798; United States v. Royal, 174 F.3d 1, 6-11 (1st Cir.1999); People v. Burgener, 29 Cal.4th 833, 129 Cal.Rptr.2d 747, 62 P.3d 1, 22 (2003); Diggs v. United States, 906 A.2d 290, 296-97 (D.C.2006); Commonwealth v. Arriaga, 438 Mass. 556, 781 N.E.2d 1253, 1264-65 (2003); People v. Smith, 463 Mich. 199, 615 N.W.2d 1, 2-3 (2000).
A few courts, persuaded that absolute disparity and comparative disparity are inadequate measures of underrepresentation, particularly where the group in question comprises a relatively small percentage of the relevant population, have looked to other measures in conjunction with or in lieu of absolute disparity and comparative disparity.
One such measure is referred to as "absolute impact" or "substantial impact." This measure is arrived at by simply multiplying the absolute disparity by the size of a jury panel. It thereby measures the extent to which an absolute disparity actually decreases the number of members of a particular group on a typical jury panel when compared to the number on a perfectly representational jury panel. For example, if the absolute disparity is 5% and the jury panel has 60 potential jurors, the absolute impact is three fewer members of the group on the typical jury panel.
This measure has been employed by some courts because it concretely demonstrates the effect of a disparity. See, e.g., United States v. Rioux, 97 F.3d 648, 657-58 (2d Cir.1996); United States v. Biaggi, 909 F.2d 662, 678 (2d Cir.1990); United States v. Test, 550 F.2d 577, 590 (10th Cir.1976); United States v. Jenkins, 496 F.2d 57, 66 (2d Cir. 1974); Gibbs, supra, 758 A.2d at 337 (rejecting absolute disparity, comparative disparity, and statistical decision analysis in favor of absolute impact where group comprised only 6.7% of the population). Absolute impact, however, is also susceptible of criticism on the basis it understates the disparity where the group comprises a relatively small percentage of the population. Kairys, supra, 65 Cal. L.Rev. at 800.
The final measure (more precisely, a group of measures) is referred to as "statistical decision theory" or "statistical significance." Statistical decision theory seeks to calculate "the probability that the observed underrepresentation of the group . . . was the result of chance." Detre, supra, 103 Yale L.J. at 1918; see also Kaye, supra, 25 Jurimetrics J. at 278; Kairys, supra, 65 Cal. L.Rev. at 792. Typically, this probability is expressed in terms of a number of "standard deviations" or in terms of a percentage of the likelihood the disparity is attributable to chance.
The standard deviation of a random variable is a measure of its dispersion about its mean. . . . The statistical significance, or unlikelihood of the observed underrepresentation having occurred as a result of random selection, can be expressed as the number of standard deviations between the actual number of group members on the wheel and the expected number for a random selection. The greater the number of standard deviations, the less likely that the underrepresentation could have resulted from a random selection.
Detre, supra, 103 Yale L.J. at 1919 n. 30; see also Kaye, supra, 25 Jurimetrics J. at 278. When the probability of a disparity occurring by chance is expressed by a percentage rather than a number of standard deviations, statisticians typically use 5% (one chance in twenty) as the cut-off for concluding that the probability is "statistically significant"  that is, that the disparity is unlikely the result of chance.
In Castaneda, supra, the Supreme Court held that an absolute disparity of 40% was sufficient to make out a prima facie case of an equal protection violation; however, the Court added a lengthy footnote noting the statistical significance of twenty-nine standard deviations, and observing that a number "greater than two or three standard deviations . . . would be suspect to a social scientist." Castaneda, supra, 430 U.S. at 496 n. 17, 97 S.Ct. at 1281.
After Castaneda, a few courts have considered statistical decision theory (including standard deviations) in determining under-representation, *162 though none has adopted it as the sole legally relevant method of assessing fair and reasonable representation in the fair cross-section context. See McGinnis v. Johnson, 181 F.3d 686, 690 n. 6 (5th Cir. 1999) (considering standard deviations in dictum); People v. Buford, 132 Cal.App.3d 288, 182 Cal.Rptr. 904, 909 (1982); Paz, supra, 798 P.2d at 7 (approving analysis of methodologies set forth in State v. Lopez, 107 Idaho 726, 692 P.2d 370, 375-77 (App.1984), and declining to adopt one measure to the exclusion of others); Smith, supra, 615 N.W.2d at 2-3; cf. Alston v. Manson, 791 F.2d 255, 257-59 (2d Cir.1986) (applying statistical decision theory to equal protection claim); Moultrie v. Martin, 690 F.2d 1078, 1082 (4th Cir.1982) (same).
The use of statistical decision theory in this context has been criticized on a number of grounds. The Court in Castaneda, supra, did not equate the number of standard deviations sufficient to "be suspect to a social scientist"  that is, statistically significant  with legal significance. Doing so runs the risk of mixing apples and oranges. Statistical decision theory measures the probability that any underrepresentation is random, not whether a group is fairly and reasonably represented. See Ford v. Seabold, 841 F.2d 677, 684 n. 5 (6th Cir.1988); Detre, supra, 103 Yale L.J. at 1928 (asserting that "[t]he probability that the composition of a jury wheel arose by random selection from the community is not directly related to the defendant's chances of drawing a jury of a certain composition"); Kaye, supra, 25 Jurimetrics J. at 283. Further, it focuses on randomness in a process that is inherently not random in that jury panels "entail[ ] reasoned disqualifications based on numerous factors." Rioux, supra, 97 F.3d at 655. Finally, it "involves complicated calculations resulting in answers that are difficult to visualize and to evaluate." Kairys, supra, 65 Cal. L.Rev. at 794.
Commentators have suggested using other, more complicated statistical measures. See, e.g., Detre, supra, 103 Yale L.J. at 1930-37; Kaye, supra, 25 Jurimetrics J. at 285-89. To date, however, no court has applied measures other than those discussed above. While we do not rule out the possibility that other measures may be helpful in a particular case, we need not consider any such measures here because the measures available to us are sufficient to resolve defendant's claim. In any event, the parties have not relied on any other measures.

