dissenting in part and concurring in part, with whom HATCHETT and CLARK, Circuit Judges join:
Warren McCleskey has presented convincing evidence to substantiate his claim that Georgia has administered its death penalty in a way that discriminates on the basis of race. The Baldus Study, characterized as “far and away the most complete and thorough analysis of sentencing” ever carried out,1 demonstrates that in Georgia *908a person who kills a white victim has a higher risk of receiving the death penalty than a person who kills a black victim. Race alone can explain part of this higher risk. The majority concludes that the evidence “confirms rather than condemns the system” and that it fails to support a constitutional challenge. I disagree. In my opinion, this disturbing evidence can and does support a constitutional claim under the Eighth Amendment. In holding otherwise, the majority commits two critical errors: it requires McCleskey to prove that the State intended to discriminate against him personally and it underestimates what his evidence actually did prove. I will address each of these concerns before commenting briefly on the validity of the Bal-dus Study and addressing the other issues in this case.
1. THE EIGHTH AMENDMENT AND RACIAL DISCRIMINATION IN THE ADMINISTRATION OF THE DEATH PENALTY
McCleskey claims that Georgia administers the death penalty in a way that discriminates on the basis of race. The district court opinion treated this argument as one arising under the Fourteenth Amendment2 and explicitly rejected the petitioner’s claim that he could raise the argument under the Eighth Amendment, as well. The majority reviews each of these possibilities and concludes that there is little difference in the proof necessary to prevail under any of the theories: whatever the constitutional source of the challenge, a petitioner must show a disparate impact great enough to compel the conclusion that purposeful discrimination permeates the system. These positions reflect a misunderstanding of the nature of an Eighth Amendment claim in the death penalty context: the Eighth Amendment prohibits the racially discriminatory application of the death penalty and McCleskey does not have to prove intent to discriminate in order to show that the death penalty is being applied arbitrarily and capriciously.
A. The Viability of an Eighth Amendment Challenge
As the majority recognizes, the fact that a death penalty statute is facially valid does not foreclose an Eighth Amendment challenge based on the systemwide application of that statute. The district court most certainly erred on this issue. Applying the death penalty in a racially discriminatory manner violates the Eighth Amendment. Several members of the majority in Furman v. Georgia, 408 U.S. 238, 245-57, 310, 364-65, 92 S.Ct. 2726, 2729-36, 2762, 2790-91, 33 L.Ed.2d 346 (1972) (concurring opinions of Douglas, Stewart, Marshall, JJ.), relied in part on the disproportionate impact of the death penalty on racial minorities in concluding that the death penalty as then administered constituted arbitrary and capricious punishment.
When decisionmakers look to the race of a victim, a factor completely unrelated to the proper concerns of the sentencing process enters into determining the sentence. Reliance on the race of the victim means that the sentence is founded in part on a morally and constitutionally repugnant judgment regarding the relative low value of the lives of black victims. Cf Zant v. Stephens, 462 U.S. 862, 103 S.Ct. 2733, 77 L.Ed.2d 235 (1983) (listing race of defendant as a factor “constitutionally impermissible or totally irrelevant to the sentencing process”). There is no legitimate basis in reason for relying on race in the sentencing process. Because the use of race is both irrelevant to sentencing and impermissible, sentencing determined in part by race is arbitrary and capricious and therefore a *909violation of the Eighth Amendment. See Furman v. Georgia, 408 U.S. 238, 256, 92 S.Ct. 2726, 2735, 33 L.Ed.2d 346 (1972) (Douglas, J., concurring) (“the high service rendered by the ‘cruel and unusual’ punishment clause of the Eighth Amendment is to require judges to see to it that general laws are not applied sparsely, selectively, and spottily to unpopular groups”).
B. The Eighth Amendment and Proof of Discriminatory Intent .
The central concerns of the Eighth Amendment deal more with decisionmaking processes and groups of cases than with individual decisions or cases. In a phrase repeated throughout its later cases, the Supreme Court in Gregg v. Georgia, 428 U.S. 153, 195 n. 46, 96 S.Ct. 2909, 2935 n. 46, 49 L.Ed.2d 859 (1976) (plurality opinion), stated that a “pattern of arbitrary and capricious sentencing” would violate the Eighth Amendment. In fact, the Court has consistently adopted a systemic perspective on the death penalty, looking to the operation of a state’s entire sentencing structure in determining whether it inflicted sentences in violation of the Eighth Amendment. See, e.g., Eddings v. Oklahoma, 455 U.S. 104,112,102 S.Ct. 869, 875, 71 L.Ed.2d 1 (1982) (capital punishment must be imposed “fairly, and with reasonable consistency, or not at all”); Godfrey v. Georgia, 446 U.S. 420,100 S.Ct. 1759, 64 L.Ed.2d 398 (1980) (“[I]f a State wishes to authorize capital punishment it has a constitutional responsibility to tailor and apply its law in a manner that avoids the arbitrary and capricious infliction of the death penalty.”).
