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

No. 01-4208
UNITED STATES OF AMERICA,
                                                    Plaintiff-Appellee,
                                  v.

JOHN VEYSEY,
                                                Defendant-Appellant.
                          ____________
             Appeal from the United States District Court
        for the Northern District of Illinois, Eastern Division.
            No. 99 CR 381—Rebecca R. Pallmeyer, Judge.
                          ____________
        ARGUED JUNE 2, 2003—DECIDED JUNE 26, 2003
                          ____________


  Before POSNER, EASTERBROOK, and WILLIAMS, Circuit
Judges.
  POSNER, Circuit Judge. John Veysey appeals from his
conviction, after a jury trial, and sentence of 110 years
in prison for mail and wire fraud, arson, and the re-
lated offense of felony by fire. The facts are amazing, but
we shall resist the temptation to recount them at length.
In 1991 Veysey set fire to his house and inflated the
claim that he then filed with his insurer. The insurer paid,
and the house was rebuilt. The following year Veysey
married a woman named Kemp, increased the insurance
on the house, removed the valuable contents of the house,
2                                               No. 01-4208

along with himself and his wife, and then cut the natural-
gas line inside the house, causing the house to fill up with
gas and explode spectacularly, utterly destroying it. He
grossly exaggerated the value of the property allegedly
lost in the explosion—some did not exist and some he
had removed before the explosion. The insurance com-
pany (a different one) paid, and he used part of the pro-
ceeds to buy another house. The next year he tried to kill
his wife by driving his van with her in it into a river. When
that failed he killed her by poisoning her, and collected
$200,000 in the proceeds of insurance policies on her life.
He placed personal ads in newspapers, seeking to meet
women. He became engaged to one of the women he
met through his ads, named Donner, but broke his en-
gagement after failing to procure a $1 million policy on
her life. He then took up with a Ms. Beetle. This was in
1996 and the same year he burned down his house, again
submitting an inflated estimate of the loss and receiv-
ing substantial proceeds from the insurance company (a
different one, again). He then married Beetle, and they
moved into a rented house. She insured her life for $500,000
with him as beneficiary. One night in 1998, after drugging
her, he set fire to the house, hoping to kill both her and
their infant son, on whom he had also taken out a life
insurance policy and who was in the house with her. They
were rescued, and soon afterwards Veysey and Beetle
divorced. The house was rebuilt and Veysey persuaded
a woman named Hilkin to move in with him after she
had accumulated some $700,000 in life insurance and
named him as the primary beneficiary. He apparently
intended to murder her, but he was arrested before his
plans matured. There is more, but these are the highlights.
  We reverse the usual order of discussion and begin
with the sentence, since the reader may wonder how,
egregious as Veysey’s conduct was, it warranted the equiva-
No. 01-4208                                                3

lent of a life sentence when the single count of arson
(the burning down of the rented house) carried a maxi-
mum sentence of 20 years, mail and wire fraud carry a
maximum sentence of 5 years, and the use of fire in a
felony (its use to commit the mail and wire fraud, that is,
the fraud against the fire and life insurance companies)
carries a maximum sentence of 10 years. The answer is
that Veysey was convicted of 16 separate counts of mail
or wire fraud and that the judge imposed the maximum
sentence of 5 years on each count and made the sentences
run consecutively, for a total of 80 years, and consecutively
as well to the 20-year sentence for arson that she im-
posed and the 10-year sentence for using fire in a felony
that she also imposed; thus 110 years.
  The federal sentencing guidelines direct the judge, when
there are multiple counts of conviction, to impose maxi-
mum and consecutive sentences to the extent necessary
to make the total punishment equal in severity to what
the guidelines would require were it not for the statutory
maxima. U.S.S.G. § 5G1.2(d); see also United States v.
Dumes, 

, 384 (7th Cir. 2002). Because Veysey’s
remarkable spree included murder as well as attempted
murder, multiple arsons, and multiple frauds, the guide-
line sentence would have been life. U.S.S.G. §§ 2A1.1(a),
2F1.1, Application Note 14; see also United States v. Lanas,