b. Defendant's Expert Witness's Testimony
Defendant's expert witness on statistics, Dr. Robert Bardwell, testified as to statistical disparities between the percentage of African-Americans and Hispanics in Arapahoe County and their inclusion in Arapahoe County jury panels for the years 1993-2003. Because defendant was tried in July 2003, we consider his claim, and Dr. Bardwell's analysis, in light of the selection procedure then in effect (that is, prospective jurors residing in Aurora remained in the Arapahoe County jury wheel) and the relevant statistics for that year.
Dr. Bardwell testified that for the year 2003, African-Americans comprised 7.7% of the population of Arapahoe County (based on interpolations of census data from the years 1990 and 2000) and 7.4% of the potential jurors in the weekly jury panels, and that Hispanics comprised 12.9% of the population of Arapahoe County and 12.6% of the potential jurors in the weekly jury panels. He attributed the lower rates of representation in the jury panels vis-à-vis the population of Arapahoe County to two factors acting in combination: (1) the two groups are present in Aurora in greater proportion than in Arapahoe County as a whole; and (2) members of the two groups who reside in Aurora are more likely to be called for jury service because they are eligible for such service in multiple jurisdictions. Thus, persons residing in Aurora (which is comprised of proportionately more African-Americans and Hispanics than is Arapahoe County as a whole) are more likely to have higher service ranks and thereby be excluded from jury panels in Arapahoe County.
According to Dr. Bardwell, the disparities are "statistically significant" because they exceed the "five percent level," a divergence of 1.65 standard deviations. As discussed, this *163 mode of analysis (a species of statistical decision theory) measures the likelihood that the disparities are random.
With respect to African-Americans, Dr. Bardwell opined that the probability of the .3% disparity being attributable to chance was .008% (or eight chances in 100,000). With respect to Hispanics, Dr. Bardwell opined that the probability of the .3% disparity being attributable to chance was .12% (or 120 chances in 100,000).