Without this systemic perspective, review of sentencing would be extremely limited, for the very idea of arbitrary and capricious sentencing takes on its fullest meaning in a comparative context. A non-arbitrary sentencing structure must provide some meaningful way of distinguishing between those who receive the death sentence and those who do not. Godfrey v. Georgia, 446 U.S. 420, 433, 100 S.Ct. 1759, 1767, 64 L.Ed.2d 398 (1980); Furman v. Georgia, 408 U.S. 238, 313, 92 S.Ct. 2726, 2764, 33 L.Ed.2d 346 (1972) (White, J., concurring). Appellate proportionality review is not needed in every case but consistency is still indispensable to a constitutional sentencing system.3 The import of any single sentencing decision depends less on the intent of the decisionmaker than on the outcome in comparable cases. Effects evidence is well suited to this type of review.
This emphasis on the outcomes produced by the entire system springs from the State’s special duty to insure fairness with regard to something as serious as a death sentence. See Zant v. Stephens, 462 U.S. 862, 103 S.Ct. 2733, 2741, 77 L.Ed.2d 235 (1983); Lockett v. Ohio, 438 U.S. 586, 605, 98 S.Ct. 2954, 2965, 57 L.Ed.2d 973 (1978); Woodson v. North Carolina, 428 U.S. 280, 305, 96 S.Ct. 2978, 2991, 49 L.Ed.2d 944 (1976) (plurality opinion). Monitoring patterns of sentences offers an especially effective way to detect breaches of that duty. Indeed, because the death penalty retains the need for discretion to make individualized judgments while at the same time heightening the need for fairness and consistency, Eddings v. Oklahoma, supra, 455 U.S. at 110-12, 102 S.Ct. at 874-75, patterns of decisions may often be the only acceptable basis of review. Discretion hinders inquiry into intent: if unfairness and inconsistency are to be detected even when they are not overwhelming or obvious, effects evidence must be relied upon.
Insistence on systemwide objective standards to guide sentencing reliably prevents aberrant decisions without having to probe the intentions of juries or other decision-makers. Gregg v. Georgia, supra, 428 *910U.S. at 198, 96 S.Ct. at 2936; Woodson v. North Carolina, supra, 428 U.S. at 303, 96 S.Ct. at 2990 (objective standards necessary to “make rationally reviewable the process for imposing the death penalty”). The need for the State to constrain the discretion of juries in the death penalty area is unusual by comparison to other areas of the law. -It demonstrates the need to rely on systemic controls as a way to reconcile discretion and consistency; the same combined objectives argue for the use of effects evidence rather than waiting for evidence of improper motives in specific cases.
Objective control and review cf. sentencing structures is carried so far that a jury or other decisionmaker may be presumed to have intended a non-arbitrary result when the outcome is non-arbitrary by an objective standard; the law, in short, looks to the result rather than the actual motives.4 In Westbrook v. Zant, 704 F.2d 1487, 1504 (11th Cir.1983), this Court held that, even though a judge might not properly instruct a sentencing jury regarding the proper definition of aggravating circumstances, the “uncontrolled discretion of an uninstructed jury” can be cured by review in the Georgia Supreme Court. The state court must find that the record shows the presence of statutory aggravating factors that a jury could have relied upon. If the factors are present in the record it does not matter that the jury may have misunderstood the role of aggravating circumstances. If the State can unintentionally succeed in preventing arbitrary and capricious sentencing, it would seem that the State can also fail in its duty even though none of the relevant decisionmakers intend such a failure.5
In sum, the Supreme Court’s systemic and objective perspective in the review and control of death sentencing indicates that a pattern of death sentences skewed by race alone will support a claim of arbitrary and capricious sentencing in violation of the Eighth Amendment. See Furman v. Georgia, 408 U.S. 238, 253, 92 S.Ct. 2726, 2733, 33 L.Ed.2d 346 (1972). (Douglas, J., concurring) (“We cannot say that these defendants were sentenced to death because they were black. Yet our task is not restricted to an effort to divine what motives impelled these death penalties.”). The majority’s holding on this issue conflicts with every other constitutional limit on the death penalty. After today, in this Circuit arbitrariness based on race will be more difficult to *911eradicate than any other sort of arbitrariness in the sentencing system.
II. PROVING DISCRIMINATORY EFFECT AND INTENT WITH THE BALDUS STUDY
The statistical study conducted by Dr. Baldus provides the best possible evidence of racially disparate impact. It began with a single unexplained fact: killers of white victims in Georgia over the last decade have received the death penalty eleven times more often than killers of black victims.6 It then employed several statistical techniques, including regression analysis, to isolate the amount of that disparity attributable to both racial and non-racial factors. Each of the techniques yielded a statistically significant racial influence of at least six percent; in other words, they all showed that the pattern of sentencing could only be explained by assuming that the race of the victim made all defendants convicted of killing white victims at least six percent more likely to receive the death penalty. Other factors7 such as the number of aggravating circumstances or the occupation of the victim could account for some of the eleven-to-one differential, but the race of the victim remained one of the strongest influences.
