
    Warren McCLESKEY, Petitioner-Appellee, Cross-Appellant, v. Ralph KEMP, Warden, Respondent-Appellant, Cross-Appellee.
    No. 84-8176.
    United States Court of Appeals, Eleventh Circuit.
    Jan. 29, 1985.
    
      Mary Beth Westmoreland, Asst. Atty. Gen., Atlanta, Ga., for respondent-appellant, cross-appellee.
    Robert H. Stroup, Atlanta, Ga., John Charles Boger, Anthony G. Amsterdam, New York University-School of Law, New York City, for petitioner-appellee, cross-appellant.
    Before GODBOLD, Chief Judge, RO-NEY, TJOFLAT, JAMES C. HILL, FAY, VANCE, KRAVITCH, JOHNSON, ALBERT J. HENDERSON, HATCHETT, R. LANIER ANDERSON, III, and CLARK, Circuit Judges.
   RONEY, Circuit Judge,

with whom Judges TJOFLAT, JAMES C. HILL, FAY, VANCE, ALBERT J. HENDERSON and R. LANIER ANDERSON, III, join :

This case was taken en banc principally to consider the argument arising in numerous capital cases that statistical proof shows the Georgia capital sentencing law is being administered in an unconstitutionally discriminatory and arbitrary and capricious matter. After a lengthy evidentiary hearing which focused on a study by Professor David C. Baldus, the district court concluded for a variety of reasons that the statistical evidence was insufficient to support the claim of unconstitutionality in the death sentencing process in Georgia. We affirm the district court’s judgment on this point.

The en banc court has considered all the other claims involved on this appeal. On the State’s appeal, we reverse the district court’s grant of habeas corpus relief on the claim that the prosecutor failed to disclose a promise of favorable treatment to a state witness in violation of Giglio v. United States, 405 U.S. 150, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972). We affirm the judgment denying relief on all other points raised by the defendant, that is: (1) that defendant received ineffective assistance of counsel; (2) that jury instructions contravened the due process clause in violation of Sandstrom v. Montana, 442 U.S. 510, 99 S.Ct. 2450, 61 L.Ed.2d 39 (1979); and (3) that the exclusion of death-scrupled jurors violated the right to an impartial and unbiased jury drawn from a representative cross-section of the community.

Thus, concluding that the district court should have denied the petition for writ of habeas corpus, we affirm on all claims denied by the court, but reverse the grant of habeas corpus relief on the Giglio claims.

FACTS

Warren MeCleskey was arrested and charged with the murder of a police officer during an armed robbery of the Dixie Furniture Store. The store was robbed by a band of four men. Three entered through the back door and one through the front. While the men in the rear of the store searched for cash, the man who entered through the front door secured the showroom by forcing everyone there to lie face down on the floor., Responding to a silent alarm, a police officer entered the store by the front door. Two shots were fired. One shot struck the police officer in the head causing his death. The other glanced off a cigarette lighter in his chest pocket.

MeCleskey was identified by two of the store personnel as the robber who came in the front door. Shortly after his arrest, MeCleskey confessed to participating in the robbery but maintained that he was not the triggerman. MeCleskey confirmed the eyewitness’ accounts that it was he who entered through the front door. One of his accomplices, Ben Wright, testified that MeCleskey admitted to shooting the officer. A jail inmate housed near MeCleskey testified that MeCleskey made a “jail house confession” in which he claimed he was the triggerman. The police officer was killed by a bullet fired from a .38 caliber Rossi handgun. MeCleskey had stolen a .38 caliber Rossi in a previous holdup.

PRIOR PROCEEDINGS

The jury convicted MeCleskey of murder and two counts of armed robbery. At the penalty hearing, neither side called any witnesses. The State introduced documentary evidence of McCleskey’s three prior convictions for armed robbery.

The jury sentenced MeCleskey to death for the murder of the police officer and to consecutive life sentences for the two counts of armed robbery. These convictions and sentences were affirmed by the Georgia Supreme Court. McClesky v. State, 245 Ga. 108, 263 S.E.2d 146, cert. denied, 449 U.S. 891, 101 S.Ct. 253, 66 L.Ed.2d 119 (1980). MeCleskey then petitioned for habeas corpus relief in state court. This petition was denied after an evidentiary hearing. The Georgia Supreme Court denied McCleskey’s application for a certificate of probable cause to appeal. The United States Supreme Court denied a petition for a writ of certiorari. MeCleskey v. Zant, 454 U.S. 1093, 102 S.Ct. 659, 70 L.Ed.2d 631 (1981).

MeCleskey then filed his petition for ha-beas corpus relief in federal district court asserting, among other things, the five constitutional challenges at issue on this appeal. After an evidentiary hearing and consideration of extensive memoranda filed by the parties, the district court entered the lengthy and detailed judgment from which these appeals are taken. MeCleskey v. Zant, 580 F.Supp. 338 (N.D.Ga.1984).

This opinion addresses each issue asserted on appeal in the following order: (1) the Giglio claim, (2) constitutionality of the application of Georgia’s death penalty, (3) effective assistance of counsel, (4) death-qualification of jurors, and (5) the Sand-strom issue.

GIGLIO CLAIM

The district court granted habeas corpus relief to MeCleskey because it determined that the state prosecutor failed to reveal that one of its witnesses had been promised favorable treatment as a reward for his testimony. The State violates due process when it obtains a conviction through the use of false evidence or on the basis of a witness’s testimony when that witness has failed to disclose a promise of favorable treatment from the prosecution. Giglio v. United States, 405 U.S. 150, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972).

We hold that (1) there was no promise in this case, as contemplated by Giglio; and (2) in any event, had there been a Giglio violation, it would be harmless. Thus, we reverse the grant of habeas corpus relief on this ground.

Offie Gene Evans, a prisoner incarcerated with McCleskey, was called by the State on rebuttal to strengthen its proof that McCleskey was the triggerman at the holdup. Evans testified that McCleskey admitted to him in jail that he shot the policeman and that McCleskey said he had worn makeup to disguise his appearance during the robbery.

The “Promise ”

At McCleskey’s state habeas corpus hearing, Evans gave the following account of certain conversations with state officials.

THE COURT: Mr. Evans, let me ask you a question. At the time that you testified in Mr. McCleskey’s trial, had you been promised anything in exchange for your testimony?
THE WITNESS: No, I wasn’t. I wasn’t promised nothing about — I wasn’t promised nothing by the D.A. but the Detective told me that he would — he said he was going to do it himself, speak a word for me. That was what the Detective told me.
Q: (by McCleskey’s attorney): The Detective said he would speak a word for you?
A: Yeah.

A deposition of McCleskey’s prosecutor that was taken for the state habeas corpus proceeding reveals that the prosecutor contacted federal authorities after McCles-key’s trial to advise them of Evans’ cooperation and that the escape charges were dropped.

The Trial Testimony

At the trial, the State brought out on direct examination that Evans was incarcerated on the charge of escape from a federal halfway house. Evans denied receiving any promises from the prosecutor and downplayed the seriousness of the escape charge.

Q: [by prosecutor]: Mr. Evans, have I promised you anything for testifying today?
A: No, sir, you ain’t.
Q: You do have an escape charge still pending, is that correct?
A: Yes, sir. I’ve got one, but really it ain’t no escape, what the peoples out there tell me, because something went wrong out there so I just went home. I stayed at home and when I called the man and told him that I would be a little late coming in, he placed me on escape charge and told me there wasn’t no use of me coming back, and I just stayed on at home and he come and picked me up.
Q: Are you hoping that perhaps you won’t be prosecuted for that escape?
A: Yeah, I hope I don’t, but I don’t— what they tell me, they ain’t going to charge me with escape no way.
Q: Have you asked me to try to fix it so you wouldn’t get charged with escape?
A: No, sir.
Q: Have I told you I would try to fix it for you?
A: No, sir.

The State Habeas Corpus Decision

The state court rejected McCleskey’s Giglio claim on the following reasoning:

Mr. Evans at the habeas hearing denied that he was promised anything for his testimony. He did state that he was told by Detective Dorsey that Dorsey would ‘speak a word’ for him. The detective’s ex parte communication recommendation alone is not sufficient to trigger the applicability of Giglio v. United States, 405 U.S. 150 [92 S.Ct. 763, 31 L.Ed.2d 104] (1972).
The prosecutor at petitioner’s trial, Russel J. Parker, stated that he was unaware of any understandings between Evans and any Atlanta Police Department detectives regarding a favorable recommendation to be made on Evans’ federal escape charge. Mr. Parker admitted that there was opportunity for Atlanta detectives to put in a good word for Evans with federal authorities. However, he further stated that when any police officer has been killed and someone ends up testifying for the State, putting his life in danger, it is not surprising that charges, like those against Evans, will be dropped.
In the absence of any other evidence, the Court cannot conclude an agreement existed merely because of the subsequent disposition of criminal charges against a witness for the State.

Although it is reasonable to conclude that the state court found that there was no agreement between Evans and the prosecutor, no specific finding was made as to Evans’ claim that a detective promised to “speak a word for him.” The court merely held as a matter of law that assuming Evans was telling the truth, no Giglio violation had occurred.

Was It a Promise?

The Supreme Court’s rationale for imposing this rule is that “[t]he jury’s estimate of the truthfulness and reliability of a given witness may well be determinative of guilt or innocence.” Napue v. Illinois, 360 U.S. 264, 269, 79 S.Ct. 1173, 1177, 3 L.Ed.2d 1217 (1959). The Court has never provided definitive guidance on when the Government’s dealings with a prospective witness so affect the witness’ credibility that they must be disclosed at trial. In Giglio, a prosecutor promised the defendant’s alleged co-conspirator that no charges would be brought against him if he testified against the defendant. In Napue, a prosecutor promised a witness that in exchange for his testimony the prosecutor would recommend that the sentence the witness was presently serving be reduced.

In this case, the detective’s promise to speak a word falls far short of the understandings reached in Giglio and Napue. As stated by this Court, “[t]he thrust of Giglio and its progeny has been to ensure that the jury know the facts that might motivate a witness in giving testimony.” Smith v. Kemp, 715 F.2d 1459, 1467 (11th Cir.), cert. denied, — U.S.—, 104 S.Ct. 510, 78 L.Ed.2d 699 (1983). The detective’s statement offered such a marginal benefit, as indicated by Evans, that it is doubtful it would motivate a reluctant witness, or that disclosure of the statement would have had any effect on his credibility. The State’s nondisclosure therefore failed to infringe McCleskey’s due process rights.

Was Any Violation Harmless?

In any event, there is no “reasonable likelihood” that the State’s failure to disclose the detective’s cryptic statement or Evans’ different escape scenario affected the judgment of the jury. See Giglio, 405 U.S. at 154, 92 S.Ct. at 766. Evans’ credibility was exposed to substantial impeachment even without the detective’s statement and the inconsistent description of his escape. The prosecutor began his direct examination by having Evans recite a litany of past convictions. Evans admitted to convictions for forgery, two burglaries, larceny, carrying a concealed weapon, and theft from the United States mail. On cross examination, McCleskey’s attorney attempted to portray Evans as a “professional criminal”. Evans also admitted that he was testifying to protect himself and one of McCleskey’s codefendants. In light of this substantial impeachment evidence, we find it unlikely that the undisclosed information would have affected the jury’s assessment of Evans’ credibility. See United States v. Anderson, 574 F.2d 1347, 1356 (5th Cir.1978).

McCleskey claims Evans’ testimony was crucial because the only other testimony which indicated he pulled the trigger came from his codefendant, Ben Wright. Ben Wright’s testimony, McCleskey urges, would have been insufficient under Georgia law to convict him without the corroboration provided by Evans. In Georgia, an accomplice’s testimony alone in felony cases is insufficient to establish a fact. O.C.G.A. § 24-4-8. Wright’s testimony, however, was corroborated by McCleskey’s own confession in which McCleskey admitted participation in the robbery. See Arnold v. State, 236 Ga. 534, 224 S.E.2d 386, 388 (1976). Corroboration need not extend to every material detail. Blalock v. State, 250 Ga. 441, 298 S.E.2d 477, 479-80 (1983); Cofer v. State, 166 Ga.App. 436, 304 S.E.2d 537, 539 (1983).

The district court thought Evans’ testimony critical because of the information he supplied about makeup and McCleskey’s intent in shooting the police officer. Although we agree that his testimony added weight to the prosecution’s case, we do not find that it could “in any reasonable likelihood have affected the judgment of the jury.” Giglio, 405 U.S. at 154, 92 S.Ct. at 766 (quoting Napue v. Illinois, 360 U.S. at 271, 79 S.Ct. at 1178). Evans, who was called only in rebuttal, testified that McCleskey had told him that he knew he had to shoot his way out, and that even if there had been twelve policemen he would have done the same thing. This statement, the prosecutor argued, showed malice. In his closing argument, however, the prosecutor presented to the jury three reasons supporting a conviction for malice murder. First, he argued that the physical evidence showed malicious intent because it indicated that McCleskey shot the police officer once in the head and a second time in the chest as he lay dying on the floor. Second, the prosecutor asserted that McCleskey had a choice, either to surrender or to kill the officer. That he chose to kill indicated malice. Third, the prosecutor contended that McCleskey’s statement to Evans that he still would have shot his way out if there had been twelve police officers showed malice. This statement by McCles-key was not developed at length during Evans’ testimony and was mentioned only in passing by the prosecutor in closing argument.

Evans’ testimony that McCleskey had made up his face corroborated the identification testimony of one of the eyewitnesses. Nevertheless, this evidence was not crucial to the State’s case. That McCles-key was wearing makeup helps to establish he was the robber who entered the furniture store through the front door. This fact had already been directly testified to by McCleskey’s accomplice and two eyewitnesses as well as corroborated by McCles-key’s own confession. That Evans’ testimony buttresses one of the eyewitnesses’ identifications is relatively unimportant.

Thus, although Evans’ testimony might well be regarded as important in certain respects, the corroboration of that testimony was such that the revelation of the Giglio promise would not reasonably affect the jury’s assessment of his credibility and therefore would have had no effect on the jury’s decision. The district court’s grant' of habeas corpus relief on this issue must be reversed.

CONSTITUTIONAL APPLICATION OF GEORGIA’S DEATH PENALTY

In challenging the constitutionality of the application of Georgia’s capital statute, McCleskey alleged two related grounds for relief: (1) that the “death penalty is administered arbitrarily, capriciously, and whimsically in the State of Georgia,” and (2) it “is imposed ... pursuant to a pattern and practice ... to discriminate on the grounds of race,” both in violation of the Eighth and Fourteenth Amendments of the Constitution.