c. Assessment of the Statistical Evidence
Despite Dr. Bardwell's testimony, for constitutional purposes we are persuaded that the representation of persons in the two groups in question in jury panels from which juries were selected in Arapahoe County in 2003 was fair and reasonable in relation to the number of such persons in Arapahoe County.
Given the relatively low figures for both absolute disparity and comparative disparity in this case, the People predictably urge us to rely solely on those figures, and argue that courts routinely find no underrepresentation even in cases where the comparative figures are much higher. Defendant, on the other hand, argues that because the number of standard deviations here exceeds the "two or three" regarded as "suspect to a social scientist" in Castaneda, supra, we must conclude that he satisfied the second prong of the prima facie test. We decline to hold that one measure must be assessed to the exclusion of others. Nonetheless, we ultimately conclude that defendant did not satisfy his burden based on the measures available in this case.
Absolute disparity should be afforded substantial weight, though a court should take care not to give it undue weight where the group comprises a very small percentage of the population. Here, the absolute disparities are extremely small, both .3%, and therefore constitute compelling evidence of fair and reasonable representation.
Courts in Colorado and in other jurisdictions have routinely found fair and reasonable representation where the absolute disparity does not exceed 11.5%. See Sepeda, supra, 196 Colo. at 20, 581 P.2d at 728(5%); Orange, supra, 447 F.3d at 798 & n. 7 (listing cases); Weaver, supra, 267 F.3d at 243 (listing cases). Indeed, in cases involving similarly large groups, courts have refused to find constitutionally significant underrepresentation even where the absolute disparities were much greater than those here. See, e.g., United States v. Chanthadara, 230 F.3d 1237, 1256 (10th Cir.2000) (African-Americans comprised 7.9% of population, absolute disparity of 3.23%); United States v. Suttiswad, 696 F.2d 645, 649 (9th Cir.1982) (African-Americans comprised 9.3% of population, absolute disparity of 2.8%; Hispanics comprised 11.7% of population, absolute disparity of 7.7%). But see Paz, supra, 798 P.2d at 8-9 (holding that absolute disparities in consecutive years of 2.9%, 3.3%, and 2.3% were sufficient to satisfy second prong of prima facie test where group comprised 9.7% of the population).
Where, as here, the absolute disparity is very small (considered in relation to the group's percentage of the population), a defendant will be hard pressed to meet the second prong of the prima facie test. To hold otherwise would effectively impose a requirement of mathematical equivalence between the group's representation in jury panels and its percentage of the relevant population, a requirement that has been firmly rejected. See Swain v. Alabama, 380 U.S. 202, 208, 85 S.Ct. 824, 829-30, 13 L.Ed.2d 759 (1965), overruled on other grounds by Batson v. Kentucky, 476 U.S. 79, 106 S.Ct. 1712, 90 L.Ed.2d 69 (1986); Jenkins, supra, 496 F.2d at 65.
Analysis of comparative disparities in this case also indicates fair and reasonable representation. The groups at issue here do not comprise large percentages of the population, a fact which, as noted, may cause a measure of comparative disparity to overstate the degree of underrepresentation. Yet, as Dr. Bardwell testified, the comparative disparities here are only 3.9% for African-Americans and 2.3% for Hispanics. Courts have found that much greater disparities are not indicative of constitutionally substantial underrepresentation. See, e.g., Orange, supra, 447 F.3d at 798-99 (5.11% of population, 36.82% comparative disparity); Chanthadara, *164 supra, 230 F.3d at 1257 (7.9% of population, 40.89% comparative disparity); United States v. Clifford, 640 F.2d 150, 155 (8th Cir.1981) (15.6% of population, 46% comparative disparity).
Analysis of the "absolute impacts" here further demonstrates fair and reasonable representation. One would expect 7.7 African-Americans and 12.9 Hispanics in a perfectly representational jury panel of 100 persons (the jury panel in this case included between 90 and 100 persons). The .3% absolute disparity for both groups drops the expected representation to 7.4 African-Americans and 12.6 Hispanics, absolute impacts of .3 (out of 100) for each group. This equates to one fewer African-American and one fewer Hispanic every 333 potential jurors. This impact does not approach constitutional significance. Cf. Rioux, supra, 97 F.3d at 657-58 (difference of two or three African-Americans and Hispanics out of 125 potential jurors insubstantial); Biaggi, supra, 909 F.2d at 678 (difference of two African-Americans and three Hispanics out of 60 insubstantial); Test, supra, 550 F.2d at 590 (difference of two African-Americans out of 50 insubstantial); Jenkins, supra, 496 F.2d at 66 (difference of one African-American out of 60 insubstantial); Gibbs, supra, 758 A.2d at 338 (difference of three Hispanics out of 100 insubstantial).
Given the aforementioned evidence of absolute disparity, comparative disparity, and absolute impact, as well as the limitations of statistical decision theory in this context, we decline to give significant weight to Dr. Bardwell's opinion that the disparities are "statistically significant." We disagree with his assertion that the groups' percentages of representation in the population are too small to allow for meaningful evaluation using the other measures discussed above. Nor are we persuaded that "statistical significance" equates to legal significance for purposes of the fair cross-section requirement.
In sum, we conclude that defendant's evidence was legally insufficient to establish constitutionally significant underrepresentation of African-Americans and Hispanics in jury panels at the time of his trial. Accordingly, we need not address the third prong of the fair cross-section prima facie case  that any underrepresentation was due to systematic exclusion  or the trial court's finding that the system used by the State Court Administrator serves compelling state interests.