Assuming that the study actually proves what it claims to prove, an assumption the majority claims to make, the evidence undoubtedly shows a disparate impact. Regression analysis has the great advantage of showing that a perceived racial effect is an actual racial effect because it controls for the influence of non-racial factors. By screening out non-racial explanations for certain outcomes, regression analysis offers a type of effects evidence that approaches evidence of intent, no matter what level of disparity is shown. For example, the statistics in this case show that a certain number of death penalties were probably imposed because of race, without ever inquiring directly into the motives of jurors or prosecutors.
Regression analysis is becoming a common method of proving discriminatory effect in employment discrimination suits. In fact, the Baldus Study shows effects at least as dramatic and convincing as those in statistical studies offered in the past. Cf. Segar v. Smith, 738 F.2d 1249 (D.C.Cir.1984); Wade v. Mississippi Cooperative Extension Service, 528 F.2d 508 (5th Cir.1976). Nothing more should be necessary to prove that Georgia is applying its death penalty statute in a way that arbitrarily and capriciously relies on an illegitimate factor — race.8
Even if proof of discriminatory intent were necessary to make out a constitutional challenge, under any reasonable definition of intent the Baldus Study provides sufficient procf. The majority ignores the fact that McCleskey has shown discriminatory intent at work in the sentencing system even though he has not pointed to any specific act or actor responsible for discriminating against him in particular.9
The law recognizes that even though intentional discrimination will be difficult to detect in some situations, its workings are still pernicious and real. Rose v. Mitchell, 443 U.S. 545, 559, 99 S.Ct. 2993, 3001, 61 L.Ed.2d 739 (1979). Under some circumstances, therefore, proof of discriminatory effect will be an important first step in *912proving intent, Crawford v. Board of Education, 458 U.S. 527, 102 S.Ct. 3211, 73 L.Ed.2d 948 (1982), and may be the best available proof of intent. Washington v. Davis, 426 U.S. 229, 241-42, 96 S.Ct. 2040, 2048-49, 48 L.Ed.2d 597 (1976); United States v. Texas Educational Agency, 579 F.2d 910, 913-14 & nn. 5-7 (5th Cir.1978), cert. denied, 443 U.S. 915, 99 S.Ct. 3106, 61 L.Ed.2d 879 (1979).
For instance, proof of intentional discrimination in the selection of jurors has traditionally depended on showing racial effects. See Castaneda v. Partida, 430 U.S. 482, 97 S.Ct. 1272, 51 L.Ed.2d 498 (1977); Turner v. Fouche, 396 U.S. 346, 90 S.Ct. 532, 24 L.Ed.2d 532 (1970); Gibson v. Zant, 705 F.2d 1543 (11th Cir.1983). This is because the discretion allowed to jury commissioners, although legitimate, could easily be used to mask conscious or unconscious racial discrimination. The Supreme Court has recognized that the presence of this sort of discretion calls for indirect methods of procf. Washington v. Davis, 426 U.S. 229, 241-42, 96 S.Ct. 2040, 2048-49, 48 L.Ed.2d 597 (1976); Arlington Heights v. Metropolitan Housing Corp., 429 U.S. 252, 266 n. 13, 97 S.Ct. 555, 564 n. 13, 50 L.Ed.2d 450 (1977).
This Court has confronted the same problem in an analogous setting. In Searcy v. Williams, 656 F.2d 1003, 1008-09 (5th Cir.1981), aff’d sub nom. Hightower v. Searcy, 455 U.S. 984,102 S.Ct. 1605, 71 L.Ed.2d 844 (1982), the court overturned a facially valid procedure for selecting school board members because the selections fell into an overwhelming pattern of racial imbalance. The decision rested in part on the discretion inherent in the selection process: “The challenged application of the statute often involves discretion or subjective criteria utilized at a crucial point in the decision-making process.”
The same concerns at work in the jury discrimination context operate with equal force in the death penalty context. The prosecutor has considerable discretion and the jury has bounded but irreducible discretion. Defendants cannot realistically hope to find direct evidence of discriminatory intent. This is precisely the situation envisioned in Arlington Heights, where the Court pointed out that “[sjometimes a clear pattern, unexplainable on grounds other than race, emerges from the effect of the state action even when the governing legislation appears neutral on its face____ The evidentiary inquiry is then relatively easy.” 429 U.S. at 266, 97 S.Ct. at 564.
As a result, evidence of discriminatory effects presented in the Baldus Study, like evidence of racial disparities in the composition of jury pools10 and in other contexts,11 excludes every reasonable inference other than discriminatory intent at work in the system. This Circuit has acknowledged on several occasions that evidence of this sort could support a constitutional challenge. Adams v. Wainwright, 709 F.2d 1443, 1449 (11th Cir.1983); Smith v. Balkcom, 660 F.2d 573 (5th Cir. Unit B 1981), modified in part, 671 F.2d 858, cert. denied, 459 U.S. 882, 103 S.Ct. 181, 74 L.Ed.2d 148 (1982); Spinkellink, supra, at 614.