The district court granted petitioner’s motion for an evidentiary hearing on his claim of system-wide racial discrimination under the Equal Protection Clause of the Fourteenth Amendment. The court noted that “it appears ... that petitioner’s Eighth Amendment argument has been rejected by this Circuit in Spinkellink v. Wainwright, 578 F.2d 582, 612-14 (5th Cir.1978) ... [but] petitioner’s Fourteenth Amendment claim may be appropriate for consideration in the context of statistical evidence which the petitioner proposes to present.” Order of October 8, 1982, at 4.

An evidentiary hearing was held in August, 1983. Petitioner's case in chief was presented through the testimony of two expert witnesses, Professor David C. Bal-dus and Dr. George Woodworth, as well as two principal lay witnesses, Edward Gates and L.G. Warr, an official employed by Georgia Board of Pardons and Paroles. The state offered the testimony of two expert witnesses, Dr. Joseph Katz and Dr. Roger Burford. In rebuttal, petitioner recalled Professor Baldus and Dr. Wood-worth, and presented further expert testimony from Dr. Richard Berk.

In a comprehensive opinion, reported at 580 F.Supp. 338, the district court concluded that petitioner failed to make out a prima facie case of discrimination in sentencing based on either the race of victims or the race of defendants. The Court discounted the disparities shown by the Bal-dus study on the ground that the research (1) showed substantial flaws in the data base, as shown in tests revealing coding errors and mismatches between items on the Procedural Reform Study (PRS) and Comprehensive Sentencing Study (CSS) questionnaires; (2) lacked accuracy and showed flaws in the models, primarily because the models do not measure decisions based on knowledge available to decision-maker and only predicts outcomes in 50 percent of the cases; and (3) demonstrated multi-collinearity among model variables, showing interrelationship among the variables and consequently distorting relationships, making interpretation difficult.

The district court further held that even if a prima facie case had been established, the state had successfully rebutted the showing because: (1) the results were not the product of good statistical methodology, (2) other explanations for the study results could be demonstrated, such as, white victims were acting as proxies for aggravated cases and that black-victim cases, and (3) black-victim cases, being left cases, and (3) black-victim cases being left behind at the life sentence and voluntary manslaughter stages, are less aggravated and more mitigated than the white-victim cases disposed of in similar fashion.

The district court concluded that petitioner failed to carry his ultimate burden of persuasion, because there is no consistent statistically significant evidence that the death penalty is being imposed on the basis of the race of defendant. In particular there was no statistically significant evidence produced to show that prosecutors are seeking the death penalty or juries are imposing the death penalty because the defendant is black or the victim is white. Petitioner conceded that the study is incapable of demonstrating that he was singled out for the death penalty because of the race of either himself or his victim, and, therefore, petitioner failed to demonstrate that racial considerations caused him to receive the death penalty.

We adopt the following approach in addressing the argument that the district court erred in refusing to hold that the Georgia statute is unconstitutionally applied in light of the statistical evidence. First, we briefly describe the statistical Baldus study that was done in this case. Second, we discuss the evidentiary value such studies have in establishing the ultimate facts that control a constitutional decision. Third, we discuss the constitutional law in terms of what must be proved in order for petitioner to prevail on an argument that a state capital punishment law is unconstitutionally applied because of race discrimination. Fourth, we discuss whether a generalized statistical study such as this could ever be sufficient to prove the allegations of ultimate fact necessary to sustain a successful constitutional attack on a defendant’s sentence. Fifth, we discuss whether, this study is valid to prove what it purports to prove. Sixth, we decide that this particular study, assuming its validity and that it proves what it claims to prove, is insufficient to either require or support a decision for petitioner.

In summary, we affirm the district court on the ground that, assuming the validity of the research, it would not support a decision that the Georgia law was being unconstitutionally applied, much less would it compel such a finding, the level which petitioner would have to reach in order to prevail on this appeal.

The Baldus Study

The Baldus study analyzed the imposition of sentence in homicide cases to determine the level of disparities attributable to race in the rate of the imposition of the death sentence. In the first study, Procedural Reform Study (PRS), the results revealed no race-of-defendant effects whatsoever, and the results were unclear at that stage as to race-of-victim effects.

The second study, the Charging and Sentencing Study (CSS), consisted of a random stratified sample of all persons indicted for murder from 1973 through 1979. The study examined the cases from indictment through sentencing. The purpose of the study was to estimate racial effects that were the product of the combined effects of all decisions from the point of indictment to the point of the final death-sentencing decision, and to include strength of the evidence in the cases.

The study attempted to control for all of the factors which play into a capital crime system, such as aggravating circumstances, mitigating circumstances, strength of evidence, time period of imposition of sentence, geographical areas (urban/rural), and race of defendant and victim. The data collection for these studies was exceedingly complex, involving cumbersome data collection instruments, extensive field work by multiple data collectors and sophisticated computer coding, entry and data cleaning processes.

Baldus and Woodworth completed a multitude of statistical tests on the data consisting of regression analysis, indexing factor analysis, cross tabulation, and triangulation. The results showed a 6% racial effect systemwide for white victim, black defendant cases with an increase to 20% in the mid-range of cases. There was no suggestion that a uniform, institutional bias existed that adversely affected defendants in white victim cases in all circumstances, or a black defendant in all cases.

The object of the Baldus study in Fulton County, where McCleskey was convicted, was to determine whether the sentencing pattern disparities that were observed statewide with respect to race of the victim and race of defendant were pertinent to Fulton County, and whether the evidence concerning Fulton County shed any light on Warren McCleskey’s death sentence as an aberrant death sentence, or whether racial considerations may have played a role in the disposition of his case.

.Because there were only ten cases involving police officer victims in Fulton County, statistical analysis could not be utilized effectively. Baldus conceded that it was difficult to draw any inference concerning the overall race effect in these cases because there had only been one death sentence. He concluded that based on the data there was only a possibility that a racial factor existed in McCleskey’s case.

Social Science Research Evidence

To some extent a broad issue before this Court concerns the role that social science is to have in judicial decisionmaking. Social science is a broad-based field consisting of many specialized discipline areas, such as psychology, anthropology, economics, political science, history and sociology. Cf. Sperlich, Social Science Evidence and the Courts: Reaching Beyond the Advisory Process, 63 Judicature 280, 283 n. 14 (1980). Research consisting of parametric and nonparametric measures is conducted under both laboratory controlled situations and uncontrolled conditions, such as real life observational situations, throughout the disciplines. The broad objectives for social science research are to better understand mankind and its institutions in order to more effectively plan, predict, modify and enhance society’s and the individual’s circumstances. Social science as a nonex-act science is always mindful that its research is dealing with highly complex behavioral patterns and institutions that exist in a highly technical society. At best, this research “models” and “reflects” society and provides society with trends and information for broad-based generalizations. The researcher’s intent is to use the conclusions from research to predict, plan, describe, explain, understand or modify. To utilize conclusions from such research to explain the specific intent of a specific behavioral situation goes beyond the legitimate uses for such research. Even when this research is at a high level of exactness, in design and results, social scientists readily admit their steadfast hesitancies to conclude such results can explain specific behavioral actions in a certain situation.

The judiciary is aware of the potential limitations inherent in such research: (1) the imprecise nature of the discipline; (2) the potential inaccuracies in presented data; (3) the potential bias of the researcher; (4) the inherent problems with the methodology; (5) the specialized training needed to assess and utilize the data competently, and (6) the debatability of the appropriateness for courts to use empirical evidence in decisionmaking. Cf Henry, Introduction: A Journey into the Future— The Role of Empirical Evidence in Developing Labor Law, 1981 U.Ill.L.Rev. 1, 4; Sperlich, 63 Judicature at 283 n. 14.

Historically, beginning with “Louis Bran-déis’ use of empirical evidence before the Supreme Court ... persuasive social science evidence has been presented to the courts.” Forst, Rhodes & Wellford, Sentencing and Social Science: Research for the Formulation of Federal Guidelines, 7 Hofstra L.Rev. 355 (1979). See Muller v. Oregon, 208 U.S. 412, 28 S.Ct. 324, 52 L.Ed. 551 (1908); Brown v. Board of Education, 347 U.S. 483, 74 S.Ct. 686, 98 L.Ed. 873 (1954). The Brandéis, brief presented social facts as corroborative in the judicial decisionmaking process. O’Brien, Of Judicial Myths, Motivations and Justifications: A Postscript on Social Science and the Law, 64 Judicature 285, 288 (1981). The Brandéis brief “is a well-known technique for asking the court to take judicial notice of social facts.” Sperlich, 63 Judicature at 280, 285 n. 31. “It does not solve the problem of how to bring valid scientific materials to the attention of the court____ Brandéis did not argue that the data were valid, only that they existed____ The main contribution ... was to make extra-legal data readily available to the court.” Id.

This Court has taken a position that social science research does play a role in judicial decisionmaking in certain situations, even in light of the limitations of such research. Statistics have been used primarily in cases addressing discrimination.

Statistical analysis is useful only to show facts. In evidentiary terms, statistical studies based on correlation are circumstantial evidence. They are not direct evidence. Teamsters v. United States, 431 U.S. 324, 340, 97 S.Ct. 1843, 1856, 52 L.Ed.2d 396 (1977). Statistical studies do not purport to state what the law is in a given situation. The law is applied to the facts as revealed by the research.

In this case the realities examined, based on a certain set of facts reduced to data, were the descriptive characteristics and numbers of persons being sentenced to death in Georgia. Such studies reveal, as circumstantial evidence through their study analyses and results, possible, or probable, relationships that may exist in the realities studied.

The usefulness of statistics obviously depends upon what is attempted to be proved by them. If disparate impact is sought to be proved, statistics are more useful than if the causes of that impact must be proved. Where intent and motivation must be proved, the statistics have even less utility. This Court has said in discrimination cases, however, “that while statistics alone usually cannot establish intentional discrimination, under certain limited circumstances they might.” Spencer v. Zant, 715 F.2d 1562, 1581 (11th Cir.1983), on pet. for reh’g and for reh’g en banc, 729 F.2d 1293 (11th Cir.1984). See also Eastland v. Tennessee Valley Authority, 704 F.2d 613, 618 (11th Cir.1983); Johnson v. Uncle Ben’s, Inc., 628 F.2d 419, 421 (5th Cir.1980), cert. denied, 459 U.S. 967, 103 S.Ct. 293, 74 L.Ed.2d 277 (1982). These limited circumstances are where the statistical evidence of racially disproportionate impact is so strong as to permit no inference other than that the results are the product of a racially discriminatory intent or purpose. See Smith v. Balkcom, 671 F.2d 858 (5th Cir. Unit B), cert. denied, 459 U.S. 882, 103 S.Ct. 181, 74 L.Ed.2d 148 (1982).

Statistical evidence has been received in two ways. The United States Supreme Court has simply recognized the existence of statistical studies and social science research in making certain decisions, without such studies being subject to the rigors of an evidentiary hearing. Muller v. Oregon, 208 U.S. 412, 28 S.Ct. 324, 52 L.Ed. 551 (1908); Fowler v. North Carolina, 428 U.S. 904, 96 S.Ct. 3212, 49 L.Ed.2d 1212 (1976); Woodson v. North Carolina, 428 U.S. 280, 96 S.Ct. 2978, 49 L.Ed.2d 944 (1976); Jurek v. Texas, 428 U.S. 262, 96 S.Ct. 2950, 49 L.Ed.2d 929 (1976); Proffitt v. Florida, 428 U.S. 242, 96 S.Ct. 2960, 49 L.Ed.2d 913 (1976); Gregg v. Georgia, 428 U.S. 153, 96 S.Ct. 2909, 49 L.Ed.2d 859 (1976). The “Supreme Court, for example, encountered severe criticism and opposition to its rulings on desegregation of public schools, the exclusionary rule, and the retroactivity of its decisions, precisely because the court relied on empirical generalization.” O’Brien, The Seduction of the Judiciary: Social Science and the Courts, 64 Judicature 8,19 (1980). In each of these situations the Court “focused” beyond the specifics of the case before it to the “institutions” represented and through a specific ruling effected changes in the institutions. On the other hand, statistical evidence may be presented in the trial court through direct testimony and cross-examination on statistical information that bears on an issue. Such evidence is examined carefully and subjected to the tests of relevancy, authenticity, probativeness and credibility. Cf. Henry, 1981 U.Ill.L.Rev. at 8.

One difficulty with statistical evidence is that it may raise more questions than it answers. This Court reached that conclusion in Wilkins v. University of Houston, 654 F.2d 388 (5th Cir. Unit A 1981). In Wilkins this Court held that “[mjultiple regression analysis is a relatively sophisticated means of determining the effects that any number of different factors have on a particular variable.” Id. at 402-03. This Court noted that the methodology “is subject to misuse and thus must be employed with great care.” Id. at 403. Procedurally, when multiple regression is used “it will be the subject of expert testimony and knowledgeable cross-examination from both sides. In this manner, the validity of the model and the significance of its results will be fully developed at trial, allowing the trial judge to make an informed decision as to the probative value of the analysis.” Id. Having done this, the Wilkins Court, in an employment discrimination case, held “the statistical evidence associated with the multiple regression analysis is inconclusive, raising more questions than it answers.” Id.

Even if the statistical evidence is strong there is generally a need for additional evidence. In Wade v. Mississippi Cooperative Extension Serv., 528 F.2d 508 (5th Cir.1976), the results drawn from the multivariate regression analysis were supported by additional evidence. Id. at 517. In Wade the statistics did not “stand alone” as the sole proof of discrimination.

Much has been written about the relationship of law and social science. “If social science cannot produce the required answers, and it probably cannot, its use is likely to continue to lead to a disjointed incrementalism.” Daniels, Social Science And Death Penalty Cases, 1 Law & Pol’y Q. 336, 367 (1979). “Social science can probably make its greatest contribution to legal theory by investigating the causal forces behind judicial, legislative and administrative decisionmaking and by probing the general effects of such decisions.” Na-gel, Law And The Social Sciences: What Can Social Science Contribute?, 356 A.B. A.J. 356, 357-58 (1965).

With these observations, this Court accepts social science research for what the social scientist should claim for it. As in all circumstantial evidence cases, the inferences to be drawn from the statistics are for the factfinder, but the statistics are accepted to show the circumstances.

Racial Discrimination, the Death Penalty, and the Constitution

McCleskey contends his death sentence is unconstitutional because Georgia’s death penalty is discriminatorily applied on the basis of the race of the defendant and the victim. Several different constitutional bases for this claim have been asserted. McCleskey relies on the arbitrary, capricious and irrational components of the prohibition of cruel and unusual punishment in the Eighth Amendment and the equal protection clause of the Fourteenth Amendment. The district court thought that with respect to race-of-the-victim discrimination the petitioner more properly stated a claim under the due process clause of the Fourteenth Amendment.

