Opinion for the Court filed by Circuit Judge WILLIAMS.
STEPHEN F. WILLIAMS, Circuit Judge:
A class of older Deputy U.S. Marshals alleges age discrimination in violation of the Age Discrimination in Employment Act (“ADEA”), 29 U.S.C. §§ 623, 633a
et seq.
The class consists of deputies who, while they were GS-11 Criminal Investigators, were eligible and applied for positions as GS-12 Senior Criminal Investigators; who were at least 40 years old at the time of the disputed selections; and who were not selected for vacancies for which deputies under 40 were selected.
The district court rejected the plaintiffs’ disparate impact claim on summary judgment, ruling that they failed to establish a prima facie case. It rejected their disparate treatment claim after a full trial, finding that the plaintiffs had failed to carry their burden of proof. We affirm.
* * *
The Marshals Service is part of the Department of Justice and its mission is “to provide for the security and to obey, execute, and enforce all orders of the United States
District Courts, the United States Courts of Appeals and the Court of International Trade.” 28 U.S.C. § 566 (1994). A deputy marshal can be called upon to perform a wide range of duties, including the protection of the federal judiciary, the transportation of federal prisoners, and the seizure of assets.
When the Service created the post of GS-12 Senior Criminal Investigator in 1987, it also devised a system for filling the positions, a system it has maintained, with modifications made in 1989 and 1990, through to the time of the district court’s decision in 1994. Under this system, the positions are allocated among the judicial districts; typically only those deputies working in a particular district may apply for a promotion in that district.
Any applicant must have at least one year of experience at the GS-11 level. Each submits an “Application for Law Enforcement Positions,” which includes information about the applicant in each of the first four of seven categories of information that will later be “scored,” namely experience, education, training, and awards. The applicant also submits copies of his two most recent “Annual Performance Evaluations” and his physical fitness test results (the “FIT Assessment”). These all go to the applicant’s supervisor, who adds a “Supervisory Promotion Evaluation.”
Based upon the information in this package, the merit promotion staff at the Marshals Service headquarters scores most applications under the guidance of a confidential Rating Guide (the districts originally did the scoring and are still permitted to do so if they choose). The person scoring the package can award the applicant a maximum of 100 points, divided as follows:
Experience Section 40 points
Training Section 10 points
Awards Section 10 points
Education 10 points
Annual Performance Evaluation 10 points
Physical Fitness (FIT Assessment) 10 points
Supervisory Evaluation 10 points
The scores of all the applicants for a particular vacancy are recorded on a “Verification of Scores List,” and the highest-scoring applicants are placed on a “Certification List.” The marshal for the district filling its vacancy may request the selection of any deputy on the certification list. Starting in 1988, the marshal’s recommendation was forwarded to the Career Development Board at the Service’s headquarters, along with the verification list and the certification list. The Board usually selected the candidate recommended by the marshal; in the absence of a recommendation, it typically chose the highest-scoring applicant. More recently, the marshal’s recommendation has been subject only to approval by the merit promotion staff, with the Associate Director of the Service resolving cases in which the staff raises an objection.
Although older deputies and younger (under 40) deputies were appointed in proportion to their frequency in the applicant pool, plaintiffs identify statistical disparities in two separate phases of the process. First, in some years the younger deputies did proportionately better than the older ones in four of the seven formally scored categories — Training, Education, Physical Fitness and Annual Appraisals. Second, plaintiffs offered evidence that if scores on the seven-part scoring system are held constant, younger deputies did better than older ones in the final phase of the process, actual promotion. In addition, plaintiffs specifically attack several of the criteria in the scoring system, claiming that the Service has chosen them with an intent to discriminate against older deputies.
We address the disparate treatment claim first, then the disparate impact claim.
Disparate Treatment
Age discrimination is governed by the disparate treatment analysis developed in the Title VII context.
Arnold v. U.S. Postal Service,
868 F.2d 994, 996 (D.C.Cir.1988). To prevail, the plaintiff must first establish a prima facie case by showing that the plaintiff is a member of the protected class (here, persons 40 or older) who was qualified for and applied for a position, but was rejected in favor of a younger deputy.
