These consolidated cases, one dating back to 1987, are brought on behalf of white firefighters who complain that their right to the equal protection of the laws has been infringed by affirmative-action promotions of black and Hispanic firefighters made by the Chicago Fire Department. (One of the plaintiffs also has a Title VII claim of "race norming.") The district court rendered judgment for the City after a bench trial. We affirmed a similar judgment in McNamara v. City of Chicago, 138 F.3d 1219 (7th Cir. 1998), a challenge by other white Chicago firefighters to the department's affirmative-action promotions, and the salient facts determined in that proceeding, see id. at 1222-24, are similar to those found by the district judge in the present one.

The plaintiffs concede that the fire department long engaged in deliberate discrimination against blacks and Hispanics--that, as we said in McNamara, "until sometime during the 1980s the people running the fire department endeavored with considerable success to make the department uncongenial to blacks and Hispanics." Id. at 1224. The first exam for promotion that was validated as being nondiscriminatory was given in 1987, at which time only 2.6 percent of the department's captains were black and only 1 percent Hispanic. Had promotions to captain been made on the basis of performance on the 1987 exam, 14 percent would have been of black candidates and 3.5 percent of Hispanic ones. The affirmative action plan challenged in McNamara and in the present case boosted these percentages to 20 and 5, respectively, but because there were so few minority captains to begin with, and because promotions are infrequent, the actual percentage of minority captains remains far below the minority percentage of the city's population even after correction for age, sex, and other demographic variables that tend to vary by race and ethnicity. According to the 2000 Census, 37 percent of the city's population is black and 26 percent Hispanic, though there is some overlap because some Hispanics are classified as black; most however are classified as white.

After the promotions to captain were complete in 1992, the percentage of black captains was still only 10.8 percent and of Hispanic captains only 3.6 percent-- both significantly below the target minority percentages for these ranks. Similar shortfalls characterize the other ranks as well (firefighters, engineers, lieutenants, and battalion chiefs); in addition, as shown in the following table, the minority perentages in all the upper ranks are lower than the minority percentages in the lowest rank. Notice how even in the lowest rank the minority percentages are far below the corresponding minority percentages of the city's population as a whole. As late as 1997, only 27 percent of firefighters promoted to engineer were black and 10 percent Hispanic.

Minority Percentages, Chicago Firefighters, 1996

Rank                % Black   % Hispanic
Firefighter           24.3      9.2
Engineer              17.8      5.1
Lieutenant            15.4      5.8
Captain               16.3      4.9
Battalion Chief       8.2       3.1

The plaintiffs argue, however, that population is the wrong pool to use to calculate departures from proportionality. Suppose, by way of illustration of their argument, that the fire department actually and lawfully required that captains be able to pass a Ph.D. exam in chemistry. Then the fact that the percentage of minority captains was smaller than the percentage of age- adjusted and sex-adjusted Chicagoans who are black or Hispanic would be of no legal significance. The proper comparison group would be blacks and Hispanics who were able to pass a Ph.D. exam in chemistry. See, e.g., Wards Cove Packing Co. v. Atonio, 490 U.S. 642, 651-52 (1989); City of Richmond v. J.A. Croson Co., 488 U.S. 469, 501-02 (1989); Hazelwood School Dist. v. United States, 433 U.S. 299, 308, 310-11 (1977); Peightal v. Metropolitan Dade County, 26 F.3d 1545, 1553-54 (11th Cir. 1994). The plaintiffs argue that before 1972, the exam that the City required of applicants for firefighter positions required at least as much knowledge as a high-school graduate could be expected to have, that 95 percent of the minority applicants flunked the exam, and so the comparison group should be limited to 5 percent of the minority population of Chicago. In 1970 that would be less than 2 percent of the City's population (this is a guess, but a pretty good one, since 44.4 percent of the City's population between the ages of 20 and 39 was black or Hispanic then), implying that blacks and Hispanics were actually overrepresented in the department, which in 1974 (we do not have a figure for 1970) was 4.5 percent black and Hispanic.

If this is right, then even though explicit discrimination against blacks and Hispanics by the fire department in that era is conceded, it would not justify affirmative action designed to bring the percentages of blacks and Hispanics in the department more into line with their percentages of the relevant labor pool. Although those pre- 1972 exams had a disparate impact on minorities (it can be inferred from the documents in the record that the white pass rate exceeded 20 percent, compared, as we have said, to a 5 percent pass rate for the members of the minority groups), and were never shown to be job-related, only deliberate discrimination is actionable under the equal protection clause. Personnel Administrator v. Feeney, 442 U.S. 256 (1979); Washington v. Davis, 426 U.S. 229, 239-48 (1976). And that is the only basis on which a pre-1972 exam could have been challenged, since Title VII (which makes disparate- impact discrimination actionable) was not amended to bring state and local governments within its grasp until 1972. Fitzpatrick v. Bitzer, 427 U.S. 445, 447- 48 (1976).