A petitioner need not exclude all inferences other than discriminatory intent in his or her particular case.12 Yet the major*913ity improperly stresses this particularity requirement and interprets it so as to close a door left open by the Supreme Court.13 It would be nearly impossible to prove through evidence of a system’s usual effects that intent must have been a factor in any one case; effects evidence, in this context, necessarily deals with many cases at once. Every jury discrimination charge would be stillborn if the defendant had to prove by direct evidence that the jury commissioners intended to deprive him or her of the right to a jury composed of a fair cross-section of the community. Requiring proof of discrimination in a particular case is especially inappropriate with regard to an Eighth Amendment claim, for even under the majority’s description of the proof necessary to sustain an Eighth Amendment challenge, race operating in a pervasive manner “in the system” will suffice.
The majority, after sowing doubts of this sort, nevertheless concedes that despite the particularity requirement, evidence of the system’s effects could be strong enough to demonstrate intent and purpose.14 Its subsequent efforts to weaken the implications to be drawn from the Baldus Study are uniformly unsuccessful.
For example, the majority takes comfort in the fact that the level of aggravation powerfully influences the sentencing decision in Georgia. Yet this fact alone does not reveal a “rational” system at work. The statistics not only show that the number of aggravating factors is a significant influence; they also point to the race of the victim as a factor of considerable influence. Where racial discrimination contributes to an official decision, the decision is unconstitutional even though discrimination was not the primary motive. Personnel Administrator v. Feeney, 442 U.S. 256, 279, 99 S.Ct. 2282, 2296, 60 L.Ed.2d 870 (1979).
Neither can the racial impact be explained away by the need for discretion in the administration of the death penalty or by any “presumption that the statute is operating in a constitutional manner.” The discretion necessary to the administration of the death penalty does not include the discretion to consider race: the jury may consider any proper aggravating factors, but it may not consider the race of the victim as an aggravating factor. Zant v. Stephens, 462 U.S. 862, 103 S.Ct. 2733, 2741, 77 L.Ed.2d 235 (1983). And a statute deserves a presumption of constitutionality only where there is real uncertainty as to whether race influences its application. Evidence such as the Baldus Study, showing that the pattern of sentences can only be explained by assuming a significant racial influence,15 overcomes whatever presumption exists.
The majority’s effort to discount the importance of the “liberation hypothesis” also fails. In support of his contention that juries were more inclined to rely on race when other factors did not militate toward one outcome or another, Dr. Baldus noted that a more pronounced racial influence appeared in cases of medium aggravation *914(20 percent) than in all cases combined (6 percent). The majority states that racial impact in a subset of cases cannot provide the basis for a systemwide challenge. However, there is absolutely no justification for such a claim. The fact that a system mishandles a sizeable subset of cases is persuasive evidence that the entire system operates improperly. Cf. Connecticut v. Teal, 457 U.S. 440, 102 S.Ct. 2525, 73 L.Ed.2d 130 (1984) (written test discriminates against some employees); Lewis v. City of New Orleans, 415 U.S. 130, 94 S.Ct. 970, 39 L.Ed.2d 214 (1974) (statute infringing on First Amendment interests in some cases). A system can be applied arbitrarily and capriciously even if it resolves the obvious eases in a rational manner. Admittedly, the lack of a precise definition of medium aggravation cases could lead to either an overstatement or understatement of the racial influence. Accepting, however, that the racial factor is accentuated to some degree in the middle range of cases,16 the evidence of racial impact must be taken all the more seriously.
Finally, the majority places undue reliance on several recent Supreme Court cases. It argues that Ford v. Strickland, — U.S. —, 104 S.Ct. 3498, 82 L.Ed.2d 911 (1984), Adams v. Wainwright, — U.S. —, 104 S.Ct. 2183, 80 L.Ed.2d 809 (1984), and Sullivan v. Wainwright, 464 U.S. 109, 104 S.Ct. 450, 78 L.Ed.2d 210 (1983), support its conclusion that the Baldus Study does not make a strong enough showing of effects to justify an inference of intent. But to the extent that these cases offer any guidance at all regarding the legal standards applicable to these studies,17 it is clear that the Court considered the validity of the studies rather than their sufficiency. In Sullivan, the Supreme Court refused to stay the execution simply because it agreed with the decision of this Court, a decision based on the validity of the study alone.18 Sullivan v. Wainwright, 721 F.2d 316 (11th Cir.1983) (citing prior cases rejecting statistical evidence because it did not account for non-racial explanations of the effects). As the majority mentions, the methodology of the Baldus Study easily surpasses that of the earlier studies involved in those cases.