Claims of this kind are seldom asserted with a degree of particularity, and they generally assert several constitutional precepts. On analysis, however, there seems to be little difference in the proof that might be required to prevail under any of the three theories.

In Furman v. Georgia, 408 U.S. 238, 92 S.Ct. 2726, 33 L.Ed.2d 346 (1972), the Supreme Court struck down the Georgia death penalty system on Eighth Amendment grounds, with several of the concurring justices holding that the system operated in an arbitrary and capricious manner because there was no rational way to distinguish the few cases in which death was imposed from the many in which it was not. Id. at 313, 92 S.Ct. at 2764 (White, J., concurring); id. at 309-10, 92 S.Ct. at 2762-63 (Stewart, J. concurring). Although race discrimination in the imposition of the death penalty was not the basis of the decision, it was one of several concerns addressed in both the concurring and dissenting opinions. See id. at 249-52, 92 S.Ct. at 2731-33 (Douglas, J. concurring); id. at 309-10, 92 S.Ct. at 2762-63 (Stewart, J. concurring); id. at 364-65, 92 S.Ct. at 2790-91 (Marshall, J., concurring); id. at 389-90 n. 12, 92 S.Ct. at 2803-04 n. 12 (Burger, C.J., dissenting); id. at 449, 92 S.Ct. at 2833 (Powell, J., dissenting).

Four years later, the Supreme Court approved the redrawn Georgia statute pursuant to which McCleskey was tried and sentenced. Gregg v. Georgia, 428 U.S. 153, 96 S.Ct. 2909, 49 L.Ed.2d 859 (1976). At the same time the Court approved statutes from Florida and Texas which, like Georgia, followed a guided discretion approach, but invalidated the mandatory sentencing procedure of North Carolina and Louisiana. Proffitt v. Florida, 428 U.S. 242, 96 S.Ct. 2960, 49 L.Ed.2d 913 (1976); Jurek v. Texas, 428 U.S. 262, 96 S.Ct. 2950, 49 L.Ed.2d 929 (1976); Woodson v. North Carolina, 428 U.S. 280, 96 S.Ct. 2978, 49 L.Ed.2d 944 (1976); Roberts v. Louisiana, 428 U.S. 325, 96 S.Ct. 3001, 49 L.Ed.2d 974 (1976).

Since Gregg, we have consistently held that to state a claim of racial discrimination in the application of a constitutional capital statute, intent and motive must be alleged. Sullivan v. Wainwright, 721 F.2d 316, 317 (11th Cir.1983) (statistical impact studies insufficient to show state system “intentionally discriminated against petitioner”), petition for stay of execution denied, 464 U.S. 109, 104 S.Ct. 450, 78 L.Ed.2d 210 (1983); Adams v. Wainwright, 709 F.2d 1443, 1449 (11th Cir.1983) (requiring “a showing of an intent to discriminate” or “evidence of disparate impact ... so strong that the only permissible inference' is one of intentional discrimination”), cert. denied, — U.S. —104 S.Ct. 745, 79 L.Ed.2d 203 (1984); Smith v. Balkcom, 671 F.2d 858, 859 (5th Cir.Unit B) (requiring “circumstantial or statistical evidence of racially disproportionate impact ... so strong that the results permit no other inference but that they are the product of a racially discriminatory intent or purpose”), cert. denied, 459 U.S. 882, 103 S.Ct. 181, 74 L.Ed.2d 148 (1982).

Initially in Spinkellink v. Wainwright, 578 F.2d 582 (5th Cir.1978), cert. denied, 440 U.S. 976, 99 S.Ct. 1548, 59 L.Ed.2d 796 (1979), the Court rejected Eighth and Fourteenth Amendment claims that the Florida death penalty was being applied in a discriminatory fashion on the basis of the victim’s race. The Spinkellink Court read Gregg and its companion cases “as holding that if a state follows a properly drawn statute in'imposing the death penalty, then the arbitrariness and capriciousness — and therefore the racial discrimination condemned in Furman — have been conclusively removed.” Id. at 613-14. Spinkellink can not be read to foreclose automatically all Eighth Amendment challenges to capital sentencing conducted under a facially constitutional statute. In Godfrey v. Georgia, 446 U.S. 420,100 S.Ct. 1759, 64 L.Ed.2d 398 (1980), the Supreme Court sustained an Eighth Amendment challenge to a Georgia death sentence because the Georgia court’s construction of a portion of that facially valid statute left no principled way to distinguish the cases where the death penalty was imposed from those in which it was not. See Proffitt v. Wainwright, 685 F.2d 1227, 1261 n. 52 (11th Cir.1982). Nevertheless, neither Godfrey nor Proffitt undermines this Court’s prior and subsequent pronouncements in Spinkellink, Smith, Adams, and Sullivan regarding the amount of disparate impact that must be shown under either an Eighth Amendment or equal protection analysis.

As the district court here pointed out, such a standard indicates an analytical nexus between Eighth Amendment claims and a Fourteenth Amendment equal protection claim. McCleskey v. Zant, 580 F.Supp. 338, 347 (N.D.Ga.1984). Where an Eighth Amendment claim centers around generalized showings of disparate racial impact in capital sentencing, such a connection is inescapable. Although conceivably the level or amount of disparate racial impact that would render a state’s capital sentencing system arbitrary and capricious under the Eighth Amendment might differ slightly from the level or amount of disparate racial impact that would compel an inference of discriminatory intent under the equal protection clause of the Fourteenth Amendment, we do not need to decide whether there could be a difference in magnitude that would lead to opposite conclusions on a system’s constitutionality depending on which theory a claimant asserts.

A successful Eighth Amendment challenge would require proof that the race factor was operating in the system in such a pervasive manner that it could fairly be said that the system was irrational, arbitrary and capricious. For the same reasons that the Baldus study would be insufficient to demonstrate discriminatory intent or unconstitutional discrimination in the Fourteenth Amendment context, it would be insufficient to show irrationality, arbitrariness and capriciousness under any kind of Eighth Amendment analysis.

The district court stated that were it writing on a clean slate, it would characterize McCleskey’s claim as a due process claim. The court took the position that McCleskey’s argument, while couched in terms of “arbitrary and capricious,” fundamentally contended that the Georgia death penalty was applied on the basis of a morally impermissible criterion: the race of the victim.

The district court’s theory derives some support from the Supreme Court’s decision in Zant v. Stephens, 462 U.S. 862, 103 S.Ct. 2733, 77 L.Ed.2d 235 (1983). The Court there recognized that a state may not attach the “aggravating” label as an element in capital sentencing to factors that are constitutionally impermissible or totally irrelevant to the sentencing process, such as race. If that were done, the Court said, “due process would require that the jury’s decision to impose death be set aside.” Id. 462 U.S. at —, 103 S.Ct. at 2747, 77 L.Ed.2d at 255. From this language it is clear that due process would prevent a state from explicitly making the murder of a white victim an aggravating circumstance in capital sentencing. But where the statute is facially neutral, a due process claim must-be supported by proof that a state, through its prosecutors, jurors, and judges, has implicitly attached the aggravating label to race.

Even if petitioner had characterized his claim as one under the due process clause, it would not have altered the legal standard governing the showing he must make to prevail. The application of the due process clause is “an uncertain enterprise which must discover what ‘fundamental fairness’ consists of in a particular situation by first considering any relevant precedents and then by assessing the several interests that are at stake.” Lassiter v. Department of Social Services, 452 U.S. 18, 24-25, 101 S.Ct. 2153, 2158-2159, 68 L.Ed.2d 640 (1981). Due process also requires the assessment of the risk that the procedures being used will lead to erroneous decisions. Mathews v. Eldridge, 424 U.S. 319, 335, 96 S.Ct. 893, 903, 47 L.Ed.2d 18 (1976). Where a due process claim requires a court to determine whether the race of the victim impermissibly affected the capital sentencing process, decisions under the equal protection clause, characterized as “central to the Fourteenth Amendment’s prohibition of discriminatory action by the State,” Rose v. Mitchell, 443 U.S. 545, 554-55, 99 S.Ct. 2993, 2999-3000, 61 L.Ed.2d 739 (1979), are certainly “relevant precedents” in the assessment of the risk of erroneous decisions. Thus, as in the equal protection context, the claimant under a due process theory must present evidence which establishes that in the capital sentencing process race “is a motivating factor in the decision.” Village of Arlington Heights v. Metropolitan Housing Development Corp., 429 U.S. 252, 266, 97 S.Ct. 555, 563, 50 L.Ed.2d 450 (1977).

Due process and cruel and unusual punishment cases do not normally focus on the intent of the governmental actor. But where racial discrimination is claimed, not on the basis of procedural faults or flaws in the structure of the law, but on the basis of' the decisions made within that process, then purpose, intent and motive are a natural component of the proof that discrimination actually occurred.

The Supreme Court has clearly held that to prove a constitutional claim of racial discrimination in the equal protection context, intent, purpose, and motive are necessary components. Washington v. Davis, 426 U.S. 229, 238-42, 96 S.Ct. 2040, 2046-49, 48 L.Ed.2d 597 (1976). A showing of a disproportionate impact alone is not sufficient to prove discriminatory intent unless no other reasonable inference can be drawn. Arlington Heights, 429 U.S. at 264-66, 97 S.Ct. at 562-64. This Circuit has consistently applied these principles of law. Adams v. Wainwright, 709 F.2d 1443, 1449 (11th Cir.1983), cert. denied, — U.S. —, 104 S.Ct. 745, 79 L.Ed.2d 203 (1984); Sullivan v. Wainwright, 721 F.2d 316, 317 (11th Cir.1983).

We, therefore, hold that proof of a disparate impact alone is insufficient to invalidate a capital sentencing system, unless that disparate impact is so great that it compels a conclusion that the system is unprincipled, irrational, arbitrary and capricious such that purposeful discrimination— i.e., race is intentionally being used as a factor in sentencing — can be presumed to permeate the system.

Generalized Statistical Studies and the Constitutional Standard

The question initially arises as to whether any statewide study suggesting a racial disparity in the application of a state’s death penalty could ever support a constitutional attack on a defendant’s sentence. The answer lies in whether the statistical study is sufficient evidence of the ultimate fact which must be shown.

In Smith v. Balkcom, 671 F.2d 858, 859 (5th Cir.Unit B), cert. denied, 459 U.S. 882, 103 S.Ct. 181, 74 L.Ed.2d 148 (1982), this Court said:

In some instances, circumstantial or statistical evidence of racially disproportionate impact may be so strong that the results permit no other inference but that they are the product of a racially discriminatory intent or purpose.

This statement has apparently caused some confusion because it is often cited as a proposition for \vhich it does not stand. Petitioner argues that his statistical study shows a strong inference that there is a disparity based on race. That is only the first step, however. The second step focuses on how great the disparity is. Once the disparity is proven, the question is whether-that disparity is sufficient to compel a conclusion that it results from discriminatory intent and purpose. The key to the problem lies in the principle that the proof, no matter how strong, of some disparity is alone insufficient.

In Spinkellink v. Wainwright, 578 F.2d 582, 612 (5th Cir.1978), cert. denied, 440 U.S. 976, 99 S.Ct. 1548, 59 L.Ed.2d 796 (1979), the petitioner claimed the Florida statute was being applied in a discriminatory fashion against defendants murdering whites, as opposed to blacks, in violation of the cruel and unusual punishment and equal protection components of the Constitution. Evidence of this disparity was introduced through expert witnesses. The court assumed for sake of argument the accuracy of petitioner’s statistics but rejected the Eighth Amendment argument. The court rejected the equal protection argument because the disparity shown by petitioner’s statistics could not prove racially discriminatory intent or purpose as required by Washington v. Davis, 426 U.S. 229, 96 S.Ct. 2040, 48 L.Ed.2d 597 (1976), and Village of Arlington Heights v. Metropolitan Housing Development Corp., 429 U.S. 252, 97 S.Ct. 555, 50 L.Ed.2d 450 (1977). 578 F.2d at 614-16.

In Adams v. Wainwright, 709 F.2d 1443 (11th Cir.1983), cert. denied, — U.S.—, 104 S.Ct. 745, 79 L.Ed.2d 203 (1984), the court, in denying an evidentiary hearing, accepted statistics which arguably tended to support the claim that the Florida death penalty was imposed disproportionately in cases involving white victims. The court then said:

Disparate impact alone is insufficient to establish a violation of the fourteenth amendment. There must be a showing of an intent to discriminate____ Only if the evidence of disparate impact is so strong that the only permissible inference is one of intentional discrimination will it alone suffice.

709 F.2d at 1449 (citations omitted). Here again, in commenting on the strength of the evidence, the court was referring not to the amount or quality of evidence which showed a disparate impact, but the amount of disparate impact that would be so strong as to lead inevitably to a finding of motivation and intent, absent some other explanation for the disparity.

In commenting on the proffer of the Bal-dus study in another case, Justice Powell wrote in dissent from a stay of execution pending en banc consideration of this case:

If the Baldus study is similar to the several studies filed with us in Sullivan v. Wainwright, 464 U.S. 109, 104 S.Ct. 450,78 L.Ed.2d 210 (1983), the statistics in studies of this kind, many of which date as far back as 1948, are merely general statistical surveys that are hardly particularized with respect to any alleged “intentional” racial discrimination. Surely, no contention can be made that the entire Georgia judicial system, at all levels, operates to discriminate in all cases. Arguments to this effect may have been directed to the type of statutes addressed in Furman v. Georgia, 408 U.S. 238 [92 S.Ct. 2726, 33 L.Ed.2d 346] (1972). As our subsequent cases make clear, such arguments cannot be taken seriously under statutes approved in Gregg.

Stephens v. Kemp, 464 U.S. 1027,1030, n. 2, 104 S.Ct. 562, 564 n. 2, 78 L.Ed.2d 370, 374 n. 2 (1984) (Powell, J., dissenting).

The lesson from these and other cases must be that generalized statistical studies are of little use in deciding whether a particular defendant has been unconstitutionally sentenced to death. As to whether the system can survive constitutional attack, statistical studies at most are probative of how much disparity is present, but it is a legal question as to how much disparity is required before a federal court will accept it as evidence of the constitutional flaws in the system.

This point becomes especially critical to a court faced with a request for an evidentia-ry hearing to produce future studies which will undoubtedly be made. Needless to say, an evidentiary hearing would be necessary to hear any evidence that a particular defendant was discriminated against because of his race. But general statistical studies of the kind offered here do not even purport to prove that fact. Aside from that kind of evidence, however, it would not seem necessary to conduct a full evi-dentiary hearing as to studies which do nothing more than show an unexplainable disparity. Generalized studies would appear to have little hope of excluding every possible factor that might make a difference between crimes and defendants, exclusive of race. To the extent there is a subjective or judgmental component to the discretion with which a sentence is invested, not only will no two defendants be seen identical by the sentencers, but no two sentencers will see a single case precisely the same. As the court has recognized, there are “countless racially neutral variables” in the sentencing of capital cases. Smith v. Balkcom, 671 F.2d at 859.