In effect, the plaintiffs are arguing a lack of causal connection between the City's deliberate discrimination, which they concede, against blacks and Hispanics from time immemorial to as late as the mid-1980s and the disproportionately small number of blacks and Hispanics employed by the fire department today. The plaintiffs regard the appearance of disproportionality as an artifact of the district judge's having failed to use the right comparison group--his ignoring what they contend is the high educational threshold that all applicants for jobs with the fire department had to cross. It is a curious argument, with no direct support in the case law: an employer discriminates deliberately in violation of the Constitution, but because it also discriminates without intending to do so and therefore not in violation of the Constitution or (at the time of the discrimination) of Title VII, it can provide no relief for the victims of the discrimination without infringing the constitutional rights of employees who were not discriminated against.

We need not consider the legal standing of the argument, however, because it lacks adequate factual support. The evidence consists of a newspaper article, which is inadmissible hearsay on the point, Eisenstadt v. Centel Corp., 113 F.3d 738, 742 (7th Cir. 1997), and recollections by three officials concerning the difficulty of an exam they last saw more than twenty years ago--the exam itself was not produced--offered for the implausible propositions that those pre-1972 exams required as much knowledge as a high-school graduate would be expected to have, and, even more important, that the exams were not themselves a part of the scheme of deliberate discrimination. An exam that has a disparate impact and is not job related may be innocent, but then again it may be a deliberate device to exclude minority applicants. That it was the latter is the more plausible inference given the stubbornness with which the de partment, until the mid-1980s, resisted equal treatment of blacks and Hispanics.

The plaintiffs point us to an exam that the City gave in 1995 to new applicants for firefighter positions. The white pass rate was higher (97 percent) than the pass rates of the blacks and Hispanics (54 percent and 66 percent respectively) and from this the plaintiffs ask us to infer that it is the educational deficiencies of the members of the minority groups, rather than discrimination, that is responsible for their having been underrepresented in the department in the period, before the mid- 1980s, in which their underrepresentation furnished the justification for affirmative action. But the 1995 examination has never been determined to be an accurate, unbiased test of job- related skills. It has been challenged in litigation, not yet resolved, as being discriminatory, and there is no evidence in the record of this case to validate it as a proper screen for jobs in the fire department. The district judge was therefore not required to accept it as evidence of an incapacity of members of the minority groups to meet appropriate educational standards for firefighters.

In their emphasis on the 1995 exam and the pre-1972 exams, the plaintiffs overlook a more direct problem with the pool used by the district judge (the age- and sex-adjusted Chicago population)-- namely that the fire department draws applicants from the Chicago suburbs as well as the city, and the suburbs are "whiter"--and also a more substantial problem with the City's affirmative- action program. The plaintiffs allude to the latter problem by accusing the program of "interminability," but give no more than a bare hint of what they mean by this. What they could mean, but do not say, is that affirmative action designed to remedy past discrimination must, because it is itself a form of racial discrimination and must therefore withstand the beady-eyed review that goes by the name of "strict scrutiny," e.g., City of Richmond v. Croson, supra; Billish v. City of Chicago, 989 F.2d 890, 891 (7th Cir. 1993) (en banc), cease at the point at which the consequences of the past discrimination have substantially dissipated. Adarand Constructors, Inc. v. Pena, 515 U.S. 200, 237-38 (1995); (plurality opinion); Middleton v. City of Flint, 92 F.3d 396, 411-12 (6th Cir. 1996); Taxman v. Board of Education, 91 F.3d 1547, 1564 (3d Cir. 1996) (en banc) (alternative holding); cf. People Who Care v. Rockford Board of Education, 246 F.3d 1073 (7th Cir.2001), and cases cited there. In 1987, the City administered an entrance-level test that is conceded to have been appropriate. Anyone who took the test, passed it, and was hired was eligible in 1993 to take the exam for lieutenant, and in 1994 to take the exam for engineer. Suppose that owing to rapid turnover, the pool of firefighters eligible to take the 1993 and 1994 exams was composed entirely of people hired on the basis of the 1987 exam. Suppose further that promotions based on the 1993 and 1994 exams were free from discrimination. Then, unless minority persons had been deterred by earlier discrimination from taking the 1987 exam, International Brotherhood of Teamsters v. United States, 431 U.S. 324, 365-66 (1977), there would be no basis for giving them a leg up in promotions. But if, say, only 50 percent of the pool of eligibles in 1993 and 1994 had been hired from among people who passed the 1987 exam, and the rest had been hired earlier, at a time when the fire department discriminated against minority applicants, then the pool of eligible minority applicants for promotion in 1993 and 1994 would have been artificially limited and some favoritism in promotion would have been necessary to create as many black engineers and lieutenants as could have been expected to be promoted to these ranks had the department never discriminated. The plaintiffs have failed, however, in their briefs in this court to argue that our first hypothetical gives a true picture of the facts.