Thus, the Baldus Study offers a convincing explanation of the disproportionate effects of Georgia’s death penalty system. It shows a clear pattern of sentencing that can only be explained in terms of race, and it does so in a context where direct evidence of intent is practically impossible to obtain. It strains the imagination to believe that the significant influence on sentencing left unexplained by 230 alternative factors is random rather than racial, especially in a state with an established history of racial discrimination. Turner v. Fouche, supra; Chapman v. King, 154 F.2d 460 (5th Cir.), cert. denied, 327 U.S. 800, 66 S.Ct. 905, 90 L.Ed. 1025 (1946). The petitioner has certainly presented evidence of intentional racial discrimination at work in the Georgia system. Georgia has within the meaning of the Eighth Amendment applied its statute arbitrarily and capriciously.
III. THE VALIDITY OP THE BALDUS STUDY
The majority does not purport to reach the issue of whether the Baldus Study reliably proves what it claims to prove. However, the majority does state that the district court’s findings regarding the validity *915of the study might foreclose habeas relief on this issue. Moreover, the majority opinion in several instances questions the validity of the study while claiming to be interested in its sufficiency alone. I therefore will summarize some of the reasons that the district court was clearly erroneous in finding the Baldus Study invalid.
The district court fell victim to a misconception that distorted its factual findings. The Court pointed out a goodly number of imperfections in the study but rarely went ahead to determine the significance of those imperfections. A court may not simply point to flaws in a statistical analysis and conclude that it is completely unreliable or fails to prove what it was intended to prove. Rather, the Court must explain why the imperfection makes the study less capable of proving the proposition that it was meant to support. Eastland v. Tennessee Valley Authority, 704 F.2d 613 (11th Cir.1983), cert. denied, — U.S.—, 104 S.Ct. 1415, 79 L.Ed.2d 741 (1984).
Several of the imperfections noted by the district court were not legally significant because of their minimal effect. Many of the errors in the data base match this description. For instance, the “mismatches” in data entered once for cases in the Procedural Reform Study and again for the same cases in the Charging and Sentencing Study were scientifically negligible. The district court relied on the data that changed from one study to the next in concluding that the coders were allowed too much discretion. But most of the alleged “mismatches” resulted from intentional improvements in the coding techniques and the remaining errors 19 were not large enough to affect the results.
The data missing in some cases was also a matter of concern for the district court. The small effects of the missing data leave much of that concern unfounded. The race of the victim was uncertain in 6% of the cases at most20; penalty trial information was unavailable in the same percentage of cases.21 The relatively small amount of missing data, combined with the large number of variables used in several of the models, should have led the court to rely on the study. Statistical analyses have never been held to a standard of perfection or near perfection in order for courts to treat them as competent evidence. Trout v. Lehman, 702 F.2d 1094, 1101-02 (D.C.Cir.1983). Minor problems are inevitable in a study of this scope and complexity: the stringent standards used by the district court would spell the loss of most statistical evidence.
Other imperfections in the study were not significant because there was no reason to believe that the problem would work systematically to expand the size of the race-of-the-victim factor rather than to contract it or leave it unchanged. The multi-collinearity problem is a problem of notable proportions that nonetheless did not increase the size of the race-of-the-victim factor.22 Ideally the independent variables in *916a regression analysis should not be related to one another. If one independent variable merely serves as a proxy for another, the model suffers from “multicollinearity.” That condition could either reduce the statistical significance of the variables or distort their relationships to one another. Of course, to the extent that multicollinearity reduces statistical significance it suggests that the racial influence would be even more certain if the multicollinearity had not artificially depressed the variable’s statistical significance. As for the distortions in the relationships between the variables, experts for the petitioner explained that mul-ticollinearity tends to dampen the racial effect rather than enhance it.23
The district court did not fail in every instance to analyze the significance of the problems. Yet when it did reach this issue, the court at times appeared to misunderstand the nature of this study or of regression analysis generally. In several related criticisms, it found that any of the models accounting for less than 230 independent variables were completely worthless (580 F.Supp. at 361), that the most complete models were unable to capture every nuance of every case (580 F.Supp. at 356, 371), and that the models were not sufficiently predictive to be relied upon in light of their low R² value (580 F.Supp. at 361).24 The majority implicitly questions the validity of the Baldus Study on several occasions when it adopts the first two of these criticisms.25 A proper understanding of statistical methods shows, however, that these are not serious shortcomings in the Baldus Study.
The district court mistrusted smaller models because it placed too much weight on one of the several complementary goals of statistical analysis. Dr. Baldus testified that in his opinion the 39-variable model was the best among the many models he produced. The district court assumed somewhat mechanistically that the more independent variables encompassed by a model, the better able it was to estimate the proper influence of non-racial factors. But in statistical models, bigger is not always better. After a certain point, additional independent variables become correlated with variables already being considered and distort or suppress their influence. The most accurate models strike an appropriate balance between the risk of omitting a significant factor and the risk of multicollinearity. Hence, the district court erred in rejecting all but the largest models.
