Justice POWELL delivered the opinion of the Court.

 This case presents the question whether a complex statistical study that indicates a risk that racial considerations enter [p. 283] into capital sentencing determinations proves that petitioner McCleskey's capital sentence is unconstitutional under the Eighth or Fourteenth Amendment.

I

 McCleskey, a black man, was convicted of two counts of armed robbery and one count of murder in the Superior Court of Fulton County, Georgia, on October 12, 1978.  McCleskey's convictions arose out of the robbery of a furniture store and the killing of a white police officer during the course of the robbery.

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 [p. 284] . . . . At the penalty hearing, the jury heard arguments as to the appropriate sentence.  Under Georgia law, the jury could not consider imposing the death penalty unless it found beyond a reasonable doubt that the murder was accompanied by one of the statutory aggravating circumstances.  Ga.Code Ann. § 17-10-30(c) (1982).  The jury in this case found two aggravating [p. 285] circumstances to exist beyond a reasonable doubt:  the murder was committed during the course of an armed robbery, § 17-10- 30(b)(2);  and the murder was committed upon a peace officer engaged in the performance of his duties, § 17-10-30(b)(8).  In making its decision whether to impose the death sentence, the jury considered the mitigating and aggravating circumstances of McCleskey's conduct.  § 17-10-2(c).  McCleskey offered no mitigating evidence.  The jury recommended that he be sentenced to death on the murder charge and to consecutive life sentences on the armed robbery charges.  The court followed the jury's recommendation and sentenced McCleskey to death.

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 On appeal, the Supreme Court of Georgia affirmed the convictions and the sentences.  McCleskey v. State, 245 Ga. 108, 263 S.E.2d 146 (1980). . . . McCleskey then filed a petition for a writ of habeas corpus in the [p. 286] Superior Court of Butts County.  After holding an evidentiary hearing, the Superior Court denied relief.  McCleskey v. Zant, No. 4909 (Apr. 8, 1981). . . .

 McCleskey next filed a petition for a writ of habeas corpus in the Federal District Court for the Northern District of Georgia.  His petition raised 18 claims, one of which was that the Georgia capital sentencing process is administered in a racially discriminatory manner in violation of the Eighth and Fourteenth Amendments to the United States Constitution.  In support of his claim, McCleskey proffered a statistical study performed by Professors David C. Baldus, Charles Pulaski, and George Woodworth, and (the Baldus study) that purports to show a disparity in the imposition of the death sentence in Georgia based on the race of the murder victim and, to a lesser extent, the race of the defendant.  The Baldus study is actually two sophisticated statistical studies that examine over 2,000 murder cases that occurred in Georgia during the 1970's.  The raw numbers collected by Professor Baldus indicate that defendants charged with killing white persons received the death penalty in 11% of the cases, but defendants charged with killing blacks received the death penalty in only 1% of the cases.  The raw numbers also indicate a reverse racial disparity according to the race of the defendant:  4% of the black defendants received the death penalty, as opposed to 7% of the white defendants.

 Baldus also divided the cases according to the combination of the race of the defendant and the race of the victim.  He found that the death penalty was assessed in 22% of the cases involving black defendants and white victims;  8% of the cases involving white defendants and white victims;  1% of the cases involving black defendants and black victims;  and 3% of the cases involving white defendants and black victims.  [p. 287] Similarly, Baldus found that prosecutors sought the death penalty in 70% of the cases involving black defendants and white victims;  32% of the cases involving white defendants and white victims;  15% of the cases involving black defendants and black victims; and 19% of the cases involving white defendants and black victims.

 Baldus subjected his data to an extensive analysis, taking account of 230 variables that could have explained the disparities on nonracial grounds.  One of his models concludes that, even after taking account of 39 nonracial variables, defendants charged with killing white victims were 4.3 times as likely to receive a death sentence as defendants charged with killing blacks. According to this model, black defendants were 1.1 times as likely to receive a death sentence as other defendants.  Thus, the Baldus study indicates that black defendants, such as McCleskey, who kill white victims have the greatest likelihood of receiving the death penalty. [n. 5]
 

5. Baldus' 230-variable model divided cases into eight different ranges, according to the estimated aggravation level of the offense.  Baldus argued in his testimony to the District Court that the effects of racial bias were most striking in the midrange cases.  "[W]hen the cases become tremendously aggravated so that everybody would agree that if we're going to have a death sentence, these are the cases that should get it, the race effects go away.  It's only in the mid-range of cases where the decision makers have a real choice as to what to do.  If there's room for the exercise of discretion, then the [racial] factors begin to play a role."  App. 36. Under this model, Baldus found that 14.4% of the black-victim midrange cases received the death penalty, and 34.4% of the white-victim cases received the death penalty.  See Exhibit DB 90, reprinted in Supplemental Exhibits 54.  According to Baldus, the facts of McCleskey's case placed it within the midrange.  App. 45-46.