The argument is therefore forfeited, along with another possible argument-- that unless there is very heavy turnover in the department, a policy of hiring members of minority groups in excess of its percentage of the labor pool will eventually result in overshooting the hiring goal. Suppose blacks are 25 percent of the labor pool, but only 10 percent of the fire department, so one year the department hires 40 percent blacks, and it repeats this until 25 percent of the department is black. As the years go by, those 40 percent black vintages, constituting a larger and larger fraction of the total workforce, will bring the black percentage above 25 percent even after the department has (because new hires of minority persons are now equal to the percentage of such persons in the labor pool) abandoned its affirmative-action hiring--unless the department discriminates against minorities in new hiring, which would be illegal. The easiest way to grasp this point is to imagine that at time 1, the department has 1,000 employees, of whom 900 are white and 100 are black; that at time 2, some years later, 500 of those employees have retired (450 whites and 50 blacks) and 500 new employees have been hired, of whom 200 are black, so that 25 percent of the workforce is now black; and that at time 3, the other 50 percent of the workforce in time 1 have retired (450 whites and 50 blacks) and been replaced by 125 newly hired blacks (25 percent of 500) and 375 newly hired whites. Then at time 3 the workforce will consist of 325 blacks and 675 whites--and thus will be almost one-third black, rather than one-quarter.

The only plaintiff to preserve a Title VII claim, Richard Temple, argues that the City has engaged in the practice forbidden by that statute of "race norming," which means altering scores on tests so that the mean score is the same for each race. 42 USC sec. 2000e-2(l); Billish v. City of Chicago, supra, 989 F.2d at 895; Hayden v. County of Nassau, 180 F.3d 42, 53 (2d Cir. 1999); Baynes v. AT & T Technologies, Inc., 976 F.2d 1370, 1374 n. 5 (11th Cir. 1992) (per curiam). If the average black score on a test was 100 and the average white score 110, rescoring the average black test as 110 would be forbidden race norming; likewise if, regardless of relative means, each black's score was increased by 10 points on account of his race, perhaps because it was believed that a black with a 10- point lower score than a white could perform the job just as well (in other words that blacks are better workers than test takers). What the City actually did was to "band" scores on the various promotion exams that the plaintiffs challenge and treat scores falling within each band as identical. So, for example, if 92 and 93 were both in the A band, a black who scored 92 would be deemed to have the same score as a white who scored 93.

We must consider whether banding, when it works to the advantage of a particular racial or ethnic group, is race norming. This is a question of first impression. For although banding has been upheld as a valid method of affirmative action, Boston Police Superior Officers Federation v. City of Boston, 147 F.3d 13, 24 (1st Cir. 1998); Officers for Justice v. Civil Service Commission, 979 F.2d 721 (9th Cir. 1992); Bridgeport Guardians, Inc. v. City of Bridgeport, 933 F.2d 1140, 1148 (2d Cir. 1991), none of the cases considers its consistency with the prohibition of race norming. See, e.g., Officers for Justice v. Civil Service Commission, supra, 979 F.2d at 725-26.

We have no doubt that if banding were adopted in order to make lower black scores seem higher, it would indeed be a form of race norming, and therefore forbidden. But it is not race norming per se. In fact it's a universal and normally an unquestioned method of simplifying scoring by eliminating meaningless gradations. Any school that switches from number grades to letter grades is engaged in banding. But even number grading systems are banded. Take a grading system in which 100 is the maximum grade and anything below 60 is failing. Suppose further that there are 200 questions, each to be weighted equally in the grading. Someone who answered all 200 correctly would get a score of 100. But what of someone who answered 199 correctly? Would he get a score of 99 or 100? He "should" get a score of 99.5, but normally exams are not scored so finely. So if he is given a score of 100, he has been put in a band, the 99 to 100 band, and if he is given a score of 99, he is put in another band, with anyone who answers 198 questions correctly. The narrower the range of abilities in a group being tested, the more attractive banding is. If the skill difference between someone who gets 200 questions right and someone else who gets 199 right is trivial to the point of being meaningless, then giving them different grades is misleading rather than illuminating. It is on this basis that a school will sometimes substitute letter grades for number grades, thus, for example, placing all grades of 90 to 100 in the band called A, all grades between 80 and 89 in B, and so forth. Banding in this sense does not discriminate invidiously between a student who would have gotten 85 in a number grading system and a student who would have gotten 84 in such a system, just because now both get B. Nor is banding likely to favor one group over another. Switching from number to letter grades helps the student who would have gotten a 90 and now gets the same grade as a student who would have gotten 100, but it hurts the student who would have gotten an 89 and now is lumped in with students at the bottom of the B band.