The other two criticisms mentioned earlier spring from a single source — the misinterpretation of the R² measurement.26 The failure of the models to capture every nuance of every case was an inevitable but harmless failure. Regression analysis accounts for this limitation with an R² measurement. As a result, it does not matter *917that a study fails to consider every nuance of every case because random factors (factors that influence the outcome in a sporadic and unsystematic way) do not impugn the reliability of the systemwide factors already identified, including race of the victim. Failure to consider extra factors becomes a problem only where they operate throughout the system, that is, where R² is inappropriately low.
The district court did find that the R² of the 230-variable study, which was nearly .48, was too low.27 But an R² of that size is not inappropriately low in every context.28 The R² measures random factors unique to each case: in areas where such factors are especially likely to occur, one would expect, a low R². As the experts, the district court and the majority have pointed out, no two death penalty cases can be said to be exactly alike, and it is especially unlikely for a statistical study to capture every influence on a sentence. In light of the random factors at work in the death penalty context, the district court erred in finding the R² of all the Baldus Study models too low.29
Errors of this sort appear elsewhere in the district court opinion and leave me with the definite and firm conviction that the basis for the district court’s ruling on the invalidity of the study was clearly erroneous. United States v. Gypsum Co., 333 U.S. 364, 395, 68 S.Ct. 525, 541, 92 L.Ed. 746 (1948). This statistical analysis, while imperfect, is sufficiently complete and reliable to serve as competent evidence to guide the court. Accordingly, I would reverse the judgment of the district court with regard to the validity of the Baldus Study. I would also reverse that court’s determination that an Eighth Amendment claim is not available to the petitioner. He is entitled to relief on this claim.
IV. OTHER ISSUES
I concur in the opinion of the court with regard to the death-oriented jury claim and in the result reached by the court on the ineffective assistance of counsel claim. I must dissent, however, on the two remaining issues in the case. I disagree with the holding on the Giglio issue, on the basis of the findings and conclusions of the district court and the dissenting opinion of Chief Judge Godbold. As for the Sandstrom claim, I would hold that the instruction was erroneous and that the error was not harmless.
It is by no means certain that an error of this sort can be harmless. See Connecticut v. Johnson, 460 U.S. 73, 103 S.Ct. 969, 74 L.Ed.2d 823 (1983). Even if an error could be harmless, the fact that McCleskey relied on an alibi defense does not mean that intent was “not at issue” in the case. Any element of a crime can be at issue whether or not the defendant presents evidence that disputes the prosecution’s case on that point. The jury could find that the prosecution had failed to dispel all reasonable doubts with regard to intent even though the defendant did not specifically make such an argument. Intent is at issue wherever there is evidence to support a reasonable doubt in the mind of a reasonable juror as to the existence of criminal intent. See Lamb v. Jernigan, 683 F.2d *9181332, 1342-43 (11th Cir.1982) (“no reasonable juror could have determined ... that appellant acted out of provocation or self-defense,” therefore error was harmless).
The majority states that the raising of an alibi defense does not automatically render a Sandstrom violation harmless. It concludes, however, that the raising of a non-participation defense coupled with “overwhelming evidence of an intentional killing” will lead to a finding of harmless error. The majority’s position is indistinguishable from a finding of harmless error based solely on overwhelming evidence.30 Since a defendant normally may not relieve the jury of its responsibility to make factual findings regarding every element of an offense, the only way for intent to be “not at issue” in a murder trial is if the evidence presented by either side provides no possible issue of fact with regard to intent. Thus, McCleskey’s chosen defense in this case should not obscure the sole basis for the disagreement between the majority and myself: the reasonable inferences that could be drawn from the circumstances of the killing. I cannot agree with the majority that no juror, based on any reasonable interpretation of the facts, could have had a reasonable doubt regarding intent.
- Several factors in this case bear on the issue of intent. The shooting did not occur at point-blank range. Furthermore, the officer was moving at the time of the shooting. On the basis of these facts and other circumstances of the shooting, a juror could have had a reasonable doubt as to whether the person firing the weapon intended to kill. While the majority dismisses this possibility as “mere speculation,” the law requires an appellate court to speculate about what a reasonable juror could have concluded. Sandstrom v. Montana, 442 U.S. 510, 99 S.Ct. 2450, 61 L.Ed.2d 39 (1979); United States v. Bell, 678 F.2d 547, 549 (5th Cir. Unit B 1982) (en banc), aff’d on other grounds, 462 U.S. 356, 103 S.Ct. 2398, 76 L.Ed.2d 638 (1983). Therefore, the judgment of the district court should be reversed on this ground, as well.
. This was the description given at trial by Dr. Richard Berk, member of a panel of the Nation*908al Academy of Sciences charged with reviewing all previous research on criminal sentencing issues in order to set standards for the conduct of such research.
. The district court felt bound by precedent to analyze the claim under the equal protection clause, but expressed the opinion that it might best be understood as a due process claim. It does not appear that a different constitutional basis for the claim would have affected the district court's conclusions.
