                            In the
 United States Court of Appeals
              For the Seventh Circuit
                         ____________

No. 06-2213
ELEANOR BAYLIE and FRANCES L. SMITH,
                                         Plaintiffs-Appellants,
                               v.


FEDERAL RESERVE BANK OF CHICAGO,
                                           Defendant-Appellee.
                         ____________
       Appeal from the United States District Court for the
         Northern District of Illinois, Eastern Division.
          No. 98 C 1186—William J. Hibbler, Judge.
                         ____________
  ARGUED JANUARY 3, 2007—DECIDED FEBRUARY 14, 2007
                     ____________


 Before EASTERBROOK, Chief Judge, and POSNER and
WOOD, Circuit Judges.
  EASTERBROOK, Chief Judge. This appeal presents the
tail end of a class action in which employees accused the
Federal Reserve Bank of Chicago of race, sex, and age
discrimination. Four years ago the district court decerti-
fied the class and allowed employees to pursue individ-
ual claims. Only two remain for resolution on this appeal.
The district judge concluded that these two had not
established even a prima facie case of discrimination and
granted summary judgment to the Bank.
2                                               No. 06-2213

  Although only two employees’ claims remain for decision,
their brief proceeds largely as if a class continued to seek
systemic relief. Plaintiffs rely heavily on the report of an
expert who concluded that black employees were less
likely to be promoted than white employees. They main-
tain that this report is enough by itself to require a trial.
Going to the opposite extreme, the Bank contends that
statistical evidence is never relevant outside a class
action or a suit by a public agency on behalf of employees
as a group. Both of these positions misunderstand the
role of statistical inference.
  Most contentions in litigation are empirical rather than
axiomatic. Propositions of fact are arrived at by inductive
rather than deductive means. All inferences are statisti-
cal—whether implicitly or explicitly does not matter. A
plaintiff who accuses Supervisor X of discrimination
because he never has promoted a black person, and often
says disparaging things about black workers, is drawing
a statistical inference: that if X has been indifferent to
race, then selections from the pool of employees eligible
for promotion would have included some black workers,
and in particular would have included the plaintiff.
Likewise the proposition “9 of 10 people exposed to sarin
die within 20 minutes, so sarin is deadly” is a statistical
inference, one so obvious that no expert is needed to
show causation. But the inference often may be elusive,
and then someone trained in the analysis of numbers
will help.
  Professional statistics is a rigorous means to analyze
large numbers of events and inquire whether what ap-
pear to be patterns really are the result of chance (and, if
not, which variables are associated with which outcomes).
Suppose we know that 20,000 of 100,000 persons exposed
to high dosage x-rays eventually develop cancer, and that
19,500 of 100,000 persons not so exposed develop cancer.
Should we attribute the apparent excess risk of 500
No. 06-2213                                              3

cancers to the x-ray, or might it have some other cause? Is
this excess risk real or an illusion caused by errors in
measurement and analysis, the sort of variance that
may occur by chance? A statistical analysis may be able
to answer these questions—and, if the answer is yes, the
knowledge that high-dosage x-rays increase the risk of
cancer may inform a decision whether the benefits of
the procedure are worth the extra risk. But it will not
tell us whether a given person who develops cancer did
so because of the x-ray; only 2.5% of cancers can be at-
tributed to the radiation, so 97.5% of all cancers, even
among persons exposed to high-dosage x-rays, have other
causes. This is the sense in which statistics are more
helpful in a pattern-or-practice case, where a judge will
be asked to direct the employer to change how it makes
hiring or promotion decisions.
  In individual cases, studies of probabilities are less
helpful. Suppose 1,000 employees apply for 100 promo-
tions; 150 of the workers are black and 850 white. If all
are equally qualified and the employer ignores race, then
85 white workers and 15 black workers will be promoted,
plus or minus some variation that can be chalked up to
chance. Suppose only 10 black workers are promoted. Is
that the result of discrimination or chance? Econometric
analysis (an application of statistical techniques) may
suggest the answer by taking into account both other
potentially explanatory variables and the rate of ran-
dom variance. See Mister v. Illinois Central Gulf R.R.,
832 F.2d 1427 (7th Cir. 1987); Federal Judicial Center,
Reference Manual on Scientific Evidence 83-227 (2d ed.
2000); Paul Meier, Jerome Sacks & Sandy L. Zabell, What
Happened in Hazelwood: Statistics, Employment Dis-
crimination, and the 80% Rule, 1984 Am. Bar Foundation
Research J. 139, 158-70; Thomas J. Campbell, Regression
Analysis in Title VII Cases, 36 Stan. L. Rev. 1299 (1984).
4                                               No. 06-2213