McDonnell Douglas Corp. v. Green,
411 U.S. 792, 802, 93 S.Ct. 1817, 1824, 86 L.Ed.2d 668 (1973);
Texas Department of Community Affairs v. Burdine,
450 U.S. 248, 253-54 n. 6, 101 S.Ct.
1089, 1094 n. 6, 67 L.Ed.2d 207 (1981). If the plaintiff establishes a prima facie case, the defendant must come forward with a legitimate, non-discriminatory reason for its actions. Finally, if the defendant meets its burden of production, the burden shifts back to the plaintiff to persuade the fact finder that the defendant’s reason for its action is a mere.pretext for discrimination and (thus) that the defendant acted with “discriminatory intent.”
Id.
at 252-54, 101 S.Ct. at 1093-94;
Arnold v. U.S. Postal Service,
863 F.2d 994, 996 (D.C.Cir.1988).
The plaintiffs’ prima facie case is not in dispute. We therefore turn to the district court’s conclusion that the plaintiff failed to show discriminatory intent, reviewing for clear error.
Bazemore v. Friday,
478 U.S. 385, 398, 106 S.Ct. 3000, 3007-08, 92 L.Ed.2d 315 (1986).
Non-Statistieal Evidence
The district court found that the system was indeed legitimate and non-discriminatory, “designed to measure a range of variables that, in combination, reliably indicate whether the applicant is among the best deputies in his or her district and whether the applicant has the skills and background necessary to perform a broad range of tasks.” Memorandum of June 6, 1994 (“Disparate Treatment Memorandum”) at 8. The court also framed its findings about the system partly in terms of incentives, saying-that it provided
an incentive for deputies to gain experience, update training, gain additional education, strive for awards, achieve high levels of performance, and be physically fit— all of which are important qualities in performing the varied duties of a Deputy United States Marshal.
Id.
And the court noted that the Service gave heavy weight to experience, a factor on which the older deputies did disproportionately well, as plaintiffs’ expert had conceded. Finally, it observed that promotion rates were proportional as between younger and older deputies.
At oral argument plaintiffs suggested that some of the Service’s criteria were illegitimate, because, they said, they were aimed at providing desirable incentives for deputy marshals rather than choosing the persons most fit for the jobs, in violation of regulations of the Office of Personnel Management. We are not clear why plaintiffs assume that there is a conflict between criteria aimed at selecting the most suitable candidate and at providing incentives for career development, but in any event we need not address the issue. The allusions to the theory in plaintiffs’ opening brief are sketchy at best, at no point identifying the language in OPM regulations that plaintiffs see as barring career development purposes. Lest opposing litigants be sandbagged, we do not resolve issues raised so fecklessly. See, e.g.,
Carducci v. Regan,
714 F.2d 171, 177 (D.C.Cir.1983); cf. Fed. R.App. P. 28(a)(6).
The district court also found that the plaintiffs failed to show that the Service’s reasons for using any of the seven criteria of the formal scoring were pretextual, and we find no error. The improbability of pretext is suggested by the Service’s system of scoring on physical fitness. Deputies receive 0, 1 or 2 fitness points for various degrees of fitness in each of five categories, but the system is scaled so that in each category older deputies can earn points for lower levels of fitness than younger ones. Disparate Treatment Memorandum at 11; see also the Service’s Rating Guide 5-7, 5-12. Plaintiffs seem to be imputing a rather machiavellian spirit to the Service, implicitly arguing that, although intentionally discriminating against older workers, it simultaneously lay a false trail by explicitly discriminating in their favor. Nonetheless, we work through plaintiffs’ superficially most promising attacks on the court’s rejection of their attempted proof of pretext.
Although the older deputies did proportionately better than younger ones in the experience portion of the rating system, plaintiffs argue that they would have done even better had the system not been rigged against them. The key part of the alleged rigging stems from the Service’s Deputy Development Program, which is aimed at enhancing the experience of newly hired deputies — presumably the ones for whom the incremental value of extra doses of varied experience and training is greatest.
Deputies in the program must complete assignments in six different areas over a period of three years: fugitive investigations; witness security; special assignments; asset forfeiture; headquarters; and supervisor observation. Disparate Treatment Memorandum at 12. Although plaintiffs argue that the Deputy Development Program assignment system benefits younger deputies, the district court found that these assignments do not correspond to specific tasks in the GS-12 application package and that the assignments are frequently not considered desirable.