 The District Court held an extensive evidentiary hearing on McCleskey's petition. . . .  It concluded [p. 288] that McCleskey's "statistics do not demonstrate a prima facie case in support of the contention that the death penalty was imposed upon him because of his race, because of the race of the victim, or because of any Eighth Amendment concern."  McCleskey v. Zant, 580 F.Supp. 338, 379 (ND Ga.1984).  As to McCleskey's Fourteenth Amendment claim, the court found that the methodology of the Baldus study was flawed in several respects.  Because of these defects, [p. 289] the court held that the Baldus study "fail[ed] to contribute anything of value" to McCleskey's claim.  Id., at 372 (emphasis omitted).  Accordingly, the court denied the petition insofar as it was based upon the Baldus study.

 The Court of Appeals for the Eleventh Circuit, sitting en banc, carefully reviewed the District Court's decision on McCleskey's claim.  753 F.2d 877 (1985).  It assumed the validity of the study itself and addressed the merits of McCleskey's Eighth and Fourteenth Amendment claims.  That is, the court assumed that the study "showed that systematic and substantial disparities existed in the penalties imposed upon homicide defendants in Georgia based on race of the homicide victim, that the disparities existed at a less substantial rate in death sentencing based on race of defendants, and that the factors of race of the victim and defendant were at work in Fulton County."  Id., at 895.  Even assuming the study's validity, the Court of Appeals found the statistics "insufficient to demonstrate discriminatory intent or unconstitutional discrimination in the Fourteenth Amendment context, [and] insufficient to show irrationality, arbitrariness and capriciousness under any kind of Eighth Amendment analysis."  Id., at 891.

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The court concluded:
"Viewed broadly, it would seem that the statistical evidence presented here, assuming its validity, confirms rather than condemns the system....  The marginal disparity based on the race of the victim tends to support the state's contention that the system is working far differently from the one which Furman [v. Georgia, 408 U.S. 238, 92 S.Ct. 2726, 33 L.Ed.2d 346 (1972) ] condemned.  In pre-Furman days, there was no rhyme or reason as to who got the death penalty and who did not.  But now, in the vast majority of cases, the reasons for a difference are well documented.  That they are not so clear in a small percentage of the cases is no reason to declare the entire system unconstitutional."  Id., at 899.
 The Court of Appeals affirmed the denial by the District Court of McCleskey's petition for a writ of habeas corpus insofar as the petition was based upon the Baldus study, with three judges dissenting as to McCleskey's claims based on [p. 291] the Baldus study.  We granted certiorari, 478 U.S. 1019, 106 S.Ct. 3331, 92 L.Ed.2d 737 (1986), and now affirm.

II

 McCleskey's first claim is that the Georgia capital punishment statute violates the Equal Protection Clause of the Fourteenth Amendment. [n. 7]  He argues that race has infected the administration of Georgia's statute in two ways:  persons who murder whites are more likely to be sentenced to death than persons who murder blacks, and black murderers are more likely to be sentenced to death than white murderers.  [p. 292] As a black defendant who killed a white victim, McCleskey claims that the Baldus study demonstrates that he was discriminated against because of his race and because of the race of his victim.  In its broadest form, McCleskey's claim of discrimination extends to every actor in the Georgia capital sentencing process, from the prosecutor who sought the death penalty and the jury that imposed the sentence, to the State itself that enacted the capital punishment statute and allows it to remain in effect despite its allegedly discriminatory application.  We agree with the Court of Appeals, and every other court that has considered such a challenge, that this claim must fail.
 

7. Although the District Court rejected the findings of the Baldus study as flawed, the Court of Appeals assumed that the study is valid and reached the constitutional issues.  Accordingly, those issues are before us.  As did the Court of Appeals, we assume the study is valid statistically without reviewing the factual findings of the District Court.  Our assumption that the Baldus study is statistically valid does not include the assumption that the study shows that racial considerations actually enter into any sentencing decisions in Georgia.  Even a sophisticated multiple-regression analysis such as the Baldus study can only demonstrate a risk that the factor of race entered into some capital sentencing decisions and a necessarily lesser risk that race entered into any particular sentencing decision.