   When the answer is positive (discrimination occurred;
the conclusion is statistically significant) it cannot reveal
with certainty whether any given person suffered. In
this example, 150 black workers applied for promotion;
10 were promoted and the other 140 were not. But for
discrimination, 15 would have been promoted and 135 not.
Which of the 140 non-promoted employees would have
received the other 5 promotions? The statistical analysis
does not tell us—and in civil litigation, where the plain-
tiff ’s burden is to show more likely than not that he was
harmed by a legal wrong, data of this kind will not get
a worker over that threshold.
  Statistical analysis is relevant in the technical sense
that it “has a tendency to make the existence of [a mate-
rial] fact . . . more probable or less probable than it would
be without the evidence.” Fed. R. Evid. 401. But data
showing a small increase in the probability of discrimina-
tion cannot by itself get a plaintiff over the more-likely-
than-not threshold; it must be coupled with other evidence,
which does most of the work. A disappointed worker
could ask for damages measured by the lost opportunity:
each of the 140 disappointed workers might receive as
damages 5/140 of the extra income enjoyed by those who
received promotions. That’s the loss-of-a-chance measure
of damages. See Doll v. Brown, 75 F.3d 1200 (7th Cir.
1996). But it is more suited to class-wide litigation, and
our two plaintiffs have not requested this remedy.
  What statistics did these plaintiffs offer—the kind that
permit a sound inference in an individual case (our
examples of Supervisor X and exposure to sarin) or the
kind that may support class-wide equitable relief but are
only marginally relevant when an individual plaintiff
seeks an award of damages? Plaintiffs’ expert analyzed all
non-managerial workers at the Bank between 1995 and
2000. Workers as a whole enjoyed a probability of about
0.25 of being promoted to a higher pay grade each year
No. 06-2213                                               5

(stated otherwise, the average worker was promoted once
every four years). Coefficients in an econometric regression
implied that black workers had about a 0.20 probability
and white workers about a 0.27 probability, and after
controlling for other variables the expert concluded that
5/7 of this difference (or a 0.05 chance of promotion each
year) was unaccounted for by any hypothesis other than
race. In other words, the average white worker received
an extra promotion every 20th year compared with the
average black worker, holding constant factors (such as
education) other than race. The Bank’s experts questioned
whether this result is statistically significant (that is,
whether the difference is a result of chance rather than
race) and whether it is meaningful for most of the workers.
It turns out that the most frequent “promotion” is from
temporary to full-time work. If the analysis is limited to
persons (such as plaintiffs) already working at the
Bank full time, then black workers are slightly more
likely than white workers to be promoted in any given
year.
  Given the consequence of restricting the data set to full-
time workers, this econometric analysis offers our two
plaintiffs no support. Even presented as plaintiffs’ expert
did, rolling the temporary-to-full-time promotions into
the data, the study doesn’t provide plaintiffs with much
assistance. These two plaintiffs applied for several pro-
motions annually. If race affects one promotion every
20 years, and workers seek three promotional opportuni-
ties a year, then there is one chance in 60 that a given
application would have been successful if the applicant
were white rather than black. Over many years and
many employees this effect could be substantial—which
is why such analysis is helpful in class actions—but in a
single employee’s case it does very little to get the claim
over the more-likely-than-not threshold. A worker can’t
say simply: “I’ve been here 20 years, so I’m entitled to one
6                                                No. 06-2213