Id.
And the court found that supervisors do not give deputies in the program priority in assignments, except when the deputies need particular assignments in order to complete their program requirements.
Id.
The Deputy Development Program presumably gives new hires an advantage that they would not have had in its absence. On its face that seems a completely innocent consequence of a legitimate and non-diserimi-natory decision to focus resources where they will yield the most payoff in enhanced experience. There is, however, a wrinkle to the system that looks superficially fishy. Because Congress has authorized the Service to set a maximum age for new hires, 5 U.S.C. § 3307 (1994), an age which is currently set at 37 years, and the Service has exercised that authority, the deputies in the three-year program are evidently never over 40, so that, plaintiffs evidently claim, the program is really a device for aiding deputies outside the ADEA-protected class. We have already held, however, that the authority to set an age entry maximum trumps the ADEA (so long as the authority is properly exercised, and here no claim is made to the contrary).
Stewart v. Smith,
673 F.2d 485 (D.C.Cir. 1982). It would make no sense to say that § 3307 allows the Service to engage in explicit age discrimination in hiring, but that the ADEA disables it from setting up a program legitimately designed to train new hires — at least where there is no evidence that the focus on new hires was pretextual. There being no such evidence, the fact of the Deputy Development Program, with its age-related collateral effects on the experience and other criteria of the scoring system, does not help the plaintiffs establish discriminatory intent.
A closely related claim is that deputies in the Deputy Development Program are advantaged by the requirement that in the experience segment of the application deputies set forth narratives of their experience. Deputies in the program evidently receive assistance in completing these narratives. Again, such assistance seems a non-discriminatory way of speeding the development of new hires. Nor is there any reason whatever to believe that the requirement of narratives is itself either illegitimate or pretextual. Indeed, one of the plaintiffs himself testified that in some respects the requirement of narratives aids older deputies, because they learn through experience how to use the narratives to their advantage. Disparate Treatment Memorandum at 13.
Plaintiffs also argue that the system for scoring training and awards improperly disadvantages older deputies. Training and awards are given fall credit if they occurred in the last five years before the application, half credit if earlier (originally no credit was given for earlier training and awards, but the Service later chose to give half credit). Plaintiffs offer nothing to suggest any illegitimacy or pretextuality in this system. The benefits of training erode over time (even among the young), and past triumphs decay as predictors of the future.
Finally, plaintiffs object to the Service’s policy of giving points in the education criterion for college-level course work, saying that this disadvantages older deputies because most of them do not have a college education, while most younger ones do. A minimum of ten semester hours is required to receive points, with no restrictions on the subject matter of the courses. The court accepted evidence that this aspect of the scoring system provided information about a deputy’s ability to analyze and assimilate information, and that the need for these skills had increased over the past ten years as the deputies’ responsibilities have expanded to include areas such as asset forfeiture. Disparate Treatment Memorandum at 15. Plaintiffs offer no reason to doubt these conclusions.
Statistical Evidence
Plaintiffs’ expert examined the years 1988-1993 and found that, on certain components of the promotion package, the older an applicant the more likely his scores were to be low, and that for the years listed below these negative correlations were statistically significant:
Negative Correlation with Age Year
Training 1988
Education All Years
FIT Assessment All Years
Annual Appraisal 1989,1990, 1991
She also found a number of statistically significant
positive
correlations (i.e., in favor of the older candidates):
Positive Correlation with Age Year
Experience 1989
Training 1992
Supervisory Evaluations 1989
The presence of statistically significant deviations from proportionality in
both
directions plainly cuts against the inference plaintiffs seek to draw.
In these analyses plaintiffs’ expert treated age as a continuous variable, so that, for example, a 25-year-old deputy outscoring a 35-year-old deputy would tend to increase the apparent advantage of the young. She also conducted additional analyses, however, using a “dummy variable” for age (“AGE-DUM”) that divided applicants into an under-40 category and an over-40 category, which also yielded a statistically significant negative correlation.