III. Expert Testimony on Mild Mental Retardation as it Related to Defendant's Mental State
Defendant contends that the trial court erred in precluding his expert witness, Dr. Michael Schmidt, from testifying regarding whether, due to his mild mental retardation, he formed the required culpable mental states of the crimes with which he was charged. We conclude that defendant did not preserve this issue for review.

A. Proceedings in the Trial Court
After defendant moved to bar imposition of the death penalty pursuant to §§ 18-1.3-1102 and 18-1.3-1103, he filed a motion seeking a ruling from the court that by raising mild mental retardation he was not triggering § 16-8-106, C.R.S.2006, which provides that a court may order psychiatric examinations where the defendant raises the defenses of insanity or impaired mental condition. But see People v. Flippo, 159 P.3d 100, 103 (Colo.2007) (procedural requirements of § 16-8-107(3), C.R.S.2006, apply when a defendant seeks to admit any expert testimony concerning intellectual disabilities). At a hearing on the latter motion on April 24, 2003, defendant's counsel stated that defendant was not contending that he was incapable of forming the mental states required by the charges against him. In the course of a discussion concerning what evidence of mild mental retardation defendant intended to present at trial, the court, relying on People v. Vanrees, 80 P.3d 840 (Colo.App.2003), rev'd on other grounds, 125 P.3d 403 (Colo. 2005), cert. denied, 547 U.S. 1137, 126 S.Ct. 2040, 164 L.Ed.2d 796 (2006), and People v. Requejo, 919 P.2d 874 (Colo.App.1996), indicated that defendant could present evidence of his mild mental retardation, but that defendant's expert witnesses, including Dr. Schmidt, could not be asked about the facts of this case or whether they had an opinion *165 as to whether defendant had formed the culpable mental states. Defendant's counsel did not object to those limitations.
The next day, the court entered a written order stating that defendant's psychiatric experts "will be limited in their opinions on whether the Defendant suffers from mental retardation and what are the general characteristics of a person with this disability. They may not be asked any questions regarding the facts at issue in the trial."
On May 1, 2003, the court conducted a hearing on defendant's motion to bar imposition of the death penalty. Dr. Schmidt testified as to what information he considered in diagnosing defendant and as to his ultimate diagnosis of mild mental retardation. He did not indicate that he had considered, or was even aware of, any of the facts of the case, nor did he tie any of defendant's mental deficits to any of the events which gave rise to the charges. His written report, which was admitted into evidence at the hearing, likewise did not mention the facts of the case or address whether defendant could or did form the requisite mental states.
At a motions hearing one month later, the prosecutor again raised the issue of what evidence of defendant's mild mental retardation would be allowed at trial. Defendant's counsel confirmed that he did not intend to ask Dr. Schmidt about whether defendant "could or couldn't deliberate," but asserted that Dr. Schmidt "ought to be permitted to educate the Jury about what [defendant's] particular deficits would cause in terms of his cognitive functioning." The court ruled that Dr. Schmidt could testify as to defendant's cognitive deficits and what persons with such deficits can and cannot do, but reiterated that he could not testify regarding the facts of the case.
That same day, the court entered a written order stating:
Regarding the defense of mild mental retardation, the court reiterates that it considers such a defense in the nature of a general denial and is not an affirmative defense as to any culpable mental state. As such, no expert may be asked about the facts of the allegations in this case, including any scenarios that resemble the facts in this case.
At trial, Dr. Schmidt testified as to the information he considered in diagnosing defendant, the tests he conducted, his diagnosis of mild mental retardation, defendant's particular cognitive deficits, and how persons with such deficits function in society. He also testified that he did not examine defendant to determine whether he was capable of acting with intent or reflecting before acting, and did not know anything about the facts alleged in this case.