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IV
A

. . . . [A]bsent a showing that the Georgia capital punishment system operates in an arbitrary and capricious manner, McCleskey cannot prove a constitutional [p. 307] violation by demonstrating that other defendants who may be similarly situated did not receive the death penalty. In Gregg, the Court confronted the argument that "the opportunities for discretionary action that are inherent in the processing of any murder case under Georgia law," 428 U.S., at 199, 96 S.Ct., at 2937, specifically the opportunities for discretionary leniency, rendered the capital sentences imposed arbitrary and capricious.  We rejected this contention:
"The existence of these discretionary stages is not determinative of the issues before us.  At each of these stages an actor in the criminal justice system makes a decision which may remove a defendant from consideration as a candidate for the death penalty.  Furman, in contrast, dealt with the decision to impose the death sentence on a specific individual who had been convicted of a capital offense.  Nothing in any of our cases suggests that the decision to afford an individual defendant mercy violates the Constitution. Furman held only that, in order to minimize the risk that the death penalty would be imposed on a capriciously selected group of offenders, the decision to impose it had to be guided by standards so that the sentencing authority would focus on the particularized circumstances of the crime and the defendant." Ibid. [n. 28]
 

28. The Constitution is not offended by inconsistency in results based on the objective circumstances of the crime.  Numerous legitimate factors may influence the outcome of a trial and a defendant's ultimate sentence, even though they may be irrelevant to his actual guilt.  If sufficient evidence to link a suspect to a crime cannot be found, he will not be charged.  The capability of the responsible law enforcement agency can vary widely.  Also, the strength of the available evidence remains a variable throughout the criminal justice process and may influence a prosecutor's decision to offer a plea bargain or to go to trial.  Witness availability, credibility, and memory also influence the results of prosecutions. Finally, sentencing in state courts is generally discretionary, so a defendant's ultimate sentence necessarily will vary according to the judgment of the sentencing authority.  The foregoing factors necessarily exist in varying degrees throughout our criminal justice system.

 [p. 308] Because McCleskey's sentence was imposed under Georgia sentencing procedures that focus discretion "on the particularized nature of the crime and the particularized characteristics of the individual defendant," id., at 206, 96 S.Ct., at 2940, we lawfully may presume that McCleskey's death sentence was not "wantonly and freakishly" imposed, id., at 207, 96 S.Ct., at 2941, and thus that the sentence is not disproportionate within any recognized meaning under the Eighth Amendment.

B

 Although our decision in Gregg as to the facial validity of the Georgia capital punishment statute appears to foreclose McCleskey's disproportionality argument, he further contends that the Georgia capital punishment system is arbitrary and capricious in application, and therefore his sentence is excessive, because racial considerations may influence capital sentencing decisions in Georgia.  We now address this claim.

 To evaluate McCleskey's challenge, we must examine exactly what the Baldus study may show.  Even Professor Baldus does not contend that his statisticsprove that race enters into any capital sentencing decisions or that race was a factor in McCleskey's particular case. Statistics at most may show only a likelihood that a particular factor entered into some decisions.  There is, of course, some risk of racial prejudice influencing a jury's decision in a criminal case.  There are similar risks that other kinds of prejudice will influence other criminal trials.  See infra, at 1776-1777. The question [p. 309] "is at what point that risk becomes constitutionally unacceptable," Turner v. Murray, 476 U.S. 28, 36, n. 8, 106 S.Ct. 1683, 1688, n. 8, 90 L.Ed.2d 27 (1986).  McCleskey asks us to accept the likelihood allegedly shown by the Baldus study as the constitutional measure of an unacceptable risk of racial prejudice influencing capital sentencing decisions.  This we decline to do.

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 McCleskey's argument that the Constitution condemns the discretion allowed decisionmakers in the Georgia capital sentencing system is antithetical to the fundamental role of discretion in our criminal justice system.  Discretion in the criminal justice system offers substantial benefits to the criminal defendant.  Not only can a jury decline to impose the death sentence, it can decline to convict or choose to convict of a lesser offense.  Whereas decisions against a defendant's interest may be reversed by the trial judge or on appeal, these discretionary exercises of leniency are final and unreviewable. Similarly, the capacity of prosecutorial discretion [p. 312] to provide individualized justice is "firmly entrenched in American law."  2 W. LaFave & D. Israel, Criminal Procedure § 13.2(a), p. 160 (1984).  As we have noted, a prosecutor can decline to charge, offer a plea bargain, or decline to seek a death sentence in any particular case.  See n. 28, supra.  Of course, "the power to be lenient [also] is the power to discriminate," K. Davis, Discretionary Justice 170 (1973), but a capital punishment system that did not allow for discretionary acts of leniency "would be totally alien to our notions of criminal justice."  Gregg v. Georgia, 428 U.S., at 200, n. 50, 96 S.Ct., at 2937, n. 50.