This is not to recede from the general proposition that statistical studies may reflect a disparity so great as to inevitably lead to a conclusion that the disparity results from intent or motivation. As decided by this opinion, the Baldus studies demonstrate that the Georgia system does not contain the level of disparity required to meet that constitutional standard.

Validity of the Baldus Study

The social science research of Professor Baldus purports to reveal, through statistical analysis, disparities in the sentencing of black defendants in white victim cases in Georgia. A study is valid if it measures what it purports to measure. Different studies have different levels of validity. The level of the validity of the study is directly related to the degree to which the social scientist can rely on the findings of the study as measuring what it claims to measure.

The district court held the study to be invalid because of perceived errors in the data base, the deficiencies in the models, and the multi-collinearity existing between the independent variables. We hold in this case that even if the statistical results are accepted as valid, the evidence fails to challenge successfully the constitutionality of the Georgia system. Because of this decision, it is not necessary for us to determine whether the district court was right or wrong in its faulting of the Baldus study.

The district court undertook an extensive review of the research presented. It received, analyzed and dealt with the complex statistics. The district court is to be commended for its outstanding endeavor in the handling of the detailed aspects of this case, particularly in light of the consistent arguments being made in several cases based on the Baldus study. Any decision that the results of the Baldus study justify habeas corpus relief would have to deal with the district court’s findings as to the study itself. Inasmuch as social science research has been used by appellate courts in decisionmaking, Muller v. Oregon, 208 U.S. 412, 419-21, 28 S.Ct. 324, 325-26, 52 L.Ed. 551 (1908), and has been tested like other kinds of evidence at trial, see Spink-ellink v. Wainwright, 578 F.2d 582, 612-13 (5th Cir.1978), there is a question as to the standard of review of a trial court’s finding based on a highly complex statistical study.

Findings of fact are reviewed under the clearly erroneous standard which the Supreme Court has defined as: “[a] finding is ‘clearly erroneous’ when although there is evidence to support it, the reviewing court on the entire evidence is left with the definite and firm conviction that a mistake has been committed.” United States v. United States Gypsum Co., 333 U.S. 364, 395, 68 S.Ct. 525, 542, 92 L.Ed. 746 (1948).

Whether a disparate impact reflects an intent to discriminate is an ultimate fact which must be reviewed under the clearly erroneous standard. Pullman-Standard v. Swint, 456 U.S. 273, 102 S.Ct. 1781, 72 L.Ed.2d 66 (1982). In Pullman, the Supreme Court said that Fed.R.Civ.P. 52(a)

does not make exceptions or purport to exclude certain categories of factual findings from the obligation of a court of appeals to accept a district court’s findings unless clearly erroneous. It does not divide facts into categories; in particular, it does not divide findings of fact into those that deal with ‘ultimate’ and those that deal with ‘subsidiary’ facts.

456 U.S. at 287, 102 S.Ct. at 1789.

There would seem to be two levels of findings based on statistical evidence that must be reviewed: first, the finding concerning the validity of the study itself, and second, the finding of ultimate fact based upon the circumstantial evidence revealed by the study, if valid.

The district court here found the study invalid. The court found the statistics of the study to be particularly troublesome in the areas of the data base, the models and the relationship between the independent variables. McCleskey v. Zant, 580 F.Supp. 338, 379 (N.D.Ga.1984). We pretermit a review of this finding concerning the validity of the study itself. The district court went on to hold that even if the statistics did validly reflect the Georgia system, the ultimate fact of intent to discriminate was not proven. We review this finding of fact by assuming the validity of the study and rest our holding on the decision that the study, even if valid, not only supports the district judge’s decision under the clearly erroneous standard of review, but compels it.

Sufficiency of Baldus Study

McCleskey argues that, although the post-Furman statute in Georgia now yields more predictable results, the race of the victim is a significant, but of course impermissible, factor which accounts for the imposition of the death penalty in many cases. He supports this argument with the sophisticated Baldus statistical study that, after controlling for the legitimate factors that might rationally explain the imposition of the penalty, purportedly reveals significant race-of-the-victim influence in the system; i.e., all other things being equal, white victim crimes are more likely to result in the penalty. Because the Constitution prohibits the consideration of racial factors as justification for the penalty, McCleskey asserts that the discernible racial influence on sentencing renders the operation of the Georgia system infirm.

In addition, McCleskey asserts that the race-of-the-victim influence on the system is particularly significant in the range of cases involving intermediate levels of aggravation (mid-range aggravation cases). He argues that because his case fell within that range, he has established that impermissible racial considerations operated in his case.

We assume without deciding that the Baldus study is sufficient to show what it purports to reveal as to the application of the Georgia death penalty. Baldus concluded that his 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.

A general comment about the limitations on what the Baldus study purports to show, although covered in the subsequent discussion, may be helpful. The Baldus study statistical evidence does not purport to show that McCleskey was sentenced to death because of either his race or the race of his victim. It only shows that in a group involving blacks and whites, all of whose cases are virtually the same, there would be more blacks receiving the death penalty than whites and more murderers of whites receiving the death penalty than murderers of blacks. The statisticians’ “best guess” is that race was a factor in those cases and has a role in sentencing structure in Georgia. These general statements about the results are insufficient to make a legal determination. An analysis must be made as to how much disparity is actually shown by the research.

Accepting the Baldus figures, but not the general conclusion, as accurately reflecting the Georgia experience, the statistics are inadequate to entitle McCleskey to relief on his constitutional claim.

The Georgia-based retrospective study consisted of a stratified random sample of 1,066 cases of individuals indicted for murder-death, murder-life and voluntary manslaughter who were arrested between March 28, 1973 and December 31, 1978. The data were compiled from a 41-page questionnaire and consisted of more than 500,000 entries. Through complex statistical analysis, Baldus examined relationships between the dependent variable, death-sentencing rate, and independent variables, nine aggravating and 75 mitigating factors, while controlling for background factors. In 10% of the cases a penalty trial was held, and in 5% of the cases defendants were sentenced to death.

The study subjects the Georgia data to a multitude of statistical analyses, and under each method there is a statistically significant race-of-the-victim effect operating statewide. It is more difficult, however, to ascertain the magnitude of the effect demonstrated by the Baldus study. The simple, unadjusted figures show that death sentences were imposed in 11% of the white victim cases potentially eligible for the death penalty, and in 1% of the eligible black victim cases. After controlling for various legitimate factors that could explain the differential, Baldus still concluded that there was a significant race-of-the-victim effect. The result of Baldus’ most conclusive model, on which McCleskey primarily relies, showed an effect of .06, signifying that on average a white victim crime is 6% more likely to result in the sentence than a comparable black victim crime. Bal-dus also provided tables that showed the race-of-the-victim effect to be most significant in cases involving intermediate levels of aggravation. In these cases, on average, white victim crimes were shown to be 20% more likely to result in the death penalty than equally aggravated black victim crimes.

None of the figures mentioned above is a definitive quantification of the influence of the victim’s race on the overall likelihood of the death penalty in a given case. Nevertheless, the figures all serve to enlighten us somewhat on how the system operates. The 6% average figure is a composite of all cases and contains both low aggravation cases, where the penalty is almost never imposed regardless of the victim’s race, and high aggravation cases, where both white and black victim crimes are likely to result in the penalty. When this figure is related to tables that classify eases according to the level of aggravation, the 6% average figure is properly seen as an aggregate containing both cases in which race of the victim is a discernible factor and those in which it is not.

McCleskey’s evidence, and the evidence presented by the state, also showed that the race-of-the-victim factor diminishes as more variables are added to the model. For example, the bottom line figure was 17% in the very simple models, dropped to 6% in the 230-variable model, and finally fell to 4% when the final 20 variables were added and the effect of Georgia Supreme Court review was considered.

The statistics are also enlightening on the overall operation of the legitimate factors supporting the death sentence. The Baldus study revealed an essentially rational system, in which high aggravation cases were more likely to result in the death sentence than low aggravation cases. As one would expect in a rational system, factors such as torture and multiple victims greatly increased the likelihood of receiving the penalty.

There are important dimensions that the statistics cannot reveal. Baldus testified that the Georgia death penalty system is an extremely complicated process in which no single factor or group of factors determines the outcome of a given case. No single petitioner could, on the basis of these statistics alone, establish that he received the death sentence because, and only because, his victim was white. Even in the mid-range of cases, where the race-of-the-victim influence is said to be strong, legitimate factors justifying the penalty are, by the very definition of the mid-range, present in each case.

The statistics show there is a race-of-the-victim relationship with the imposition of the death sentence discernible in enough cases to be statistically significant in the system as a whole. The magnitude cannot be called determinative in any given case.

The evidence in the Baldus study seems to support the Georgia death penalty system as one operating in a rational manner. Although no single factor, or combination of factors, will irrefutably lead to the death sentence in every case, the system in operation follows the pattern the legislature intended, which the Supreme Court found constitutional in Gregg, and sorts out cases according to levels of aggravation, as gauged by legitimate factors. The fundamental Eighth Amendment concern of Fur-man, as discussed in Gregg, which states that “there is no meaningful basis for distinguishing the few cases in which [the death sentence] is imposed from the many in which it is not” does not accurately describe the operation of the Georgia statute. 428 U.S. at 188, 96 S.Ct. at 2932.

Taking the 6% bottom line revealed in the Baldus figures as true, this figure is not sufficient to overcome the presumption that the statute is operating in a constitutional manner. In any discretionary system, some imprecision must be tolerated, and the Baldus study is simply insufficient to support a ruling, in the context of a statute that is operating much as intended, that racial factors are playing a role in the outcome sufficient to render the system as a whole arbitrary and capricious.

This conclusion is supported, and possibly even compelled, by recent Supreme Court opinions in Sullivan v. Wainwright, 464 U.S. 109, 104 S.Ct. 450, 78 L.Ed.2d 210 (1983) (denying stay of execution to allow evidentiary hearing on Eighth Amendment claim supported by statistics); Wainwright v. Adams, — U.S.—, 104 S.Ct. 2183, 80 L.Ed.2d 809 (1984) (vacating stay); and Wainwright v. Ford, — U.S. —, 104 S.Ct. 3498, 82 L.Ed.2d 911 (1984) (denying state’s application to vacate stay on other grounds). A plurality of the Court in Ford definitively stated that it had held “in two prior cases that the statistical evidence relied upon by Ford to support his claim of discrimination was not sufficient to raise a substantial ground upon which relief might be granted.” Id. at —, 104 S.Ct. at 3499, 82 L.Ed.2d at 912 (citing Sullivan and Adams). The petitioners in Sullivan, Adams, and Ford all relied on the study by Gross and Mauro of the Florida death penalty system. The bottom line figure in the Gross and Mauro study indicated a race-of-the-victim effect, quantified by a “death odds multiplier,” of about 4.8 to 1. Using a similar methodology, Baldus obtained a death odds multiplier of 4.3 to 1 in Georgia.

It is of course possible that the Supreme Court was rejecting the methodology of the Florida study, rather than its bottom line. It is true that the methodology of the Bal-dus study is superior. The posture of the Florida cases, however, persuades this Court that the Supreme Court was not relying on inadequacies in the methodology of the Florida study. The issue in Sullivan, Adams, and Ford was whether the petitioner’s proffer had raised a substantial ground sufficient to warrant an evidentiary hearing. In that context, it is reasonable to suppose that the Supreme Court looked at the bottom line indication of racial effect and held that it simply was insufficient to state a claim. A contrary assumption, that the Supreme Court analyzed the extremely complicated Gross and Mauro study and rejected it on methodological grounds, is much less reasonable.

Thus, assuming that the Supreme Court in Sullivan, Adams and Ford found the bottom line in the Gross and Mauro study insufficient to raise a constitutional claim, we would be compelled to reach the same result in analyzing the sufficiency of the comparable bottom line in the Baldus study on which McCleskey relies.

McCleskey’s argument about the heightened influence of the race-of-the-victim factor in the mid-range of cases requires a somewhat different analysis. McCleskey’s case falls within the range of cases involving intermediate levels of aggravation. The Baldus statistical study tended to show that the race-of-the-victim relationship to sentencing outcome was greater in these cases than in cases involving very low or very high levels of aggravation.

The race-of-the-victim effect increases the likelihood of the death penalty by approximately 20% in the mid-range of cases. Some analysis of this 20% figure is appropriate.

The 20% figure in this case is not analogous to a figure reflecting the percentage disparity in a jury composition case. Such a figure represents the actual disparity between the number of minority persons on the jury venire and the number of such persons in the population. In contrast, the 20% disparity in this case does not purport to be an actual disparity. Rather, the figure reflects that the variables included in the study do not adequately explain the 20% disparity and that the statisticians can explain it only by assuming the racial effect. More importantly, Baldus did not testify that he found statistical significance in the 20% disparity figure for mid-range cases, and he did not adequately explain the rationale of his definition of the mid-range of cases. His testimony leaves this Court unpersuaded that there is a rationally classified, well-defined class of cases in which it can be demonstrated that a race-of-the-victim effect is operating with a magnitude approximating 20%.

v Assuming arguendo, however, that the 20% disparity is an accurate figure, it is apparent that such a disparity only in the mid-range cases, and not in the system as a whole, cannot provide the basis for a systemwide challenge. As previously discussed, the system as a whole is operating in a rational manner, and not in a manner that can fairly be labeled arbitrary or capricious. A valid system challenge cannot be made only against the mid-range of cases. Baldus did not purport to define the mid-range of cases; nor is such a definition possible. It is simply not satisfactory to say that the racial effect operates in “close cases” and therefore that the death penalty will be set aside in “close cases.”

As discussed previously, the statistics cannot show that the race-of-the-victim factor operated in a given case, even in the mid-range. Rather, the statistics show that, on average, the race-of-the-victim factor was more likely to affect the outcome in mid-range cases than in those cases at the high and low ends of the spectrum of aggravation. The statistics alone are insufficient to show. that McCleskey’s sentence was determined by the race of his victim, or even that the race of his victim contributed to the imposition of the penalty in his case.

McCleskey’s petition does not surmount the threshold burden of stating a claim on this issue. Aside from the statistics, he presents literally no evidence that might tend to support a conclusion that the race of McCleskey’s victim in any way motivated the jury to impose the death sentence in his case.