. The Supreme Court in Pulley v. Harris, — U.S. —, 104 S.Ct. 871, 79 L.Ed.2d 29 (1984), emphasized the importance of factors other than appellate proportionality review that would control jury discretion and assure that sentences would not fall into an arbitrary pattern. The decision in Pulley deemphasizes the importance of evidence of arbitrariness in individual cases and looks exclusively to "systemic" arbitrariness. The case further underscores this court’s responsibility to be alert to claims, such as the one McCleskey makes, that allege more than disproportionality in a single sentence.
. Lockett v. Ohio, 438 U.S. 586, 98 S.Ct. 2954, 57 L.Ed.2d 973 (1978), and other cases demonstrate that the actual deliberations of the sentencer are relevant under the Eighth Amendment, for mitigating factors must have their proper place in all deliberations. But the sufficiency of intent in proving an Eighth Amendment violation does not imply the necessity of intent for all such claims.
. The only Fifth or Eleventh Circuit cases touching on the issue of discriminatory intent under the Eighth Amendment appear to be inconsistent with the Supreme Court’s approach and therefore wrongly decided. The court in Smith v. Balkcom, 660 F.2d 573, 584 (5th Cir. Unit B 1981), modified, 671' F.2d 858 (5th Cir.1982), stated that Eighth Amendment challenges based on race require a showing of intent, but the court reached this conclusion because it wrongly believed that Spinkellink v. Wainwright, 578 F.2d 582 (5th Cir.1978), compelled such a result. The Spinkellink court never reached the question of intent, holding that Supreme Court precedent foreclosed all Eighth Amendment challenges except for extreme cases where the sentence is shockingly disproportionate to the crime. 578 F.2d at 606 & n. 28. See supra note 3. The Smith court cites to a portion of the Spinkellink opinion dealing with equal protection arguments. 578 F.2d at 614 n. 40. Neither of the cases took note of the most pertinent Eighth Amendment precedents decided by the Supreme Court.
Other Eleventh Circuit cases mention that habeas corpus petitioners must prove intent to discriminate racially against them personally in the application of the death sentence. But these cases all either treat the claim as though it arose under the Fourteenth Amendment alone or rely on Smith or one of its successors. See Sullivan v. Wainwright, 721 F.2d 316 (11th Cir.1983); Adams v. Wainwright, 709 F.2d 1443 (11th Cir.1983). Of course, to the extent these cases attempt to foreclose Eighth Amendment challenges of this sort or require proof of particularized intent to discriminate, they are inconsistent with the Supreme Court’s interpretation of the Eighth Amendment. Cf. Gates v. Collier, 501 F.2d 1291, 1300-01 (5th Cir.1974) (prohibition against cruel and unusual punishment "is not limited to specific acts directed at selected individuals”).
. Among those who were eligible for the death penalty, eleven percent of the killers of white victims received the death penalty, while one percent of the killers of black victims received it.
. In one of the largest of these models, the one focused on by the district court and the majority, the statisticians used 230 different independent variables (possible influences on the pattern of sentencing), including several different aggravating and many possible mitigating factors.
. See part I, supra. Of course, proof of any significant racial effects is enough under the Eighth Amendment, for a requirement of proving large or pervasive effects is tantamount to proof of intent.
. The same factors leading to the conclusion that an Eighth Amendment claim does not require proof of intent militate even more strongly against using too restrictive an understanding of intent.
. The majority distinguishes the jury discrimination cases on tenuous grounds, stating that the disparity between the number of minority persons on the jury venire and the number of such persons in the population is an "actual disparity,” while the racial influence in this case is not. If actual disparities are to be considered, then the court should employ the actual (and overwhelming) eleven-to-one differential between white victim cases and black victim cases. The percentage figures presented by the Baldus Study are really more reliable than "actual” disparities because they control for possible non-racial factors.
. United States v. Texas Educational Agency, 579 F.2d 910 (5th Cir.1978), cert. denied, 443 U.S. 915, 99 S.Ct. 3106, 61 L.Ed.2d 879 (1979), involving a segregated school system, provides another example of effects evidence as applied to an entire decisionmaking system.
. The particularity requirement has appeared sporadically in this Court’s decisions prior to this time, although it was not a part of the original observation about this sort of statistical evidence in Smith v. Balkcom, supra.
. The dissenting opinion of Justice Powell in Stephens v. Kemp, — U.S. —, 104 S.Ct. 562, 78 L.Ed.2d 370, 372 (1984), does not undermine the clear import of cases such as the jury discrimination cases. For one thing, a dissent from a summary order does not have the prece-dential weight of a fully considered opinion of the Court. For another, the Stephens dissent considered the Baldus Study as an equal protection argument only and did not address what might be necessary to prove an Eighth Amendment violation.
. While I agree with Judge Anderson's observation that "the proof of racial motivation required in a death case ... would be less strict than that required in civil cases or in the criminal justice system generally,” I find it inconsistent with his acceptance of the majority outcome. The "exacting” constitutional supervision over the death penalty established by the Supreme Court compels the conclusion that discriminatory effects can support an Eighth Amendment challenge. Furthermore, the majority’s evaluation of the evidence in this case is, if anything, more strict than in other contexts. See note 10, supra.