Finally, the expert conducted an analysis on the final stage of the promotion process, to test whether, even if the
scoring
system was not discriminatory as between older and younger deputies, the Service might be discriminating in the final choices from the certification list. The expert ran a regression from which she concluded that, as between deputies with the same total score, older deputies were less likely to receive promotion. She found this disparity statistically significant for three of the years examined— 1988, 1989 and 1992. In this analysis she used only the continuous variable for age. Defendant attacked these statistics on three grounds, and offered alternative figures leading to the opposite conclusion about the last stage of the promotion process, i.e., tending to show that older deputies were more likely to be promoted, holding scores constant. The first alleged error is not disputed here, and we discuss it only to explain why it does
not
play a role in our assessment of the evidence. The expert assumed in the analysis of the final stage, promotion itself, that all applicants were competing for all vacancies, while in fact they competed district-by-district for specific vacancies. Thus if scores were generally higher in some districts (because of scoring variation or a different general level of qualifications), the non-appointment of a high-scoring older deputy would produce figures suggesting that younger deputies did better holding all factors constant, while in fact the older deputy had simply lost out to a higher-scoring deputy. While we think the methodological choice indeed impaired plaintiffs’ analysis of the final stage, that analysis falls because of a more drastic defect, which we address shortly. So far as the expert’s study of the
scoring
system is concerned, this aspect of her approach seems to us simply irrelevant.
The two disputed methodological issues are these: First, defendant argues that plaintiffs’ analysis of the final stage of the process was flawed because it used a continuous variable for age rather than a variable that classified a deputy as either over 40 or under 40. Second, defendant says that plaintiff failed to include certain competitions, such as those between deputies over 40. The district court found both of these critiques, as well as the now undisputed one, convincing. Turning to the two contested issues, we agree with the district court that the plaintiffs’ expert was incorrect to use the continuous variable for age, but we find the plaintiffs’ exclusion of certain contests to be proper.
Age as a Continuous Variable
The sole evidence offered in support of discrimination at the stage of ultimate promotion was plaintiffs’ regression analysis purporting to show that, holding aggregate scores constant, the younger deputies had a
greater chance of promotion. The district court rejected this on the ground that the regression was based simply on variation in age, as opposed to discrimination against those 40 or over. Because the expert used a continuous variable for age, her results do not address the issue of whether, holding scores constant, a deputy 40 years old or more is less likely to be promoted than a deputy under 40. All the regression shows is that older deputies (of any age) are less likely to be promoted, relative to younger deputies (of any age). But the entire statistical advantage of the younger deputies could have come from disparate promotion rates as between deputies in the under-40 category. Because these deputies are not protected under the ADEA, regardless of demonstrated discrimination, the inclusion of this data is fatal to the expert’s conclusion. See
Murnane v. American Airlines, Inc.,
667 F.2d 98, 99-100 & n. 3 (D.C.Cir.1981) (employer’s guideline against hiring persons over 30 considered only insofar as it was applicable to those over 40, because those under 40 are not protected under the ADEA); see also Ramona L. Paetzold and Steven L. Willbom, The Statistics of Discrimination: Using Statistical Evidence in Discrimination Cases, § 7.07 at 7-12 (1995) (observing that it would be error to infer illegal discrimination from figures simply showing statistical significance in “the relationship between age and termination for
all
employees”).
Plaintiffs urge that despite this defect, the court should have accepted the regression as having some probative value. They point especially to
Bazemore v. Friday,
478 U.S. 385, 106 S.Ct. 3000, 92 L.Ed.2d 315 (1986), in which the Court held that the lower courts erred in rejecting the plaintiffs’ regression analysis. The analysis had demonstrated a wage disparity between black and white employees with the same job title, education and tenure. The district court had rejected the regression because there were other variables, such as county-by-county wage variations, that might have accounted for the salary disparity. The Supreme Court rejected this argument, holding that “the omission of variables from a regression analysis may render the analysis less probative than it otherwise might be,” but that it does not make the analysis unacceptable as evidence.
Id.
at 400, 106 S.Ct. at 3008-09. The Court also said that the defendants had “made no attempt ... to demonstrate that when these factors were properly organized and accounted for there was no significant disparity between the salaries of blacks and whites.”