B. Defendant Failed to Preserve this Issue for Review
As noted, on appeal, defendant contends that the trial court erred in precluding Dr. Schmidt from testifying as to the relationship between defendant's mild mental retardation and his conduct as charged  that is, that he did not (as opposed to could not) form the culpable mental states necessary to convict him of the crimes. Our review of the record, however, shows that defendant never sought to offer such testimony from Dr. Schmidt or anyone else, that defendant never proposed that Dr. Schmidt be permitted to testify any more broadly than the limitations imposed by the court, and that defendant never objected to any of the court's rulings on the allowable scope of Dr. Schmidt's testimony. Dr. Schmidt was, in fact, allowed to "educate the [j]ury about what [defendant's] particular deficits would cause in terms of his cognitive functioning," just as defendant had requested.
The record does not reveal the substance of the testimony defendant contends was erroneously excluded. Defendant did not make any offer of proof as to what Dr. Schmidt would say if asked about defendant's actions on September 10, 1998. Defendant's failure to make a proper offer of proof precludes him from raising this point of error on appeal, even subject to plain error review, because a clear indication as to what Dr. Schmidt would have said is essential to analyzing any claim of error with respect to the trial court's ruling. See CRE 103(a)(2); People v. Hoover, 165 P.3d 784, 793 (Colo.App. 2006); see also United States v. Rettenberger, *166 344 F.3d 702, 706 (7th Cir.2003) (defendant's failure to make offer of proof as to expert's proposed testimony precluded review of his claim that testimony was erroneously excluded); Roach v. State, 695 N.E.2d 934, 939-40 (Ind.1998) (same; offer of proof did not cover same reason for admitting testimony asserted on appeal), reh'g granted on other grounds, 711 N.E.2d 1237 (Ind.1999); State v. Lawrence, 352 N.C. 1, 530 S.E.2d 807, 820 (2000) (same); State v. Barton, 71 Ohio App.3d 455, 594 N.E.2d 702, 712 (1991) (same); Lewis v. State, 126 S.W.3d 572, 578-79 (Tex.App.2004) (same).

IV. Refusal to Instruct the Jury that Defendant was Mildly Mentally Retarded
Defendant next argues that the trial court erred in refusing to instruct the jury that it had previously determined that he was mildly mentally retarded. Defendant's counsel requested such an instruction before the presentation of evidence and after the close of evidence. Though defendant contends on appeal that such an instruction was required by the doctrines of "judicial notice" and "law of the case," the argument in his briefs relies solely on the law of the case doctrine. Therefore, our review of defendant's contention is limited to the application of that doctrine to the facts here. See People v. Simpson, 93 P.3d 551, 555 (Colo.App.2003) ("We decline to consider a bald legal proposition presented without argument or development. . . ."). We conclude that the trial court was not obligated by virtue of the law of the case doctrine to instruct the jury that defendant was mildly mentally retarded.