Conclusion

The Supreme Court has held that to be constitutional the sentencer in death sentence cases must have some measure of discretion. Gregg v. Georgia, 428 U.S. 153, 96 S.Ct. 2909, 49 L.Ed.2d 859 (1976); Prof-fitt v. Florida, 428 U.S. 242, 96 S.Ct. 2960, 49 L.Ed.2d 913 (1976). The mandatory death sentence statutes were declared unconstitutional. Woodson v. North Carolina, 428 U.S. 280, 96 S.Ct. 2978, 49 L.Ed.2d 944 (1976); Roberts v. Louisiana, 428 U.S. 325, 96 S.Ct. 3001, 49 L.Ed.2d 974 (1976).

The very exercise of discretion means that persons exercising discretion may reach different results from exact duplicates. Assuming each result is within the range of discretion, all are correct in the eyes of the law. It would not make sense for the system to require the exercise of discretion in order to be facially constitutional, and at the same time hold a system unconstitutional in application where that discretion achieved different results for what appear to be exact duplicates, absent the state showing the reasons for the difference. The discretion is narrow, focused and directed, but still there is a measure of discretion.

The Baldus approach, however, would take the cases with different results on what are contended to be duplicate facts, where the differences could not be otherwise explained, and conclude that the different result was based on race alone. From a legal perspective, petitioner would argue that since the difference is not explained by facts which the social scientist thinks satisfactory to explain the differences, there is a prima facie case that the difference was based on unconstitutional factors, and the burden would shift to the state to prove the difference in results from constitutional considerations. This approach ignores the realities. It not only ignores quantitative differences in cases: looks, age, personality, education, profession, job, clothes, demeanor, and remorse, just to name a few, but it is incapable of measuring qualitative differences of such things as aggravating and mitigating factors. There are, in fact, no exact duplicates in capital crimes and capital defendants. The type of research submitted here tends to show which of the directed factors were effective, but is of restricted use in showing what undirected factors control the exercise of constitutionally required discretion.

It was recognized when Gregg was decided that the capital justice system would not be perfect, but that it need not be perfect in order to be constitutional. Justice White said:

Petitioner has argued, in effect, that no matter how effective the death penalty may be as a punishment, government, created and run as it must be by humans, is inevitably incompetent to administer it. This cannot be accepted as a proposition of constitutional law. Imposition of the death penalty is surely an awesome responsibility for any system of justice and those who participate in it. Mistakes will be made and discriminations will occur which will be difficult to explain. However, one of society’s most basic tasks is that of protecting the lives of its citizens and one of the most basic ways in which it achieves the task is through criminal laws against murder.

Gregg v. Georgia, 428 U.S. 153, 226, 96 S.Ct. 2909, 2949, 49 L.Ed.2d 859 (1976) (White, J., concurring).

The plurality opinion of the Gregg Court noted:

The petitioner’s argument is nothing more than a veiled contention that Fur-man indirectly outlawed capital punishment by placing totally unrealistic conditions on its use. In order to repair the alleged defects pointed to by the petitioner, it would be necessary to require that prosecuting authorities charge a capital offense whenever arguably there had been a capital murder and that they refuse to plea bargain with the defendant. If a jury refused to convict even though the evidence supported the charge, its verdict would have to be reversed and a verdict of guilty entered or a new trial ordered, since the discretionary act of jury nullification would not be permitted. Finally, acts of executive clemency would have to be prohibited. Such a system, of course, would be totally alien to our notions of criminal justice.

Id. at 199 n. 50, 96 S.Ct. at 2937 n. 50 (opinion of Stewart, Powell, and Stevens, JJ.).

Viewed broadly, it would seem that the statistical evidence presented here, assuming its validity, confirms rather than condemns the system. In a state where past discrimination is well documented, the study showed no discrimination as to the race of the defendant. 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 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.

The district court properly rejected this aspect of McCleskey’s claim.

INEFFECTIVE ASSISTANCE OF COUNSEL

McCleskey contends his trial counsel rendered ineffective assistance at both guilt/innocence and penalty phases of his trial in violation of the Sixth Amendment.

Although a defendant is constitutionally entitled to reasonably effective assistance from his attorney, we hold that McCleskey has not shown he was prejudiced by the claimed defaults in his counsel’s performance. Ineffective assistance warrants reversal of a conviction only when there is a reasonable probability that the attorney’s errors altered the outcome of the proceeding. A court may decide an ineffectiveness claim on the ground of lack of prejudice without considering the reasonableness of the attorney’s performance. Strickland v. Washington, — U.S.—, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984).

As to the guilt phase of his trial, McCles-key claims that his attorney failed to: (1) interview the prisoner who testified that McCleskey gave a jail house confession; (2) interview and subpoena as defense witnesses the victims of the Dixie Furniture Store robbery; and (3) interview the State’s ballistics expert.

McCleskey demonstrates no prejudice caused by his counsel’s failure to interview Offie Evans. We have held there was no reasonable likelihood that the disclosure of the detective’s statement to Offie Evans would have affected the verdict. There is then no “reasonable probability” that the attorney’s failure to discover this evidence affected the verdict.

As to the robbery victims, McCleskey does not contend that an in-person interview would have revealed something their statements did not. He had an opportunity to cross-examine several of the robbery victims and investigating officers at McCleskey’s preliminary hearing. The reasonableness of the attorney’s investigation need not be examined because there was obviously no prejudice.

The question is whether it was unreasonable not to subpoena the robbery victims as defense witnesses. McCleskey’s attorney relied primarily on an alibi defense at trial. To establish this defense, the attorney put McCleskey on the stand. He also called several witnesses in an attempt to discredit a Dixie Furniture Store employee’s identification of McCleskey and to show that McCleskey’s confession was involuntary. It would have undermined his defense if the attorney had called witnesses to testify as to which robber did the shooting. No prejudice can be shown by failing to subpoena witnesses as a reasonable strategy decision.

McCleskey’s attorney could have reasonably prepared to cross-examine the State’s ballistics expert by reading the expert’s report. No in-person interview was necessary. See Washington v. Watkins, 655 F.2d 1346, 1358 (5th Cir.1981), cert. denied, 456 U.S. 949, 102 S.Ct. 2021, 72 L.Ed.2d 474 (1982). The report was in the prosecutor’s file which the attorney reviewed and no contention has been made that he did not read it.

As to the sentencing phase of his trial, McCleskey asserts his attorney failed to investigate and find character witnesses and did not object to the State’s introduction of prior convictions which had been set aside.

No character witnesses testified for McCleskey at his trial. At the State habeas corpus hearing McCleskey’s attorney testified he talked with both McCleskey and his sister about potential character witnesses. They suggested no possibilities. The sister refused to testify and advised the attorney that their mother was too sick to travel to the site of the trial. McCleskey and his sister took the stand at the State habeas corpus hearing and told conflicting stories. It is clear from the state court’s opinion that it believed the attorney:

Despite the conflicting evidence on his point, ... the Court is authorized in its role as fact finder to conclude that Counsel made all inquiries necessary to present an adequate defense during the sentencing phase. Indeed, Counsel could not present evidence that did not exist.

Although this “finding of fact” is stated in terms of the ultimate legal conclusion, implicit in that conclusion is the historical finding that the attorney’s testimony was credible. See Paxton v. Jarvis, 735 F.2d 1306, 1308 (11th Cir.1984); Cox v. Montgomery, 718 F.2d 1036 (11th Cir.1983). This finding of fact is entitled to a presumption of correctness. Based on the facts as testified to by the attorney, he conducted a reasonable investigation for character witnesses.

As evidence of an aggravating circumstance the prosecutor introduced three convictions resulting in life sentences, all of which had been set aside on Fourth Amendment grounds. This evidence could not result in any undue prejudice, because although the convictions were overturned, the charges were not dropped and McCleskey pleaded guilty and received sentences of 18 years. The reduction in sentence was disclosed at trial.

The district court properly denied relief on the ineffectiveness of counsel claim.

DEATH-ORIENTED JURY

Petitioner claims the district court improperly upheld the exclusion of jurors who were adamantly opposed to capital punishment. According to petitioner, this exclusion violated his right to be tried by an impartial and unbiased jury drawn from a representative cross-section of his community. In support of this proposition, petitioner cites two district court opinions from outside circuits. Grigsby v. Mabry, 569 F.Supp. 1273 (E.D.Ark.1983), hearing en banc ordered, No. 83-2113 E.A. (8th Cir. Nov. 8, 1983), argued (March 15, 1984) and Keeten v. Garrison, 578 F.Supp. 1164 (W.D.N.C.1984), rev’d, 742 F.2d 129 (4th Cir.1984). Whatever the merits of those opinions, they are not controlling authority for this Court.

Because both jurors indicated they would not under any circumstances consider imposing the death penalty, they were properly excluded under Witherspoon v. Illinois, 391 U.S. 510, 88 S.Ct. 1770, 20 L.Ed.2d 776 (1968) . See also Boulden v. Holman, 394 U.S. 478, 89 S.Ct. 1138, 22 L.Ed.2d 433 (1969) . Their exclusion did not violate petitioner’s Sixth Amendment rights to an impartial, community-representative jury. Smith v. Balkcom, 660 F.2d 573, 582-83 (5th Cir. Unit B 1981), cert. denied, 459 U.S. 882, 103 S.Ct. 181, 74 L.Ed.2d 148 (1982); Spinkellink v. Wainwright, 578 F.2d 582, 593-94 (5th Cir.1978), cert. denied, 440 U.S. 976, 99 S.Ct. 1548, 59 L.Ed.2d 796 (1979).

THE SANDSTROM ISSUE

The district court rejected McCleskey’s claim that the trial court’s instructions to the jury on the issue of'intent deprived him of due process by shifting from the prosecution to the defense the burden of proving beyond a reasonable doubt each essential element of the crimes for which he was tried. Such burden-shifting is unconstitutional under Sandstrom v. Montana, 442 U.S. 510, 99 S.Ct. 2450, 61 L.Ed.2d 39 (1979).

McCleskey objects to the following portion of the trial court’s instruction to the jury:

One section of our law says that the acts of a person of sound mind and discretion are presumed to be the product of the person’s will, and a person of sound mind and discretion is presumed to intend the natural and probable consequences of his acts, but both of these presumptions may be rebutted.

In its analysis of whether this instruction was unconstitutional under Sandstrom, the district court examined two recent panel opinions of this Circuit, Franklin v. Francis, 720 F.2d 1206 (11th Cir.1983), cert. granted, — U.S.—, 104 S.Ct. 2677, 81 L.Ed.2d 873 (1984), and Tucker v. Francis, 723 F.2d 1504 (11th Cir.), on pet. for reh’g and reh’g en banc, 723 F.2d 1518 (11th Cir.1984). Even though the jury instructions in the two cases were identical, Franklin held that the language created a mandatory rebuttable persumption viola-tive of Sandstrom while Tucker held that it created no more than a permissive inference and did not violate Sandstrom. Noting that the challenged portion of the instruction used at McCleskey’s trial was “virtually identical” to the corresponding portions of the charges in Franklin and Tucker, the district court elected to follow Tucker as this Court’s most recent pronouncement on the issue, and it held that Sandstrom was not violated by the charge on intent.

Since the district court’s decision, the en banc court has heard argument in several cases in an effort to resolve the constitutionality of potentially burden-shifting instructions identical to the one at issue here. Davis v. Zant, 721 F.2d 1478 (11th Cir.1983), on pet. for reh’g and reh’g en banc, 728 F.2d 492 (11th Cir.1984); Drake v. Francis, 727 F.2d 990 (11th Cir.), on pet. for reh’g and for reh’g en banc, 727 F.2d 1003 (11th Cir.1984); Tucker v. Francis, 723 F.2d 1504 (11th Cir.), on pet. for reh’g and reh’g en banc, 723 F.2d 1518 (11th Cir.1984). The United States Supreme Court has heard oral argument in Franklin v. Francis, 53 U.S.L.W. 3373 (U.S. Nov. 20, 1984) [No. 83-1590]. However these cases are decided, for the purpose of this decision, we assume here that the intent instruction in this case violated Sandstrom and proceed to the issue of whether that error was harmless.

The Supreme Court requires that “before a federal constitutional error can be harmless, the court must be able to declare a belief that it was harmless beyond a reasonable doubt.” Chapman v. California, 386 U.S. 18, 24, 87 S.Ct. 824, 828, 17 L.Ed.2d 705 (1967). More recently, the Supreme Court has divided over the issue of whether the doctrine of harmless error is ever applicable to burden-shifting presumptions violative of Sandstrom. Reasoning that “[a]n erroneous presumption on a disputed element of the crime renders irrelevant the evidence on the issue because the jury may have relied upon the presumption rather than upon that evidence,” a four-justice plurality held that one of the two tests for harmless error employed by this Circuit — whether the evidence of guilt is so overwhelming that the erroneous instruction could not have contributed to the jury’s verdict — is inappropriate. Connecticut v. Johnson, 460 U.S. 73, 85-87, 103 S.Ct. 969, 976-978, 74 L.Ed.2d 823 (1983). The fifth vote to affirm was added by Justice Stevens, who concurred on jurisdictional grounds. Id. at 88, 103 S.Ct. at 978 (Stevens, J., concurring in the judgment). Four other justices, however, criticized the plurality for adopting an “automatic reversal” rule for Sandstrom error.. Id. at 98, 103 S.Ct. at 983 (Powell, J., dissenting). The Supreme Court has subsequently reviewed another case in which harmless error doctrine was applied to a Sandstrom violation. The Court split evenly once again in affirming without opinion a Sixth Circuit decision holding that “the prejudicial effect of a Sandstrom instruction is largely a function of the defense asserted at trial.” Engle v. Koehler, 707 F.2d 241, 246 (6th Cir.1983), aff’d by an equally divided court, — U.S.—, 104 S.Ct. 1673, 80 L.Ed.2d 1 (1984) (per curiam). In En-gle, the Sixth Circuit distinguished between Sandstrom violations where the defendant has claimed nonparticipation in the crime and those where the defendant has claimed lack of mens rea, holding that only the latter was so prejudicial as never to constitute harmless error. Id. Until the Supreme Court makes a controlling decision on the harmless error question, we continue to apply the standards propounded in our earlier cases.

Since Sandstrom was decided in 1979, this Circuit has analyzed unconstitutional burden-shifting instructions to determine whether they constituted harmless error. See, e.g., Mason v. Balkcom, 669 F.2d 222, 227 (5th Cir. Unit B 1982). In Lamb v. Jernigan, 683 F.2d 1332 (11th Cir.1982), cert. denied, 460 U.S. 1024, 103 S.Ct. 1276, 75 L.Ed.2d 496 (1983), the Court identified two situations in which an unconstitutional burden-shifting instruction might be harmless. First, an erroneous instruction may have been harmless if the evidence of guilt was so overwhelming that the error could not have contributed to the jury’s decision to convict. Lamb, 683 F.2d at 1342; Mason, 669 F.2d at 227. In the case before us, the district court based its finding that the Sandstrom violation was harmless on this ground. This Circuit has decided on several occasions that overwhelming evidence of guilt renders a Sandstrom violation harmless. See Jarrell v. Balkcom, 735 F.2d 1242,1257 (11th Cir.1984); Brooks v. Francis, 716 F.2d 780, 793-94 (11th Cir.1983), on pet. for reh’g and for reh’g en banc, 728 F.2d 1358 (11th Cir.1984); Spencer v. Zant, 715 F.2d 1562, 1578 (11th Cir.1983), on pet. for reh’g and for reh’g en banc, 729 F.2d 1293 (11th Cir.1984).