. The racial influence operates in the average case and is therefore probably at work in any single case. The majority misconstrues the nature of regression analysis when it says that the coefficient of the race-of-the-victim factor represents the percentage of cases in which race could have been a factor. That coefficient represents the influence of race across all the cases.
. The majority apparently ignores its commitment to accept the validity of the Baldus Study when it questions the definition of "medium aggravation cases” used by Dr. Baldus.
. The opinion in Ford mentioned this issue in a single sentence; the order in Adams was not accompanied by any written opinion at all. None of the three treated this argument as a possible Eighth Amendment claim. Finally, the "death odds multiplier” is not the most pronounced statistic in the Baldus Study: a ruling of insufficiency based on that one indicator would not be controlling here.
. Indeed, the Court indicated that it would have reached a different conclusion if the district court and this court had not been given the opportunity to analyze the statistics adequately. —U.S.—, 104 S.Ct. at 451, n. 3, 78 L.Ed.2d at 213, n. 3.
. The remaining errors affected little more than one percent of the data in any of the models. Data errors of less than 10 or 12% generally do not threaten the validity of a model.
. Dr. Baldus used an "imputation method," whereby the race of the victim was assumed to be the same as the race of the defendant. Given the predominance of murders where the victim and defendant were of the same race, this method was a reasonable way of estimating the number of victims of each race. It further reduced the significance of this missing data.
. The district court, in assessing the weight to be accorded this omission, assumed that Dr. Baldus was completely unsuccessful in predicting how many of the cases led to penalty trials. Since the prediction was based on discernible trends in the rest of the cases, the district court was clearly erroneous to give no weight to the prediction.
. The treatment of the coding conventions provides another example. The district court criti.cized Dr. Baldus for treating "U” codes (indicating uncertainty as to whether a factor was present in a case) as being beyond the knowledge of the jury and prosecutor (“absent”) rather than assuming that the decisionmakers knew about the factor ("present"). Baldus contended that, if the extensive records available on each case did not disclose the presence of a factor, chances were good that the decisionmakers did not know of its presence, either. Dr. Berk testi*916fied that the National Academy of Sciences had considered this same issue and had recommended the course taken by Dr. Baldus. Dr. Katz, the expert witness for the state, suggested removing the cases with the U codes from the study altogether. The district court’s suggestion, then, that the U codes be treated as present, appears to be groundless and clearly erroneous.
Baldus later demonstrated that the U codes did not affect the race-of-the-victim factor by recoding all the items coded with a U and treating them as present. Each of the tests showed no significant reduction in the racial variable. The district court rejected this demonstration because it was not carried out using the largest available model.
. The district court rejected this expert testimony, not because of any rebuttal testimony, but because it allegedly conflicted with the petitioner’s other theory that multicollinearity affects statistical significance. 580 F.Supp. at 364. The two theories are not inconsistent, for neither Dr. Baldus nor Dr. Woodworth denied that multicollinearity might have multiple effects. The two theories each analyze one possible effect. Therefore, the district court rejected this testimony on improper grounds.
. The R² measurement represents the influence of random factors unique to each case that could not be captured by addition of another independent variable. As R² approaches a value of 1.0, one can be more sure that the independent variables already identified are accurate and that no significant influences are masquerading as random influences.
. See, e.g., pp. 896, 899.
. See footnote 24.
. It based that finding on the fact that a model with an R² less than .5 "does not predict the outcome in half of the cases.” This is an inaccurate statement, for an R² actually represents the percentage of the original 11-to-l differential explained by all the independent variables combined. A model with an R² of less than .5 would not necessarily fail to predict the outcome in half the cases because the model improves upon pure chance as a way of correctly predicting an outcome. For dichotomous outcomes (i.e. the death penalty is imposed or it is not), random predictions could succeed half the time.
. Wilkins v. University of Houston, 654 F.2d 388, 405 (5th Cir.1981), is not to the contrary. That court stated only that it could not know whether an R² of .52 or .53 percent would be inappropriately low in that context since the parties had not made any argument on the issue.
. Furthermore, an expert for the petitioner offered the unchallenged opinion that the R² measurements in studies of dichotomous outcomes are understated by as much as 50%, placing the R² values of the Baldus Study models somewhere between .7 and .9.
. Indeed, the entire harmless error analysis employed by the court may be based on a false dichotomy between "overwhelming evidence” and elements “not at issue.” Wherever intent is an element of a crime, it can only be removed as an issue by overwhelming evidence. The observation by the plurality in Connecticut v. Johnson, supra, that a defendant may in some cases “admit” an issue, should only apply where the evidence allows only one conclusion. To allow an admission to take place in the face of evidence to the contrary improperly infringes on the jury's duty to consider all relevant evidence.