extra promotion.” All of that time except the most recent
300 days falls outside Title VII’s statute of limitations. See
National Railroad Passenger Corp. v. Morgan, 536 U.S.
101 (2002). Analysis thus must proceed vacancy-by-
vacancy in an individual case, not career-by-career.
  If a plaintiff had evidence suggesting that the probabil-
ity that race accounted for a given turn-down was (say)
49.8%, then the addition of the statistical analysis would
push the probability past 50%. In other words, the ex-
pert’s conclusion in this litigation could serve as a tie-
breaker. But first there would have to be a tie—and
plaintiffs’ evidence does not come close to making this
case a tossup that statistics might decide in their favor. Cf.
Sun v. University of Illinois, No. 06-2438 (7th Cir. Jan. 16,
2007), slip op. 23-26 (considering statistical evidence in
an individual case but finding that the data did not
create a material dispute).
  Frances Smith began as a staff assistant in 1977 and
after multiple promotions reached the rank of “senior
examiner” in 1994. Smith’s applications for further
advancement have been denied, and her principal argu-
ment is that she is no less qualified for promotion than
white “senior examiners” who the Bank did promote to
higher grades (though not different titles; “senior exam-
iner” is the highest in the progression). In addition to
contending that the econometric analysis is enough to
create a jury issue, Smith maintains that the district
judge was too demanding in requiring her to show that
the white employees to whom she compared herself were
comparable in every respect.
  The judge may well have asked too much of comparabil-
ity analysis, see Crawford v. Indiana Harbor Belt R.R.,
461 F.3d 844 (7th Cir. 2006), but that doesn’t matter. The
Bank explained why it passed Smith over: pay grades
higher than Smith’s are awarded only to examiners who
No. 06-2213                                                7

do substantial field work (that is, examine books in the
banks that the Federal Reserve regulates), and Smith has
declined to accept a position as a full-time field examiner.
Nothing in the record suggests that this explanation is
a lie, so, even if Smith has made out a prima facie case, no
reasonable jury could find the Bank’s explanation to be
a pretext for discrimination. The case is not close; the
statistical study cannot tip the balance.
  Eleanor Baylie has worked for the Bank as a secretary
since 1964; her most recent promotion, to a grade 9
position, was in 1988. Since then she has applied for
multiple positions, none of which is secretarial, in grades
10 and above. The positions for which she was passed
over have titles such as “control specialist” and “production
coordinator"; it is impossible to tell from these titles, or
the parties’ briefs, the duties of these positions and
whether Baylie would be competent to perform them.
Baylie asserts that she is at least as well qualified as the
workers who received these promotions, but her brief
contains no details about who received the promotions,
after what process. It does not contain citations to the
portions of the record bearing on her individual claim (as
opposed to the statistical analysis). There is accordingly
no reason to believe that race or sex played a role in the
decisions.
  Although, as we observed in Crawford, a district judge
should not insist that the other employees to whom a
plaintiff compares herself be identically situated, there
must be a reasoned basis for thinking the comparator
close enough in material ways so that a reasonable fact-
finder could think that race (sex, or another covered
attribute) was the difference that the employer per-
ceived. When despite ample opportunity for discovery the
plaintiff makes no serious effort to show that the favored
worker was similarly situated except with respect to race
(sex, and so on), the district judge properly concludes that
8                                               No. 06-2213

a prima facie case of discrimination has not been estab-
lished.
  So it is here. Baylie’s opening brief does not tell us who
received the promotions she sought or in what respects the
applicants were like (or unlike) her. Her reply brief
devotes one page to that subject, but the effort is too little
and too late. Baylie obviously believes in her own skills,
but employers make comparative rather than absolute
judgments. Because Baylie has not tried to show in the
necessary detail that race rather than an employer’s
honest evaluation of comparative skills accounts for the
decisions, the Bank was entitled to summary judgment
in its favor.
  Plaintiffs’ other arguments have been considered but do
not require discussion. The judgment is affirmed.

A true Copy:
      Teste:

                        ________________________________
                        Clerk of the United States Court of
                          Appeals for the Seventh Circuit




                   USCA-02-C-0072—2-14-07