, 904 (7th Cir. 2003). The judge exceeded no
statutory maximum in producing an equivalent sentence.
  Because Veysey’s sentence exceeded no statutory maxi-
mum, the rule of Apprendi v. New Jersey, 

,
490 (2000), was not violated. Apprendi holds that a fact
which results in a sentence greater than what, were it not
for the fact, would be the statutory maximum sentence
for the defendant’s crime must be proved beyond a reason-
able doubt. United States v. Bjorkman, 

, 491 (7th
4                                                  No. 01-4208

Cir. 2001). So if the maximum sentence for arson of a
nonresidential building were 10 years but of a residence
20, a defendant could not be sentenced to more than 10
years without proof beyond a reasonable doubt that the
building he had set fire to was indeed a residence. But a
fact that merely moves the defendant’s sentence around
within the statutory sentencing range need not be proved
beyond a reasonable doubt. Harris v. United States, 

, 550 (2002); Thomas v. United States, 

,
309 (7th Cir. 2003); United States v. De la Torre, 

,
611 (7th Cir. 2003).
  Veysey contends that the case should have been se-
vered for trial into seven different trials, but this is an-
other frivolous claim, and likewise his objection to evi-
dence concerning his drugging of still another woman.
So closely related were all Veysey’s criminal acts that if
there had been seven trials all those acts would have been
placed in evidence in all the trials, as showing intent,
modus operandi, and the scope of the scheme to defraud.
United States v. Prevatte, 

(7th Cir 1994); United
States v. McGauley, 

, 74 (1st Cir. 2002); United
States v. Prosperi, 

, 1345 (11th Cir. 2000).
  More substantial is Veysey’s contention that the arson
of the rented house was not subject to the federal arson
statute because the house was not “used in interstate or
foreign commerce or in any activity affecting interstate or
foreign commerce,” as required by the federal arson stat-
ute. 18 U.S.C. § 844(i). The Supreme Court has held that
arson of an owner-occupied home is not within the stat-
ute’s reach because home ownership is not an activity
affecting commerce, Jones v. United States, 

(2000)—which is why Veysey’s other three arsons were not
charged under the statute—but that arson of an apartment
building consisting of rental units is within the statute
No. 01-4208                                                 5

because the rental of real estate is an activity affecting
commerce. United States v. Russell, 

(1985).
Between the two cases the Supreme Court’s conception
of interstate commerce narrowed, but Jones reaffirms
Russell, 

, and we are given no reason
to doubt the continued authority of the earlier case.
   The present case nestles somewhere in between Jones and
Russell. The house was rented but the renter was not
engaged in a commercial activity, as was the apart-
ment house owner in Russell. The owner of the house
that Veysey rented was a typical householder, who after
living in the house for several years had moved to another
state and after trying unsuccessfully to sell the house
decided to rent it. He rented it first to a family for six
months and then to Veysey for a year at a monthly rental
of $1,300. The lease gave Veysey an option to buy the house
at the end of the year for $138,000. Had Veysey burned
down the house while the original owner was living in it,
or had he burned it down after exercising his option
and buying the house, the arson would have been beyond
the reach of the federal statute, by virtue of the Jones case.
At argument a member of the court remarked the awk-
wardness of property drifting in and out of interstate
commerce. And under pressure of that awkwardness
one might try to distinguish the present case from Russell
by noting that the owner of the apartment building in
that case was in the business of renting, while the owner
of the house that Veysey torched was an accidental renter.
He rented the house only because he couldn’t sell it at an
acceptable price. He didn’t want to be in the real estate
rental business. But he was, and the real estate rental mar-
ket is interstate, as this case illustrates; the owner was in
a different state both when he rented the house to Veysey
and when the arson occurred. To decide this case differ-
ently from Russell would imply a need to inquire in every
6                                                 No. 01-4208