A. Standard of Review
Whether a prior ruling by a court constitutes the law of the case is a question of law that we review de novo. See Nelson v. Elway, 971 P.2d 245, 249-50 (Colo.App.1998). We review a trial court's decision not to adhere to one of its prior rulings as the law of the case for an abuse of discretion. See People v. Vialpando, 954 P.2d 617, 624 (Colo. App.1997).

B. The Law of the Case Doctrine
Under the law of the case doctrine, "prior relevant rulings made in the same case are to be followed unless such application would result in error or unless the ruling is no longer sound due to changed conditions." People v. Dunlap, 975 P.2d 723, 758 (Colo.1999); see also People v. Warren, 55 P.3d 809, 813 (Colo.App.2002). "The doctrine applies to decisions of law, rather than to the resolution of factual questions. . . ." In re Estate of Walter, 97 P.3d 188, 191 (Colo.App.2003).
C. The Trial Court's Ruling Concerning Imposition of the Death Penalty was not the Law of the Case as to Defendant's Culpable Mental State
The trial court determined that defendant was mildly mentally retarded solely for the purpose of determining whether he was eligible to receive the death penalty under the applicable statutes. The jury, however, was not called on to decide whether defendant was mildly mentally retarded. Rather, it was called on to decide defendant's factual guilt or innocence of the crimes charged. Therefore, the legal issue decided by the trial court and the factual issue to be resolved by the jury were different. Cf. DeForrest v. City of Cherry Hills Village, 990 P.2d 1139, 1143 (Colo.App.1999) (trial court inappropriately applied law of the case doctrine where the underlying factual and legal issues were different as to each defendant). Hence, the trial court's ruling on the legal issue was not binding on the jury  it was not a "relevant" ruling vis-à-vis the jury's role at trial.
We note that defendant was allowed to present evidence as to his cognitive deficits, to argue based thereon that he did not form the required culpable mental states, and to present a theory of defense instruction embodying that argument. The trial court instructed the jury to consider all the evidence in determining whether the People had proved defendant's guilt beyond a reasonable doubt. Instructing the jury that defendant was mildly mentally retarded would have engendered jury confusion as to its deliberations regarding mens rea and would have *167 been unfairly prejudicial to the People by giving judicial imprimatur to defendant's theory of defense.
Defendant's reliance on Deeds v. People, 747 P.2d 1266 (Colo.1987), is misplaced. In Deeds, the court held that a jury is not permitted to second-guess a trial court's determination that a confession was voluntary, and hence admissible. Therefore, because a jury does not have to make a voluntariness determination, the trial court need not instruct the jury on the issue. Deeds, supra, 747 P.2d at 1269-72.
Here, the trial court made a legal determination that defendant was mildly mentally retarded for purposes of his eligibility to receive the death penalty. The jury was not asked to decide whether defendant was mildly mentally retarded for that or any other purpose, and accordingly, the absence of an instruction telling the jury that defendant was mildly mentally retarded did not permit the jury to second-guess the trial court.

V. Jury Instruction on Scientific Evidence
Defendant also contends that the trial court erred when it refused to give the jury his tendered instruction on the collection and analysis of scientific evidence. We disagree.

A. Standard of Review
"[I]nstructional error may result if the court's instructions create a reasonable possibility that the jury would be misled in reaching a verdict." People v. Owens, 97 P.3d 227, 237 (Colo.App.2004). Instructional errors are harmless, however, if they do not affect a defendant's substantial rights or prejudice his defense. See People v. Rodriguez, 914 P.2d 230, 273-75 (Colo.1996); People v. Baird, 66 P.3d 183, 191 (Colo.App. 2002).
When the instructions as a whole adequately advise the jury, the trial court's refusal to give an additional instruction does not affect a defendant's substantial rights. See Rodriguez, supra, 914 P.2d at 274-75; see also People v. Inman, 950 P.2d 640, 645 (Colo.App.1997) ("a trial court may properly refuse an instruction which merely restates points already encompassed in other instructions given to the jury").