Id.
at 403-04 n. 14, 106 S.Ct. at 3010 n. 14. Following
Bazemore,
courts have taken the view that a defendant cannot undermine a regression analysis simply by pointing to variables not taken into account that might conceivably have pulled the analysis’s sting. See, e.g.,
Palmer v. Shultz,
815 F.2d 84, 106 (D.C.Cir.1987) (possible impact of individual preferences insufficient to justify rejection of plaintiffs’ analysis);
Segar v. Smith,
738 F.2d 1249, 1277 (D.C.Cir.1984) (similar);
EEOC v. General Telephone Co.,
885 F.2d 575, 582 (9th Cir.1989) (similar);
Sobel v. Yeshiva Univ.,
839 F.2d 18, 33-34 (2d Cir.1988) (similar). Courts have not, however, understood
Bazemore
to require acceptance of regressions from which clearly major variables have been omitted — such as education and prior work experience,
Sheehan v. Purolator, Inc.,
839 F.2d 99, 103 (2d Cir.1988), or, in decisions on academic pay, rank and tenure, the quality of teaching and research, and community and institutional service,
Penh v. Oregon State Bd. of Higher Educ.,
816 F.2d 458, 464-65 (9th Cir.1987) (distinguished in
General Telephone,
885 F.2d at 581-82).
Here, however, we do not deal with a regression that simply omits a variable of potential significance. Instead we have one that (if valid at all) supports an inference that is not legally relevant — that, holding aggregate scores constant, variations in age over the entire age range of applicants, are statistically associated with promotion. It thus fails to show a disparity that disfavors deputies 40 or older. To have required the defendant to have constructed and conducted the proper analysis to correct the plaintiffs’ error would be to improperly shift the burden of proof.
Nor does the other aspect of Bazemore’s analysis of statistical proof suggest that the court should have given plaintiffs’ regression any weight. The decision considered whether the inclusion of pre-Title VII data invali
dated the plaintiffs’ statistical analysis and concluded that it did not, because
proof that an employer engaged in racial discrimination prior to the effective date of Title VII might in some circumstances support the inference that such discrimination continued, particularly where relevant aspects of the decisionmaking process had undergone little change.
Id.
at 402, 106 S.Ct. at 8010; see also
Valentino v. U.S. Postal Service,
674 F.2d 66, 71 n. 26 (D.C.Cir.1982). The inclusion of pre-Title VII data might be thought analogous to the use of the continuous variable for age in our case, in the sense that both involve the inclusion of data that relate to unactionable discrimination. In
Bazemore,
however, the inclusion of pre-Title VII data provided information about an employer’s treatment of the protected class (just at a different time), whereas statistical disparities within the under-40 category say nothing about treatment of the protected class.
Exclusion of Certain Promotion Decisions
Plaintiffs’ expert excluded those promotion contests-where there were no applicants who were over 40, where there were no applicants under age 40, or where there was no competition for the promotion. The district court found that this was an error because it “excluded pertinent information concerning part of the plaintiff class.” Disparate Treatment Memorandum at 16. This conclusion, however, disregards the definition of the class, and therefore, the nature of the claims being made by the plaintiffs. The class is specifically defined as those deputies over 40 who were denied promotions in contests in which deputies under 40 were promoted.
We think the district court’s reasoning is in error on this point.
Adequacy of Evidence on Scoring
Although neither the defendants nor the district court have been clear on the effect of the statistical criticisms on the expert’s findings about the
scoring,
we cannot see that the criticisms are applicable. First, in her alternative treatment of the scoring, the plaintiffs’ expert did use the variable AGEDUM, which properly divided the deputies into over-40 v. under-40. Second, the failure to consider the district-by-district nature of the competition was significant only in regard to plaintiffs’ evidence as to possible discrimination in the final stage of the promotion process, evidence we’ve rejected because of the use of age as a continuous variable. Thus there remains the question whether the district court erred in excluding the evidence on the scoring itself, and if so, whether the error was harmless.