Second, the erroneous instruction may be harmless where the instruction shifts the burden on an element that is not at issue at trial. Lamb, 683 F.2d at 1342. This Circuit has adopted this rationale to find a Sandstrom violation harmless. See Drake v. Francis, 727 F.2d 990, 999 (11th Cir.), on pet. for reh’g and for reh’g en banc, 727 F.2d 1003 (11th Cir.1984); Collins v. Francis, 728 F.2d 1322, 1330-31 (11th Cir.1984), pet. for reh’g en banc denied, 734 F.2d 1481 (11th Cir.1984). There is some indication that even the plurality in Connecticut v. Johnson would endorse this type of harmless error in limited circumstances:

[A] Sandstrom error may be harmless if the defendant conceded the issue of intent____ In presenting a defense such as alibi, insanity, or self-defense, a defendant may in some cases admit that the act alleged by the prosecution was intentional, thereby sufficiently reducing the likelihood that the jury applied the erroneous instruction as to permit the appellate court to consider the error harmless.

460 U.S. at 87, 103 S.Ct. at 978 (citations omitted).

Our review of the record reveals that the Sandstrom violation in this case is rendered harmless error under this second test. Before discussing whether intent was at issue in McCleskey’s trial, however, we note that intent is an essential element of the crime with which he was charged. Georgia law provides three essential elements to the offense of malice murder: (1) a homicide; (2) malice aforethought; and (3) unlawfulness. Lamb v. Jernigan, 683 F.2d at 1336. The “malice” element means the intent to kill in the absence of provocation. Id. The erroneous instruction on intent, therefore, involved an essential element of the criminal offense charged, and the state was required to prove the existence of that element beyond a reasonable doubt. In re Winship, 397 U’S. 358, 364, 90 S.Ct. 1068, 1072, 25 L.Ed.2d 368 (1970). The question therefore becomes whether McCleskey conceded the element of intent by presenting a defense that admits that the act alleged was intentional.

Of course, a defendant in a criminal trial may rely entirely on the presumption of innocence and the State’s burden of proving every element of the crime beyond a reasonable doubt. Connecticut v. Johnson, 460 U.S. at 87 n. 16,103 S.Ct. at 978 n. 16. In such a case, determining whether a defendant had conceded the issue of intent might well be impossible. The record reveals, however, that McCleskey chose not to take that course. Rather, he took the stand at trial and testified that he was not a participant in the Dixie Furniture Store robbery which resulted in the killing of Officer Schlatt. The end of McCleskey’s testimony on direct examination summarizes his alibi defense:

Q. Were you at the Dixie Furniture Store that day?
A. No.
Q. Did you shoot anyone?
A. No, I didn’t.
Q. Is everything you have said the truth?
A. Positive.

In closing argument, McCleskey’s attorney again stressed his client’s alibi defense. He concentrated on undermining the credibility of the eyewitness identifications that pinpointed McCleskey as the triggerman and on questioning the motives of the other robbery participants who had testified that McCleskey had fired the fatal shots. McCleskey’s attorney emphasized that

if Mr. McCleskey was in the front of the store and Mr. McCleskey had the silver gun and if the silver gun killed the police officer, then he would be guilty. But that is not the circumstances that have been proven.

Although. McCleskey’s attorney’s arguments were consistent with the alibi testimony offered by McCleskey himself, the jury chose to disbelieve that testimony and rely instead on the testimony of eyewitnesses , and the other participants in the robbery.

We therefore hold that in the course of asserting his alibi defense McCleskey effectively conceded the issue of intent, thereby rendering the .»Sandstrom violation harmless beyond a reasonable doubt. In so holding, we do not imply that whenever a defendant raises a defense of alibi a Sandstrom violation on an intent or malice instruction is automatically rendered harmless error. Nor do we suggest that defendant must specifically argue that intent did not exist in order for the issue of intent to remain before the jury. But where the State has presented overwhelming evidence of an intentional killing and where the defendant raises a defense of nonparticipation in the crime rather than lack cf. mens rea, a Sandstrom violation on an intent instruction such as the one at issue here is harmless beyond a reasonable doubt. See Collins v. Francis, 728 F.2d at 1331; Engle v. Koehler, 707 F.2d at 246.

In this case the officer entered and made it almost to the middle of the store before he was shot twice with a .38 caliber Rossi revolver. The circumstances of this shooting, coupled with McCleskey’s decision to rely on an alibi defense, elevate to mere speculation any scenario that would create a reasonable doubt on the issue of intent. The district court properly denied habeas corpus relief on this issue.

CONCLUSION

The judgment of the district court in granting the petition for writ of habeas corpus is reversed and the petition is hereby denied.

REVERSED and RENDERED.

TJOFLAT, Circuit Judge,

concurring:

I concur in the court’s opinion, though I would approach the question of the constitutional application of the death penalty in Georgia somewhat differently.' I would begin with the established proposition that Georgia’s capital sentencing model is facially constitutional. It contains the safeguards necessary to prevent arbitrary and capricious decision making, including decisions motivated by the race of the defendant or the victim. These safeguards are present in every stage of a capital murder prosecution in Georgia, from the grand jury indictment through the execution of the death sentence. Some of these safeguards are worth repeating.

At the indictment stage, the accused can insist that the State impanel a grand jury that represents a fair cross section of the community, as required by the sixth and fourteenth amendments, and that the State not deny a racial group, in violation of the equal protection clause of the fourteenth amendment, the right to participate as jurors. In Georgia this means that a representative portion of blacks will be on the grand jury.

The same safeguards come into play in the selection of the accused’s petit jury. In addition, the accused can challenge for cause any venireman found to harbor a racial bias against the accused or his victim. The accused can peremptorily excuse jurors suspected of such bias and, at the same time, prevent the prosecutor from exercising his peremptory challenges in a way that systematically excludes a particular class of persons, such as blacks, from jury service. See, e.g., Willis v. Zant, 720 F.2d 1212 (11th Cir.1983), cert. denied, — U.S. —, 104 S.Ct. 3548, 82 L.Ed.2d 851 (1984).

If the sentencer is the jury, as it is in Georgia (the trial judge being bound by the jury’s recommendation), it can be instructed to put aside racial considerations in reaching its sentencing recommendation. If the jury recommends the death sentence, the accused, on direct appeal to the Georgia Supreme Court, can challenge his sentence on racial grounds as an independent assignment of error or in the context of proportionality review. And, if the court affirms his death sentence, he can renew his challenge in a petition for rehearing or by way of collateral attack.

In assessing the constitutional validity of Georgia’s capital sentencing scheme, one could argue that the role of the federal courts — the Supreme Court on certiorari from the Georgia Supreme Court and the entire federal judicial system in habeas corpus review — should be considered. For they provide still another layer of safeguards against the arbitrary and capricious imposition of the death penalty.

Petitioner, in attacking his conviction and death sentence, makes no claim that either was motivated by a racial bias in any stage of his criminal prosecution. His claim stems solely from what has transpired in other homicide prosecutions. To the extent that his data consists of cases in which the defendant’s conviction and sentence— whether a sentence to life imprisonment or death — is constitutionally unassailable, the data, I would hold, indicates no invidious racial discrimination as a matter of law. To the extent that the data consists of convictions and/or sentences that are constitutionally infirm, the data is irrelevant. In summary, petitioner’s data, which shows nothing more than disproportionate sentencing results, is not probative of a racially discriminatory motive on the part of any of the participants in Georgia’s death penalty sentencing model — either in petitioner’s or any other case.

VANCE, Circuit Judge,

concurring:

Although I concur in Judge Roney’s opinion, I am troubled by its assertion that there is “little difference in the proof that might be required to prevail” under either eighth amendment or fourteenth amendment equal protection claims of the kind presented here . According to Furman, an eighth amendment inquiry centers on the general results of capital sentencing systems, and condemns those governed by such unpredictable factors as chance, caprice or whim. An equal protection inquiry is very different. It centers not on systemic irrationality, but rather the independent evil of intentional, invidious discrimination against given individuals.

I am conscious of the dicta in the various Furman opinions which note with disapproval the possibility that racial discrimination was a factor in the application of the death penalty under the Georgia and Texas statutes then in effect. To my mind, however, such dicta merely indicate the possibility that a system that permits the exercise of standardless discretion not only may be capricious, but may give play to discriminatory motives which violate equal protection standards as well. Whether a given set of facts make out an eighth amendment claim of systemic irrationality under Fur-man is, therefore, a question entirely independent of whether those facts establish deliberate discrimination violative of the equal protection clause.

I am able to concur because in neither the case before us nor in any of the others presently pending would the difference influence the outcome. As Judge Roney points out, petitioner’s statistics are insufficient to establish intentional discrimination in the capital sentence imposed in his case. As to the eighth amendment, I doubt that a claim of arbitrariness or caprice is even presented, since petitioner’s case is entirely devoted to proving that the death penalty is being applied in an altogether explicable— albeit impermissible — fashion.

Claims such as that of petitioner are now presented with such regularity that we may reasonably hope for guidance from the Supreme Court by the time my expressed concerns are outcome determinative in a given case.

KRAVITCH, Circuit Judge,

concurring:

I concur in the majority opinion except as to the Giglio issue. In my view, for reasons stated in Chief Judge Godbold’s dissent, the facts surrounding Evans’ testimony did constitute a Giglio violation. I agree with the majority, however, that any error was harmless beyond a reasonable doubt.

I also join Judge Anderson’s special concurrence on the “Constitutional Application of the Georgia Death Penalty.”

R. LANIER ANDERSON, III, Circuit Judge,

concurring with whom KRAVITCH, Circuit Judge, joins as to the constitutional application of the Georgia Death Statute:

I join Judge Roney’s opinion for the majority, and write separately only to emphasize, with respect to the Part entitled “Constitutional Application of Georgia’s Death Penalty,” that death is different in kind from all other criminal sanctions, Woodson v. North Carolina, 428 U.S. 280, 305, 96 S.Ct. 2978, 2991, 49 L.Ed.2d 944 (1976). Thus, the proof of racial motivation required in a death case, whether pursuant to an Eighth Amendment theory or an equal protection theory, presumably would be less strict than that required in civil cases or in the criminal justice system generally. Constitutional adjudication would tolerate less risk that a death sentence was influenced by race. The Supreme Court’s Eighth Amendment jurisprudence has established a constitutional supervision over the conduct of state death penalty systems which is more exacting than that with respect to the criminal justice system generally. Woodson v. North Carolina, id. at 305, 96 S.Ct. at 2991 (“Because of that qualitative difference, there is a corre-

sponding difference in the need for reliability in the determination that death is the appropriate punishment.”). There is no need in this ease, however, to reach out and try to define more precisely what evidentia-ry showing would be required. Judge Ro-ney’s opinion demonstrates with clarity why the evidentiary showing in this case is insufficient.

GODBOLD, Chief Judge,

dissenting in part, and concurring in part, with whom JOHNSON, HATCHETT and CLARK, Circuit Judges, join as to the dissent on the Giglio issue :

At the merits trial Evans, who had been incarcerated with McCleskey, testified that McCleskey admitted to him that he shot the policeman and acknowledged that he wore makeup to disguise himself during the robbery. Evans also testified that he had pending against him a [federal] escape charge, that he had not asked the prosecutor to “fix” this charge, and that the prosecutor had not promised him anything to testify.

At the state habeas hearing the following transpired:

The Court: Mr. Evans, let me ask you a question. At the time that you testified in Mr. McCleskey’s trial, had you been promised anything in exchange for your testimony?
The witness: No, I wasn’t. I wasn’t promised nothing about — I wasn’t promised nothing by the D.A. But the Detective told me that he would — he said he was going to do it himself, speak a word for me. That was what the Detective told me.
By Mr. Stroup:
Q: The Detective told you that he would speak a word for you?
A: Yeah.
Q: That was Detective Dorsey?
A: Yeah.

State Habeas Transcript at 122.

The district court granted habeas relief to McCleskey under Giglio v. U.S., 405 U.S. 150, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972). At the threshold the district court pointed out that Giglio applies not only to “traditional deals” made by the prosecutor in exchange for testimony but also to “any promises or understandings made by any member of the prosecutorial team, which includes police investigators.” 580 F.Supp. at 380. The court then made these subsidiary findings: (1) that Evans’s testimony was highly damaging; (2) that “the jury was clearly left with the impression that Evans was unconcerned about any charges which were pending against him and that no promises had been made which would affect his credibility,” id. at 381; (3) that at petitioner’s state habeas hearings Evans testified “that one of the detectives investigating the case had promised to speak to federal authorities on his behalf,” id.; (4) that the escape charges pending against Evans were dropped subsequent to McCleskey’s trial.

The en banc court seems to me to err on several grounds. It blurs the proper application of Giglio by focusing sharply on the word “promise.” The proper inquiry is not limited to formal contracts, unilateral or bilateral, or words of contract law, but “to ensure that the jury knew the facts that might motivate a witness in giving testimony.” Smith v. Kemp, 715 F.2d 1459, 1467 (11th Cir.1983). Giglio reaches the informal understanding as well as the formal. The point is, even if the dealings are informal, can the witness reasonably view the government’s undertaking as offering him a benefit and can a juror knowing of it reasonably view it as motivating the witness in giving testimony? The verbal undertaking made in this instance by an investigating state officer, who is a member of the prosecution team, that he will “put in a word for him” on his pending federal charge was an undertaking that a jury was entitled to know about.

Second, the en banc court finds the benefit too marginal. Of course, the possible benefit to a potential witness can be so minimal that a court could find as a matter of law no Giglio violation occurred. A trivial offer is not enough. The subject matter of the offer to Evans was substantial, or at least a jury was entitled to consider it so. After McCleskey was tried and convicted, the federal charge was dropped.

Third, the court concludes there was no reasonable likelihood that Evans’s testimony affected the judgment of the jury. Co-defendant Wright was the only eyewitness. He was an accomplice, thus his testimony, unless corroborated, was insufficient to establish that McCleskey was the trigger-man. The en banc court recognizes this problem but avoids it by holding that Wright’s testimony was corroborated by “McCleskey’s own confession.” This could refer to either of two admissions of guilt by McCleskey. He “confessed” to Wright, but Wright’s testimony on this subject could not be used to corroborate Wright’s otherwise insufficient accomplice testimony. Testimony of an accomplice cannot be corroborated by the accomplice’s own testimony. The other “confession” was made to Evans and testified to by Evans. Thus Evans is not a minor or incidental witness. Evans’ testimony, describing what McCles-key “confessed” to him, is the corroboration for the testimony of the only eyewitness, Wright. And that eyewitness gave the only direct evidence that McCleskey killed the officer.