B. The Trial Court Correctly Refused the Instruction
Defendant tendered the following jury instruction on the collection and analysis of scientific evidence:
In deciding what weight, if any, to give to scientific evidence, you may consider any evidence offered bearing upon the accuracy and reliability of the procedures employed in the collection and analysis of a particular sample.
In refusing defendant's proffered instruction, the trial court found:
[Instruction No. 12] tells the Jury that they're to assess the credibility of experts just as they would the credibility of any other lay witnesses. Instruction No. 12, when combined with Instruction No. 9, tells them they can look at all the circumstances surrounding a witness's testimony, can evaluate their credibility. I believe that those two Instructions in combination satisfy the need for the Jury to be told that they can look at the accuracy and reliability of the procedures leading up to whatever they were examining. And of course, the  the Defense is free to argue that point to the Jury.
We agree with the trial court that Instructions Nos. 9 and 12 adequately informed the jury that it could consider the procedures used by a witness to collect and analyze evidence. Instruction No. 9 informed the jury that it could
[c]onsider each witness's knowledge, motive, state of mind, demeanor, and manner while on the stand. Consider the witness's means of knowledge, ability to observe, and strength of memory. Consider also any relationship each witness may have to either side of the case; the manner in which each witness might be affected by the verdict; and the extent to which, if at all, each witness is either supported or contradicted by other evidence in the case. You should consider all facts and circumstances shown by the evidence which affect the credibility of the witness's testimony. *168 You may believe all of the testimony of a witness, or part of it, or none of it.
Instruction No. 12 advised:
You have heard witnesses who have testified as experts. You are not bound by the testimony of experts; their testimony is to be weighed as that of any other witness. It is entirely your decision to determine what weight shall be given their testimony.
Instructions Nos. 9 and 12 together properly informed the jury that it could consider, as defendant requested, "the accuracy and reliability of the procedures employed in the collection and analysis" of the evidence by informing the jury that the testimony of expert witnesses was "to be weighed as that of any other witness" and that it should consider "all facts and circumstances shown by the evidence which affect the credibility of the witness's testimony" as well as each witness's knowledge and ability to observe. Therefore, the trial court was not required to submit defendant's tendered instruction to the jury. See Inman, supra, 950 P.2d at 645; People v. Banks, 804 P.2d 203, 206 (Colo.App. 1990).

VI. Prosecutorial Misconduct
Finally, defendant contends that his convictions must be reversed because during closing argument the prosecutor denigrated defendant's counsel and suggested that defendant's theory of defense was asserted in bad faith. We are not persuaded.

A. Standard of Review
We review this contention for plain error because defendant did not object at trial to the prosecutor's comments. See Wilson v. People, 743 P.2d 415, 419 (Colo. 1987). "To constitute plain error, prosecutorial misconduct must be `flagrant or glaringly or tremendously improper'. . . ." People v. Cevallos-Acosta, 140 P.3d 116, 122 (Colo. App.2005) (quoting in part People v. Salyer, 80 P.3d 831, 839 (Colo.App.2003)). "Prosecutorial misconduct in closing argument rarely constitutes plain error." Cevallos-Acosta, supra, 140 P.3d at 123.
In reviewing for plain error, we look at "the severity and frequency of the misconduct, any curative measures taken to alleviate the misconduct, and the likelihood that the misconduct constituted a material factor leading to [the] defendant's conviction." People v. Jones, 832 P.2d 1036, 1040 (Colo.App.1991); see also People v. Liggett, 114 P.3d 85, 89 (Colo.App.2005), aff'd, 135 P.3d 725 (Colo.2006). The trial court is in the best position to evaluate the propriety of counsel's argument and its potential impact on jurors in the context of the entire proceedings. See Domingo-Gomez v. People, 125 P.3d 1043, 1049-50 (Colo.2005); People v. Gutierrez, 622 P.2d 547, 554 (Colo.1981).