If there was any error, it was plainly harmless. First, although plaintiffs offered data showing statistically significant disparities, they never offered to show the
size
of the disparities, even though, where the sample size is large enough, a very slight disparity can be statistically significant. See Paetzold & Willborn § 4.13 at 4-31 & n.97. Second, where the
criteria
producing the alleged disparities are legitimate and non-pre-textual, as the court found, we doubt that evidence of disparities can add much. Once it is determined, for example, that fitness is a legitimate criterion, it is not informative to learn that the old do less well than the young (even after the scaling in their favor). Finally, as we have already noted, the same data showed statistically significant disparities
in favor of the older deputies.
This is true even for one of the criteria for which plaintiffs point to disparities running against them: training (1988 — statistically significant disparities in favor of young; 1992— statistically significant disparities in favor of old). Accordingly, any possible error in exclusion of the data was plainly harmless. See, e.g.,
Neuren v. Adduci, Mastriani, Meeks & Schill,
43 F.3d 1507, 1512 (D.C.Cir.1995).
Disparate Impact
Even where there is proportionality as between members of the protected class and others in promotion rates, as here, under Title VII a non-proportionality in some earlier phase of the selection process can be the basis of a disparate impact claim.
Connecticut v. Teal,
457 U.S. 440, 102 S.Ct. 2525, 73 L.Ed.2d 130 (1982). Plaintiffs argue that the non-proportionalities in some of the segments of the seven-factor scoring system in fact give rise to such a claim and require us to reverse the district court’s grant of summary judgment in defendant’s favor.
We assume without deciding that disparate impact analysis applies to age discrimination claims.
The parties’ dispute here has largely revolved around the issue of whether
Teal
allows a disparate impact claim for scoring in a phase of the process that is non-dispositive, 1.e., a phase that may affect applicants’ aggregate scores (and thus the probability of promotion), but that does not
in itself
create an
outright barrier
to promotion. In this connection the parties offer conflicting views as to whether our decision in
Arnold v. U.S. Postal Service,
863 F.2d 994, 999 (D.C.Cir.1988) (applying
Teal
only where a factor is a “free-standing element”) limits disparate impact analysis to such barriers — where there is no “bottom-line” disparity. We need not resolve that dispute, however, because plaintiffs have simply failed to show that the disparities in the intermediate phases of the process actually disadvantaged them at all.
Disparate impact analysis requires that plaintiffs show that the practice attacked caused at least some members of the class to be deprived of a promotion, or at least the opportunity of being considered for a promotion. “[T]he plaintiff must offer statistical evidence of a kind and degree sufficient to show that the practice in question has caused the exclusion of applicants for jobs or promotions.”
Watson v. Fort Worth Bank & Trust,
487 U.S. 977, 994, 108 S.Ct. 2777, 2789, 101 L.Ed.2d 827 (1988) (O’Connor, J., concurring); see also
Robinson v. Polaroid Corp.,
732 F.2d 1010 (1st Cir.1984).
By requiring plaintiffs to demonstrate “causation,” we do not mean that they must point to an outright barrier to promotion, precisely the issue we do not decide. Nor do we mean that they must show a bottom-line disparity. For example, suppose that plaintiffs had demonstrated that there was disparity on fitness scores, that promotions went strictly according to rank on the list, and that some older deputies would have been promoted if not for the disparity. The plaintiffs would then have demonstrated a causal link between disparate results in the fitness tests and the end results, even though the fitness test was not an absolute barrier (because lower scores on it could be compensated for by higher scores in other sections of the promotion package).
Here plaintiffs have demonstrated no impact caused by low scores. They have pointed to no person who was deprived of promotion due to low scores. Further, as we said before, although they showed that the disparity between old and young was statistically significant for some factors, they offered no evidence on the
size
of the disparity or its effect on
any
promotion decision involving a match up between old and young candidates. Nor do they show that the lower scores on the relevant portions of the promotion package in practice decreased the
probability
of promotion (even holding all factors constant). For all we know from the plaintiffs’ data, the magnitude of the disparity is
de minimis.
See, again, Paetzold & Willborn § 4.13 at 4r-31 & n.97. If we were to dispense with a causation requirement, it would, ironically, allow a group of older deputies to prevail on the ground that the fitness test gave them lower scores even if all the
older deputies — and none of the younger ones — were promoted. We affirm the district court’s grant of summary judgment for defendants.
The judgment of the district court is
Affirmed.