    C

 At most, the Baldus study indicates a discrepancy that appears to correlate with race.  Apparent disparities in sentencing are an inevitable part of our criminal justice system. [p. 313] The discrepancy indicated by the Baldus study is "a far cry from the major systemic defects identified in Furman," Pulley v. Harris, 465 U.S., at 54, 104 S.Ct., at 881. As this Court has recognized, any mode for determining guilt or punishment "has its weaknesses and the potential for misuse."  Singer v. United States, 380 U.S. 24, 35, 85 S.Ct. 783, 790, 13 L.Ed.2d 630 (1965).  See Bordenkircher v. Hayes, 434 U.S. 357, 365, 98 S.Ct. 663, 669, 54 L.Ed.2d 604 (1978). Specifically, "there can be 'no perfect procedure for deciding in which cases governmental authority should be used to impose death.' "  Zant v. Stephens, 462 U.S. 862, 884, 103 S.Ct. 2733, 2746, 77 L.Ed.2d 235 (1983) (quoting Lockett v. Ohio, 438 U.S., at 605, 98 S.Ct., at 2965 (plurality opinion of Burger, C.J.)).  Despite these imperfections, our consistent rule has been that constitutional guarantees are met when "the mode [for determining guilt or punishment] itself has been surrounded with safeguards to make it as fair as possible."  Singer v. United States, supra, 380 U.S., at 35, 85 S.Ct., at 790.  Where the discretion that is fundamental to our criminal process is involved, we decline to assume that what is unexplained is invidious.  In light of the safeguards designed to minimize racial bias in the process, the fundamental value of jury trial in our criminal justice system, and the benefits that discretion provides to criminal defendants, we hold that the Baldus study does not demonstrate a constitutionally significant risk of racial bias affecting the Georgia capital sentencing process.

    [p. 314] V

 Two additional concerns inform our decision in this case.  First, McCleskey's claim, taken to its logical conclusion, [p. 315] throws into serious question the principles that underlie our entire criminal justice system.  The Eighth Amendment is not limited in application to capital punishment, but applies to all penalties.  Solem v. Helm, 463 U.S. 277, 289-290, 103 S.Ct. 3001, 3009, 77 L.Ed.2d 637 (1983);  see Rummel v. Estelle, 445 U.S. 263, 293, 100 S.Ct. 1133, 1149, 63 L.Ed.2d 382 (1980) (POWELL, J., dissenting). Thus, if we accepted McCleskey's claim that racial bias has impermissibly tainted the capital sentencing decision, we could soon be faced with similar claims as to other types of penalty. Moreover, the claim that his sentence [p. 316] rests on the irrelevant factor of race easily could be extended to apply to claims based on unexplained discrepancies that correlate to membership in other minority groups, and [p. 317] even to gender. Similarly, since McCleskey's claim relates to the race of his victim, other claims could apply with equally logical force to statistical disparities that correlate with the race or sex of other actors in the criminal justice system, such as defense attorneys , or judges. Also, there is no logical reason that such a claim need be limited to racial or sexual bias.  If arbitrary and capricious punishment is the touchstone under the Eighth Amendment, such a claim could--at least in theory--be based upon any arbitrary variable, such as the defendant's facial characteristics, or the physical attractiveness of the defendant or the victim, that some statistical [p. 318] study indicates may be influential in jury decisionmaking.  As these examples illustrate, there is no limiting principle to the type of challenge brought by McCleskey.  [p. 319] The Constitution does not require that a State eliminate any demonstrable disparity that correlates with a potentially irrelevant factor in order to operate a criminal justice system that includes capital punishment.  As we have stated specifically in the context of capital punishment, the Constitution does not "plac[e] totally unrealistic conditions on its use."  Gregg v. Georgia, 428 U.S., at 199, n. 50, 96 S.Ct., at 2937, n. 50.

 Second, McCleskey's arguments are best presented to the legislative bodies.  It is not the responsibility--or indeed even the right--of this Court to determine the appropriate punishment for particular crimes.  It is the legislatures, the elected representatives of the people, that are "constituted to respond to the will and consequently the moral values of the people." Furman v. Georgia, 408 U.S., at 383, 92 S.Ct., at 2800 (Burger, C.J., dissenting).  Legislatures also are better qualified to weigh and "evaluate the results of statistical studies in terms of their own local conditions and with a flexibility of approach that is not available to the courts," Gregg v. Georgia, supra, 428 U.S., at 186, 96 S.Ct., at 2931.  Capital punishment is now the law in more than two-thirds of our States.  It is the ultimate duty of courts to determine on a case-by-case basis whether these laws are applied consistently with the Constitution.  Despite McCleskey's wide- ranging arguments that basically challenge the validity of capital punishment in our multiracial society, the only question before us is whether in his case, see supra, at 1761-1762, the law of Georgia was properly applied.  We agree with the District Court and the Court of Appeals for the Eleventh Circuit that this was carefully and correctly done in this case.

[p. 320] VI

 Accordingly, we affirm the judgment of the Court of Appeals for the Eleventh Circuit.

 It is so ordered.