B. Permissible Scope of Prosecutor's Argument
During closing argument, the prosecutor may comment on the evidence admitted at trial, the reasonable inferences that can be drawn therefrom, and the instructions of law given to the jury. People v. Shepherd, 43 P.3d 693, 697 (Colo.App.2001); see also Cevallos-Acosta, supra, 140 P.3d at 122. Additionally, "a prosecutor `may employ rhetorical devices and engage in oratorical embellishment and metaphorical nuance, so long as he or she does not thereby induce the jury to determine guilt on the basis of prejudice or passion, inject irrelevant issues or evidence into the case, or accomplish some other improper purpose.'" People v. Petschow, 119 P.3d 495, 508 (Colo.App.2004) (quoting People v. Dashner, 77 P.3d 787, 793 (Colo.App.2003), disapproved of by Domingo-Gomez, supra, 125 P.3d at 1051 n. 3).
"`The lack of an objection may demonstrate defense counsel's belief that the live argument, despite its appearance in a cold record, was not overly damaging.'" Cevallos-Acosta, supra, 140 P.3d at 122 (quoting People v. Wallace, 97 P.3d 262, 269 (Colo. App.2004)); accord People v. Rodriguez, 794 P.2d 965, 972 (Colo.1990).

C. The Prosecutor's Statements were not Flagrant or Glaringly or Tremendously Improper
Defendant's theory of defense instruction stated:
Mr. Washington asserts as follows:

*169 Mr. Washington accompanied Mr. Canister to the apartment in order to recover Mr. Canister's property from [DH]. Neither Mr. Canister, Mr. Owens, nor Mr. Washington brought a gun to the apartment.
During the attempt to recover Mr. Canister's property, the residents became angry and threatening and were immobilized and quieted with whatever came to hand in order to permit Mr. Canister to recover his property without incident.
[MN] offered Mr. Washington and Mr. Owens drugs and initiated sexual contact in order to distract and kill them, because [DH] was angered by Mr. Canister's demands for return of his property. Sexual contact between [MN] and Mr. Owens and Washington was initiated by [MN], was consensual, and was not the product of force or intimidation.
While Mr. Canister was searching for his property, [PS] broke free and ran into the living room with a gun in his hand. [PS] fired the gun. [MN] also broke free, and, Mr. Washington believes, also fired a gun. Answering fire was returned by means of a gun found at the apartment. A crossfire occurred in the small apartment living room.
Because of Mr. Washington's mental retardation and cognitive deficits, he was unable to accurately assess the threat posed to himself and others in the chaos of the moment or to process information and react as would an unimpaired person.
Neither Mr. Washington, Canister, or Owens took the personal property of any resident.
In his closing argument, the prosecutor addressed defendant's theory of defense instruction and the evidence that contradicted defendant's theory. The prosecutor commented that certain portions of the theory were "sheer utter nonsense," and that while the eyewitness's testimony was subjected to cross-examination, "[t]his silly instruction is not subjected to anything." The prosecutor further commented that the only reason the jury had to consider the self-defense instructions was because of the theory of defense instruction. In rebuttal argument, the prosecutor also noted that defense counsel did not mention the sex assaults in his closing argument and commented, "I submit he could not even tell you that with a straight face. It's written down, but it's a little harder to say it, to put it in words when it is so offensive, so absurd and so unfounded in the evidence."
Even if we assume these statements were improper, they were not "flagrant or glaringly or tremendously improper." Accordingly, we can say with fair assurance that, in light of the entire record, the statements made by the prosecutor did not substantially influence the verdict or affect the fundamental fairness of the proceedings. See Wilson, supra, 743 P.2d at 419. We therefore conclude that the prosecutor's statements in closing argument did not rise to the level of plain error.
Defendant's contention that because the prosecutor did not object to the theory of defense instruction, he was precluded from challenging the evidence to support it is unpersuasive. Generally, a defendant is entitled to an instruction embracing his theory of the case when there is any evidence to support the theory, even if the only supporting evidence is highly improbable testimony. See People v. Nunez, 841 P.2d 261, 264-65 (Colo.1992). The fact that there may be evidence sufficient to support such an instruction under this undemanding standard does not preclude a prosecutor from commenting on the weakness of that evidence or the existence of other evidence undermining a defendant's theory of defense.
The judgment is affirmed.
Judge MÁRQUEZ and Judge TAUBMAN concur.