The plaintiffs argue that even if affirmative action in fire department promotions is justified by the history and lingering effects of the department's long-standing discrimination against minority persons, the requirement of"narrow tailoring" required the City to lessen the burden on the white employees in one of three ways: creating vacancies for blacks by adopting an early retirement plan that would lure whites into retiring early, making way for the blacks and Hispanics; paying whites passed over for promotions in favor of minority persons what the whites would have been paid had they been promoted instead; or promoting whites on the same schedule they would have been promoted on had it not been for affirmative action, and thus simply promoting more people rather than promoting some minority firefighters in place of some white ones ("wrap-around promotions"). These methods of softening the blow sound very different but are really the same: the cost of affirmative action is shifted from the whites actually disadvantaged by it, that is, the whites who are competing for promotions with the beneficiaries of affirmative action, to the taxpayers, who would be funding the early retirement plan, the "as if promoted" pay raise, and the redundant promotions (the wrap arounds).

This argument misunderstands "narrow tailoring." Because affirmative action, at least when it takes the form of giving persons a leg up in hiring or promotion on the basis of their race (or, in the case of Hispanics, ethnicity, which for these purposes is equated to race), is a form of racial discrimination, the courts insist not only that there be a compelling case for it but also that it discriminate as little as is consistent with the achievement of its valid objective. See Majeske v. City of Chicago, 218 F.3d 816, 819-24 (7th Cir. 2000); McNamara v. City of Chicago, supra, 138 F.3d at 1222, and cases cited in both these opinions. In the present setting this means that as few white firefighters should have their promotions delayed to make way for blacks and Hispanics as is consistent with remedying the lingering effects of the fire department's long history of racial discrimination. With the plaintiffs' other arguments rejected, it is apparent that this requirement has been met. What the plaintiffs seek by their "narrow tailoring" argument is not narrowing the scope of the affirmative action plan but shifting its incidence from the white firefighters to the City's taxpayers, a group that, ironically, includes a large number of blacks and Hispanics, while on the other hand some at least of the disadvantaged white firefighters may have benefited from the lack of competition from nonwhites in the era of racial discrimination. But that irony is not our point. Our point is that the financial incidence of an affirmative action plan is normally a detail from the constitutional standpoint. This would be obvious if white firefighters had "affirmative action insurance," insuring them against the cost of delayed promotions due to affirmative action pro grams. The existence of such insurance would not transform the case from one of discrimination against white firefighters to discrimination against the members of the insurance pool. For compelling reasons of practicality, courts generally ignore the incidence of challenged conduct; hence the rejection of a "passing on" defense in antitrust, Illinois Brick Co. v. Illinois, 431 U.S. 720, 731-33 (1977), and hence the economic-loss doctrine of tort law. E.g., All-Tech Telecom, Inc. v. Amway Corp., 174 F.3d 862, 865 (7th Cir. 1999). Likewise it would not be practical for the district judge or us to decide whether the City's taxpayers are the more appropriate group to bear the burden of the affirmative action program than the white firefighters.

What is true is that any individual hurt by an affirmative action plan can complain that the burden on him is undue, for example if he's being told to give up his job. See, e.g., Wygant v. Jackson Board of Education, 476 U.S. 267, 282-84 (1986) (plurality); McNamara v. City of Chicago, supra, 138 F.3d at 1222; Taxman v. Board of Education, supra, 91 F.3d at 1564; Peightal v. Metropolitan Dade County, supra, 26 F.3d at 1561. But this principle is not in play when the only complaint is about a modest delay in promotion. Boston Police Superior Officers Federation v. City of Boston, supra, 147 F.3d at 24; Peightal v. Metropolitan Dade County, supra, 26 F.3d at 1561-62. All but one of the plaintiffs has been promoted to the job he sought, just on a slightly retarded timetable. The burden of delay that they have thus sustained is insufficient to warrant the courts in deciding whether to shift that burden to the taxpaying public, an inquiry that would involve judges in indefinite and intractable issues of public finance. For all we know, the burden has already been shifted, by changes in the compensation of Chicago firefighters designed to protect them against the consequences of the affirmative action plan.

One of the plaintiffs, it is true, John Fitzgerald, has not yet been promoted-- has in fact been waiting three years to be promoted and because his score on the 1989 test is now so old will have to take another captain's test before he can be promoted, promising further delay. But we do not understand him to be seeking relief separate from his fellow plaintiffs, such as an immediate promotion, but instead to have joined with them in seeking to have the affirmative action plan invalidated. He has not preserved an individual claim.