The district court properly granted the writ on Giglio grounds. Its judgment should be affirmed.

JOHNSON, Circuit Judge,

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, demonstrates that in Georgia a 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 Amendment 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 violation 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. 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 U.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. 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.

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 eradicate 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. 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 factors 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.

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.

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 proving 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 pools and in other contexts, 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. Yet the majority improperly stresses this particularity requirement and interprets it so as to close a door left open by the Supreme Court. 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. 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, 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 (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, 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, 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. 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 of 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 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 most; penalty trial information was unavailable in the same percentage of cases. 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. Ideally the independent variables in a 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.

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). The majority implicitly questions the validity of the Baldus Study on several occasions when it adopts the first two of these criticisms. 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. 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 that 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. But an R² of that size is not inappropriately low in every context. 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.

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 1332, 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. 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.

HATCHETT, Circuit Judge,

dissenting in part, and concurring in part:

In this case, the Georgia system of imposing the death penalty is shown to be unconstitutional. Although the Georgia death penalty statutory scheme was held constitutional “on its face” in Gregg v. Georgia, 428 U.S. 153, 96 S.Ct. 2909, 49 L.Ed.2d 859 (1976), application of the scheme produces death sentences explainable only on the basis of the race of the defendant and the race of the victim.

I write to state clearly and simply, without the jargon of the statisticians, the results produced by the application of the Georgia statutory death penalty scheme, as shown by the Baldus Study.

The Baldus Study is valid. The study was designed to answer the questions when, if ever, and how much, if at all, race is a factor in the decision to impose the death penalty in Georgia. The study gives the answers: In Georgia, when the defendant is black and the victim of murder is white, a 6 percent greater chance exists that the defendant will receive the death penalty solely because the victim is white. This 6 percent disparity is present throughout the total range of death-sentenced black defendants in Georgia. While the 6 percent is troublesome, it is the disparity in the mid-range on which I focus. When cases are considered which fall in the mid-range, between less serious and very serious aggravating circumstances, where the victim is white, the black defendant has a 20 percent greater chance of receiving the death penalty because the victim is white, rather than black. This is intolerable; it is in this middle range of cases that the decision on the proper sentence is most difficult and imposition of the death penalty most questionable.

The disparity shown by the study arises from a variety of statistical analyses made by Dr. Baldus and his colleagues. First, Baldus tried to determine the effect of race of the victim in 594 cases (PRS study) comprising all persons convicted of murder during a particular period. To obtain better results, consistent with techniques approved by the National Academy of Sciences, Baldus identified 2,500 cases in which persons were indicted for murder during a particular period and studied closely 1,066 of those cases. He identified 500 factors, bits of information, about the defendant, the crime, and other circumstances surrounding each case which he thought had some impact on a death sentence determination. Additionally, he focused on 230 of these factors which he thought most reflected the relevant considerations in a death penalty decision. Through this 230-factor model, the study proved that black defendants indicted and convicted for murder of a white victim begin the penalty stage of trial with a significantly greater probability of receiving the death penalty, solely because the victim is white.

Baldus also observed thirty-nine factors, including information on aggravating circumstances, which match the circumstances in this case. This focused study of the aggravating circumstances in the mid-range of severity indicated that “white victim crimes were shown to be 20 percent more likely to result in a death penalty sentence than equally aggravated black victim crimes.” Majority at 896.

We must not lose sight of the fact that the 39-factor model considers information relevant to the impact of the decisions being made by law enforcement officers, prosecutors, judges, and juries in the decision to impose the death penalty. The majority suggests that if such a disparity resulted from an identifiable actor or agency in the prosecution and sentencing process, the present 20 percent racial disparity could be great enough to declare the Georgia system unconstitutional under the eighth amendment. Because this disparity is not considered great enough to satisfy the majority, or because no identification of an actor or agency can be made with precision, the majority holds that the statutory scheme is approved by the Constitution. Identified or unidentified, the result of the unconstitutional ingredient of race, at a significant level in the system, is the same on the black defendant. The inability to identify the actor or agency has little to do with the constitutionality of the system.

The 20 percent greater chance in the mid-range cases (because the defendant is black and the victim is white), produces a disparity that is too high. The study demonstrates that the 20 percent disparity, in the real world, means that one-third of the black defendants (with white victims) in the mid-range cases will be affected by the race factor in receiving the death penalty. Race should not be allowed to take a significant role in the decision to impose the death penalty.

The Supreme Court has reminded us on more than one occasion that “if 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.” Godfrey v. Georgia, 446 U.S. 420, 428, 100 S.Ct. 1759, 1764, 64 L.Ed.2d 398 (1980). A statute that intentionally or unintentionally allows for such racial effects is unconstitutional under the eighth amendment. Because the majority holds otherwise, I dissent.

CLARK, Circuit Judge,

dissenting in part and concurring in part :

We are challenged to determine how much racial discrimination, if any, is tolerable in the imposition of the death penalty. Although I also join in Judge Johnson’s dissent, this dissent is directed to the majority’s erroneous conclusion that the evidence in this case does not establish a prima facie Fourteenth Amendment violation.

The Study

The Baldus study, which covers the period 1974 to 1979, is a detailed study of over 2,400 homicide cases. From these homicides, 128 persons received the death penalty. Two types of racial disparity are established — one based on the race of the victim and one based on the race of the defendant. If the victim is white, a defendant is more likely to receive the death penalty. If the defendant is black, he is more likely to receive the death penalty. One can only conclude that in the operation of this system the life of a white is dearer, the life of a black cheaper.

Before looking at a few of the figures, a perspective is necessary. Race is a factor in the system only where there is room for discretion, that is, where the decision maker has a viable choice. In the large number of cases, race has no effect. These are cases where the facts are so mitigated the death penalty is not even considered as a possible punishment. At the other end of the spectrum are the tremendously aggravated murder cases where the defendant will very probably receive the death penalty, regardless of his race or the race of the victim. In between is the mid-range of cases where there is an approximately 20% racial disparity.

The Baldus study was designed to determine whether like situated cases are treated similarly. As a starting point, an unan-alyzed arithmetic comparison of all of the cases reflected the following:

Death Sentencing Rates by Defendant/ Victim Racial Combination

These figures show a gross disparate racial impact — that where the victim was white there were 11% death sentences, compared to only 1.3 percent death sentences when the victim was black. Similarly, only 8% of white defendants compared to 22% of black defendants received the death penalty when the victim was white. The Supreme Court has found similar gross disparities to be sufficient proof of discrimination to support a Fourteenth Amendment violation.

The Baldus study undertook to determine if this racial sentencing disparity was caused by considerations of race or because of other factors or both. In order to find out, it was necessary to analyze and compare each of the potential death penalty cases and ascertain what relevant factors were available for consideration by the decision makers. There were many factors such as prior capital record, contemporaneous offense, motive, killing to avoid arrest or for hire, as well as race. The study showed that race had as much or more impact than any other single factor. See Exhibits DB 76-78, T-776-87. Stated another way, race influences the verdict just as much as any one of the aggravating circumstances listed in Georgia’s death penalty statute. Therefore, in the application of the statute in Georgia, race of the defendant and of the victim, when it is black/white, functions as if it were an aggravating circumstance in a discernible number of cases. See Zant v. Stephens, 462 U.S. 862, 103 S.Ct. 2733, 2747, 77 L.Ed.2d 235 (1983) (race as an aggravating circumstance would be constitutionally impermissible).

Another part of the study compared the disparities in death penalty sentencing according to race of the defendant and race of the victim and reflected the differences in the sentencing depending upon the predicted chance of death, i.e., whether the type of case was or was not one where the death penalty would be given.

Columns A and B reflect the step progression of least aggravated to most aggravated cases. Table 43, DB, Ex. 91. Columns C and D compare sentencing rates of black defendants to white defendants when the victim is white and reflect that in Steps 1 and 2 no death penalty was given in those 41 cases. In Step 8, 45 death penalties were given in 50 cases, only two blacks and three whites escaping the death penalty — this group obviously representing the most aggravated cases. By comparing Steps 3 through 7, one can see that in each group black defendants received death penalties disproportionately to white defendants by differences of .27, .19, .15, .22, and .25. This indicates that unless the murder is so vile as to almost certainly evoke the death penalty (Step 8), blacks are approximately 20% more likely to get the death penalty.

The right side of the chart reflects how unlikely it is that any defendant, but more particularly white defendants, will receive the death penalty when the victim is black.

Statistics as Proof

The jury selection cases have utilized different methods of statistical analysis in determining whether a disparity is sufficient to establish a prima facie case of purposeful discrimination. Early jury selection cases, such as Swain v. Alabama, used very simple equations which primarily analyzed the difference of minorities eligible for jury duty from the actual number of minorities who served on the jury to determine if a disparity amounted to a substantial underrepresentation of minority jurors. Because this simple method did not consider many variables in its equation, it was not as accurate as the complex statistical equations widely used today.

The mathematical disparities that have been accepted by the Court as adequate to establish a prima facie case of purposeful discrimination range approximately from 14% to 40%. “Whether or not greater disparities constitute prima facie evidence of discrimination depends upon the facts of each case.”

Statistical disparities in jury selection cases are not sufficiently comparable to provide a complete analogy. There are no guidelines in decided cases so in this case we have to rely on reason. We start with a sentencing procedure that has been approved by the Supreme Court. The object of this system, as well as any constitutionally permissible capital sentencing system, is to provide individualized treatment of those eligible for the death penalty to insure that non-relevant factors, i.e. factors that do not relate to this particular individual or the crime committed, play no part in deciding who does and who does not receive the death penalty. The facts disclosed by the Baldus study, some of which have been previously discussed, demonstrate that there is sufficient disparate treatment of blacks to establish a prima facie case of discrimination.

This discrimination, when coupled with the historical facts, demonstrate a prima facie Fourteenth Amendment violation of the Equal Protection Clause. It is that discrimination against which the Equal Protection Clause stands to protect. The majority, however, fails to give full reach to our Constitution. While one has to acknowledge the existence of prejudice in our society, one cannot and does not accept its application in certain contexts. This is nowhere more true than in the administration of criminal justice in capital cases.

The Fourteenth Amendment and Equal Protection

“A showing of intent has long been required in all types of equal protection cases charging racial discrimination.” The Court has required proof of intent before it will strictly scrutinize the actions of a legislature or any official entity. In this respect, the intent rule is a tool of self-restraint that serves the purpose of limiting judicial review and policymaking.

The intent test is not a monolithic structure. As with all legal tests, its focus will vary with the legal cpntext in which it is applied. Because of the variety of situations in which discrimination can occur, the method of proving intent is the critical focus. The majority, by failing to recognize this, misconceives the meaning of intent in the context of equal protection jurisprudence.

Intent may be proven circumstantially by utilizing a variety of objective factors and can be inferred from the totality of the relevant facts. The factors most appropriate in this case are: (1) the presence of historical discrimination; and (2) the impact, as shown by the Baldus study, that the capital sentencing law has on a suspect class. The Supreme Court has indicated that:

Evidence of historical discrimination is relevant to drawing an inference of purposeful discrimination, particularly ... where the evidence shows that discriminatory practices were commonly utilized, that they were abandoned when enjoined by courts or made illegal by civil rights legislation, and that they were replaced by laws and practices which, though neutral on their face, serve to maintain the status quo.

Evidence of disparate impact may demonstrate that an unconstitutional purpose may continue to be at work, especially where the discrimination is not explainable on non-racial grounds. Table 43, supra p. 4, the table and the accompanying evidence leave unexplained the 20% racial disparity where the defendant is black and the victim is white and the murders occurred under very similar circumstances.

Although the Court has rarely found the existence of intent where disproportionate impact is the only proof, it has, for example, relaxed the standard of proof in jury selection cases because of the “nature” of the task involved in the selection of jurors. Thus, to show an equal protection violation in the jury selection cases, a defendant must prove that “the procedure employed resulted in a substantial under-representation of his race or of the identifiable group to which he belongs.” The idea behind this method is simple. As the Court pointed out, “[i]f a disparity is sufficiently large, then it is unlikely that it is due solely to chance or accident, and, in the absence of evidence to the contrary, one must conclude that racial or other class-related factors entered into the selection process.” Once there is a showing of a substantial underrepresentation of the defendant’s group, a prima facie case of discriminatory intent or purpose is established and the state acquires, the burden of rebutting the case.

In many respects the imposition of the death penalty is similar to the selection of jurors in that both processes are discretionary in nature, vulnerable to the bias of the decision maker, and susceptible to a rigorous statistical analysis.

The Court has refrained from relaxing the standard of proof where the case does not involve the selection of jurors because of its policy of: (1) deferring to the reasonable acts of administrators and executives; and (2) preventing the questioning of tax, welfare, public service, regulatory, and licensing statutes where disparate impact is the only proof. However, utilizing the standards of proof in the jury selection cases to establish intent in this case will not contravene this policy because: (1) deference is not warranted where the penalty is grave and less severe alternatives are available; and (2) the court did not contemplate capital sentencing statutes when it established this policy. Thus, statistics alone could be utilized to prove intent in this case. But historical background is also relevant and supports the statistical conclusions.

“Discrimination on the basis of race, odious in all aspects, is especially pernicious in the administration of Justice.” It is the duty of the courts to see to it that throughout the procedure for bringing a person to justice, he shall enjoy “the protection which the Constitution guarantees.” In an imperfect society, one has to admit that it is impossible to guarantee that the administrators of justice, both judges and jurors, will successfully wear racial blinders in every case. However, the risk of prejudice must be minimized and where clearly present eradicated.

Discrimination against minorities in the criminal justice system is well documented. This is not to say that progress has not been made, but as the Supreme Court in 1979 acknowledged,

we also cannot deny that, 114 years after the close of the War between the States and nearly 100 years after Strauder [100 U.S. 303, 25 L.Ed. 664] racial and other forms of discrimination still remain a fact of life, in the administration of justice as in our society as a whole. Perhaps today that discrimination takes a form more subtle than before. But it is no less real or pernicious.

If discrimination is especially pernicious in the administration of justice, it is nowhere more sinister and abhorrent than when it plays a part in the decision to impose society’s ultimate sanction, the penalty of death. It is also a tragic fact that this discrimination is very much a part of the country’s experience with the death penalty. Again and as the majority points out, the new post-Furman statutes have improved the situation but the Baldus study shows that race is still a very real factor in capital cases in Georgia. Some of this is conscious discrimination, some of it unconscious, but it is nonetheless real and it is important that we at least admit that discrimination is present.

Finally, the state of Georgia also has no compelling interest to justify a death penalty system that discriminates on the basis of race. Hypothetically, if a racial bias reflected itself randomly in 20% of the convictions, one would not abolish the criminal justice system. Ways of ridding the system of bias would be sought but absent a showing of bias in a given case, little else could be done. The societal imperative of maintaining a criminal justice system to apprehend, punish, and confine perpetrators of serious violations of the law would outweigh the mandate that race or other prejudice not infiltrate the legal process. In other words, we would have to accept that we are doing the best that can be done in a system that must be administered by people, with all their conscious and unconscious biases.

However, such reasoning cannot sensibly be invoked and bias cannot be tolerated when considering the death penalty, a punishment that is unique in its finality. The evidence in this case makes a prima facie case that the death penalty in Georgia is being applied disproportionately because of race. The percentage differentials are not de minimis. To allow the death penalty under such circumstances is to approve a racial preference in the most serious decision our criminal justice system must make. This is a result our Constitution cannot tolerate.

The majority in this case does not squarely face up to' this choice and its consequences. Racial prejudice/preference both conscious and unconscious is still a part of the capital decision making process in Georgia. To allow this system to stand is to concede that in a certain number of cases, the consideration of race will be a factor in the decision whether to impose the death penalty. The Equal Protection Clause of the Fourteenth Amendment does not allow this result. The decision of the district court on the Baldus issue should be reversed and the state required to submit evidence, if any is available, to disprove the prima facie case made by the plaintiff. 
      
      All of the Judges of the Court concur in the judgment as to the death-oriented jury claim and the ineffective assistance of counsel claim. Judges Tjoflat, Vance and Anderson join in the opinion but each has written separately on the constitutional application of the Georgia death sentence.
      Judge Kravitch has written separately to concur only in the harmless error portion of the opinion on the Giglio issue but joins in the opinion on all other issues.
      Chief Judge Godbold dissents from the judgment of the Court on the Giglio issue but joins in the opinion on all other issues.
      Judges Johnson, Hatchett and Clark dissent from the judgment of the Court on the constitutional application of the Georgia death sentence and the Sandstrom and Giglio issues and each has written a separate dissenting opinion.
     
      
      . I have not addressed the due process analysis employed by the district court because the petitioner did not rely on it in his brief.
     
      
       I dissent on only the Giglio issue. I concur in Judge Roney's opinion on all other issues.
     
      
      . This was the description given at trial by Dr. Richard Berk, member of a panel of the National 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 testified 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.
     
      
      . Although I concur with the majority opinion on the ineffective assistance of counsel and death-oriented jury issues, I write separately to express my thoughts on the Baldus Study.
      I also join Chief Judge Godbold's dissent, as to the Giglio issue, and Judge Johnson’s dissent.
     
      
      . Nothing in the majority opinion regarding the validity, impact, or constitutional significance of studies on discrimination in application of the Florida death penalty scheme should be construed to imply that the United States Supreme Court has squarely passed on the Florida studies. Neither the Supreme Court nor the Eleventh Circuit has passed on the Florida studies, on a fully developed record (as in this case), under fourteenth and eighth amendment challenges.
     
      
       Although I concur with the majority opinion on the ineffective assistance of counsel and death oriented jury issues, I write separately to express my thoughts on the Baldus Study. I also join Chief Judge Godbold’s dissent and Judge Johnson's dissent.
     
      
      . DB Exhibit 63.
     
      
      . See discussion below at Page 9.
     
      
      . An individualized method of sentencing makes it possible to differentiate each particular case “in an objective, evenhanded, and substantially rational way from the many Georgia murder cases in which the death penalty may not be imposed." Zant v. Stephens, 462 U.S. 862, 103 S.Ct. 2733, 77 L.Ed.2d 235, 251.
     
      
      . o.C.G.A. § 17-10-30.
     
      
      . The eight sub-groups were derived from the group of cases where the death penalty was predictably most likely based upon an analysis of the relevant factors that resulted in the vast majority of defendants receiving the death penalty — 116 out of the total 128. This group was then sub-divided into the eight sub-groups in ascending order giving consideration to more serious aggravating factors and larger combinations of them as the steps progress. Tr. pages 877-83.
     
      
      . In Villafane v. Mattson, 504 F.Supp. 78 (D.Conn.1980), the court noted that four forms of analysis have been used: (1) the absolute difference test used in Swain v. Alabama, 380 U.S. 202, 85 S.Ct. 824, 13 L.Ed.2d 759 (1965); (2) the ratio approach; (3) a test that moves away from the examination of percentages and focuses on the differences caused by underrepresen-tation in each jury; and (4) the statistical decision theory which was fully embraced in Castaneda v. Partida, 430 U.S. at 496 n. 17, 97 S.Ct. at 1281 n. 17. See also Finkelstein, The Application of Statistical Decision Theory to the Jury Discrimination Cases, 80 Harv.L.Rev. 338 (1966).
     
      
      . See Swain v. Alabama, 380 U.S. 202, 85 S.Ct. 824, 13 L.Ed.2d 759 (1965); Villafane v. Manson, 504 F.Supp. at 83.
     
      
      . See Finkelstein, The Application of Statistical Decision Theory to the Jury Discrimination Cases, 80 Harv.L.Rev. 338, 363 (1966) (“The Court did not reach these problems in Swain because of its inability to assess the significance of statistical data without mathematical tools.”).
     
      
      . Castaneda v. Partida, 430 U.S. at 495-96, 97 S.Ct. at 1280-82 (disparity of 40%); Turner v. Fouche, 396 U.S. 346, 90 S.Ct. 532, 24 L.Ed.2d 567 (1970) (disparity of 23%); Whitus v. Georgia, 385 U.S. 545, 87 S.Ct. 643, 17 L.Ed.2d 599 (1967) (disparity of 18%); Sims v. Georgia, 389 U.S. 404, 88 S.Ct. 523, 19 L.Ed.2d 634 (1967) (disparity of 19.7%); Jones v. Georgia, 389 U.S. 24, 88 S.Ct. 4, 19 L.Ed.2d 25 (1967) (disparity of 14.7%). These figures result from the computation used in Swain.
      
     
      
      . United States ex rel Barksdale v. Blackburn, 639 F.2d 1115, 1122 (5th Cir.1981) (en banc).
     
      
      . Gregg v. Georgia, 428 U.S. 153, 96 S.Ct. 2909, 49 L.Ed.2d 859 (1976).
     
      
      . The sentencing body’s decision must be focused on the "particularized nature of the crime and the particularized characteristics of the individual defendant.” 428 U.S. at 206, 96 S.Ct. at 2940. See also Lockett v. Ohio, 438 U.S. 586, 98 S.Ct. 2954, 57 L.Ed.2d 973 (1978) ("the need for treating each defendant in a capital case with degree of respect due the uniqueness of the individual is far more important than in non-capital cases.” 438 U.S. at 605, 98 S.Ct. at 2965); Eddings v. Oklahoma, 455 U.S. 104, 102 S.Ct. 869, 71 L.Ed.2d 1 does focus on a characteristic of the particular defendant, albeit an impermissible one. See infra, p. 3.
     
      
      . Rogers v. Lodge, 458 U.S. 613, 102 S.Ct. 3272, 3276, 73 L.Ed.2d 1012 (1982).
     
      
      . Id. at n. 5 ("Purposeful racial discrimination invokes the strictest scrutiny of adverse differential treatment. Absent such purpose, differential impact is subject only to the test of rationality.”); see also Sellers, The Impact of Intent on Equal Protection Jurisprudence, 84 Dick.L.Rev. 363, 377 (1979) ("the rule of intent profoundly affects the Supreme Court’s posture toward equal protection claims.’’).
     
      
      . The intent rule "serves a countervailing concern of limiting judicial policy making. Washington v. Davis can be understood ... as a reflection of the Court’s own sense of institutional self-restraint — a limitation on the power of judicial review that avoids having the Court sit as a super legislature____” Note, Section 1981: Discriminatory Purpose or Disproportionate Impact, 80 Colum.L.R. 137, 160-61 (1980); see also Washington v. Davis, 426 U.S. 229, 247-48, 84 S.Ct. 2040, 2051, 48 L.Ed.2d 597 (1976).
     
      
      . See Village of Arlington Heights v. Metropolitan Housing Development Corp., 429 U.S. 252, 266, 97 S.Ct. 555, 564, 50 L.Ed.2d 450 (1977).
     
      
      . Id. See also Rogers v. Lodge, 102 S.Ct. at 3280.
     
      
      . Rogers v. Lodge, 102 S.Ct. at 3280.
     
      
      . In Washington v. Davis, 426 U.S. at 242, 96 S.Ct. at 2049, the Court stated: "It is also not infrequently true that the discriminatory impact ... may for all practical purposes demonstrate unconstitutionality because in various circumstances the discrimination is very difficult to explain on nonracial grounds." See also Personnel Administrator of Mass. v. Feeny, 442 U.S. 256, 99 S.Ct. 2282, 2296 n. 24, 60 L.Ed.2d 870 (1979) ( Washington and Arlington recognize that when a neutral law has a disparate impact upon a group that has historically been a victim of discrimination, an unconstitutional purpose may still be at work).
     
      
      . Village of Arlington Heights v. Metropolitan Housing Development Corp., 429 U.S. at 267 n. 13, 97 S.Ct. at 564 n. 13 ("Because of the nature of the jury-selection task, however, we have permitted a finding of constitutional violation even when the statistical pattern does not approach the extremes of Yick Wo [118 U.S. 356, 6 S.Ct. 1064, 30 L.Ed. 220] or Gomillion [364 U.S. 339, 81 S.Ct. 125, 5 L.Ed.2d 110]"); see also International Bro. of Teamsters v. United States, 431 U.S. 324, 339, 97 S.Ct. 1843, 1856, 52 L.Ed.2d 396 (1977) (“We have repeatedly approved the use of statistical proof ... to establish a prima facie case of racial discrimination in jury selection cases.”).
     
      
      . Castaneda v. Partida, 430 U.S. 482, 494, 97 S.Ct. 1272, 1280, 51 L.Ed.2d 498 (1977).
     
      
      . Id. at n. 13.
     
      
      . Id. at 495, 97 S.Ct. at 1280.
     
      
      . Joyner, Legal Theories for Attacking Racial Disparity in Sentencing, 18 Crim.L.Rep. 101, 110-11 (1982) (“In many respects sentencing is similar to the selections of jury panels as in Castaneda."). The majority opinion notes that the Baldus study ignores quantitative difference in cases: "looks, age, personality, education, profession, job, clothes, demeanor, and re-morse____” Majority opinion at 62. However, it' is these differences that often are used to mask, either intentionally or unintentionally, racial prejudice.
     
      
      . See Washington v. Davis, 426 U.S. at 248, 96 S.Ct. at 2051; Note, Section 1981: Discriminatory Purpose or Disproportionate Impact, 80 Co-lum.L.R. 137, 146-47 (1980).
     
      
      . Rose v. Mitchell, 443 U.S. 545, 556, 99 S.Ct. 2993, 61 L.Ed.2d 739 (1979).
     
      
      . Rose, supra, 443 U.S. at 557, 99 S.Ct. at 3000.
     
      
      . As Robespierre contended almost 200 years ago:
      Even if you imagine the most perfect judicial system, even if you find the most upright and the most enlightened judges, you will still have to allow place for error or prejudice.
      
        Robespierre (G. Rude ed. 1967).
     
      
      . See, e.g., Johnson v. Virginia, 373 U.S. 61, 83 S.Ct. 1053, 10 L.Ed.2d 195 (1963) (invalidating segregated seating in courtrooms); Hamilton v. Alabama, 376 U.S. 650, 84 S.Ct. 982, 11 L.Ed.2d 979 (1964) (conviction reversed when black defendant was racially demeaned on cross-examination); Davis v. Mississippi, 394 U.S. 721, 89 S.Ct. 1394, 22 L.Ed.2d 676 (1969) (mass fingerprinting of young blacks in search of rape suspect overturned). See also Rose v. Mitchell, supra (racial discrimination in grand jury selection); Rogers v. Britton, 476 F.Supp. 1036 (E.D. Ark.1979). A very recent and poignant example of racial discrimination in the criminal justice system can be found in the case of Bailey v. Vining, unpublished order, civ. act. no. 76-199 (M.D.Ga.1978). In Bailey, the court declared the jury selection system in Putnam County, Georgia to be unconstitutional. The Office of the Solicitor sent the jury commissioners a memo demonstrating how they could underrep-resent blacks and women in traverse and grand juries but avoid a prima facie case of discrimination because the percentage disparity would still be within the parameters of Supreme Court and Fifth Circuit case law. See notes 7-8 supra and relevant text. The result was that a limited number of blacks were handpicked by the jury commissioners for service.
     
      
      . Rose, supra, 443 U.S. at 558-59, 99 S.Ct. at 3001.
     
      
      . See, e.g., Furman v. Georgia, 408 U.S. 238, 92 S.Ct. 2726, 33 L.Ed.2d 346 (1972) (see especially the opinions of Douglas, J., concurring, id. at 249-252, 92 S.Ct. at 2731-2733; Stewart, J., concurring, id. at 309-310, 92 S.Ct. at 2762; Marshall, J., concurring, id. at 364-365, 92 S.Ct. at 2790; Burger, C.J., dissenting, id. at 389-390 n. 12, 92 S.Ct. at 2803-2804 n. 12; Powell, J., dissenting, id. at 449, 92 S.Ct. at 2833).
     
      
      . This historical discrimination in the death penalty was pointed out by Justice Marshall in his concurring opinion in Furman, supra. 408 U.S. at 364-65, 92 S.Ct. at 2790, ‘‘[i]ndeed a look at the bare statistics regarding executions is enough to betray much of the discrimination.” Id. See also footnote 32 for other opinions in Furman discussing racial discrimination and the death penalty. For example, between 1930 and 1980, 3,863 persons were executed in the United States, 54% of those were blacks or members of minority groups. Of the 455 men executed for rape, 89.5% were black or minorities. Sarah T. Dike, Capital Punishment in the United States, p. 43 (1982). Of the 2,307 people executed in the South during that time period, 1659 were black. During the same fifty-year period in Georgia, of the 366 people executed, 298 were black. Fifty-eight blacks were executed for rape as opposed to only three whites. Six blacks were executed for armed robbery while no whites were. Hugh A. Bedau, ed., The Death Penalty in America (3rd ed. 1982).
     
      
      . See, e.g., Woodson v. North Carolina, 428 U.S. 280, 305, 96 S.Ct. 2978, 49 L.Ed.2d 944 (1976).
     