case into the motives for renting, and the inquiry would
complicate decision making without offsetting gain.
We repeat that the real estate rental market really is an
interstate market and the rental in this case was an inter-
state transaction.
  The last issue we consider is Veysey’s objection to testi-
mony by an actuary, Charles L. McClenahan, that the
probability of four residential fires occurring by chance
during the 106 months between April 1989 (when Veysey
bought the first house that he is known to have set fire
to) and January 1998 (when he set fire to his last house)
was only one in 1.773 trillion; he described this as a con-
servative estimate. We can imagine two distinct grounds
for Veysey’s objection to the actuary’s evidence. The first,
which, though the stronger, Veysey’s lawyer has not
made—and in fact expressly disclaimed, when pressed,
at argument—is that the calculation was based on im-
plicit assumptions that are untenable.
   A simplified version of what the actuary did is that he
first determined the number of serious residential fires
in the United States over the interval in which houses
occupied by Veysey caught fire four times (with “serious”
defined as a fire that caused a loss equal to or greater than
20 percent of the amount of fire insurance on the house,
and so defined serious fires are 5.3 percent of all residential
fires), then divided that number by the number of houses
in the United States, and finally multiplied the result-
ing probability by itself four times. Suppose (we are using
hypothetical figures for the sake of simplicity) the prob-
ability that a specific house would have caught fire dur-
ing the 106-month interval were one in 1,000. Then, on
the assumption of independence (an important qualifica-
tion, discussed next), the probability that two specific
houses would have caught fire during the interval would
No. 01-4208                                                  7

be one in a million (1/1,000 x 1/1,000), the probability
that three specific houses would have caught fire would
be one in a billion, and the probability that four would
have caught fire would be one in a trillion.
  This simplified calculation does modest violence to the
actuary’s method, as the mathematics of repeatable
events is somewhat complex. When the actuary divided
the number of fires by the number of houses, the result-
ing quotient was not really the probability of a fire hap-
pening to a specific house, but an input into a formula
designed to assess the probability of a repeated event,
in this case a serious fire in a series of Veysey’s dwellings.
But as with our simple version, the actuary’s actual compu-
tation assumed that the probabilities of each of a per-
son’s multiple fires are independent of each other—that
the fact that you had a fire at one time or in one of your
houses would not affect the probability that you would
have a second fire in that house or a fire in your next
house. The assumption was not defended by the actuary,
and is unrealistic. Compare Branion v. Gramley, 

, 1265 (7th Cir. 1988). A fire in a house or in an apart-
ment is likely to be the result, at least in part, of careless-
ness on the part of the occupant, implying that he is
more likely to have another fire than a person who has
never had a fire (though against this it can be argued
that someone who has experienced a fire will be more
careful to avoid a repetition—once burned is twice shy).
Moreover, even if the assumption of independence were
defensible, the actuary’s calculation would be flawed by
his failure to limit the reference group to residences com-
parable in design, materials, age, value, region, and other
factors relevant to the likelihood of a fire in Veysey’s
residences.
  But Veysey as we have said does not object to the actu-
ary’s methodology. His objection is that the actuary
8                                                 No. 01-4208

usurped the jury’s function by testifying in effect that
Veysey was guilty of the crimes with which he was charged
way beyond a reasonable doubt, as the probability of his
innocence was not 1 or 2 or 5 percent or whatever might
be thought the implicit probability of innocence sufficient
to prevent a finding of guilt beyond a reasonable doubt,
but, if the actuary was believed, a mere .0000000000564
percent. Veysey’s counsel goes so far as to argue that
statistical evidence should never be admissible to estab-
lish an element of a crime. Fingerprint or DNA evidence
is admissible, he acknowledges, but the jury must not
be told what the probability is that such evidence ac-
tually establishes the proposition for which it is intro-
duced, such as that the defendant’s fingerprints were on
the murder weapon.
   In making this argument Veysey’s counsel is gesturing
toward an academic literature (well summarized in Ronald
J. Allen, “On the Significance of Batting Averages and
Strikeout Totals: A Clarification of the ‘Naked Statistical
Evidence’ Debate, the Meaning of ‘Evidence,’ and the
Requirement of Proof Beyond A Reasonable Doubt,” 65 Tul.
L. Rev. 1093 (1991)) that argues that judges and jurors,
because they lack knowledge of statistical theory, are both
overawed and easily deceived by statistical evidence, see,
e.g., Laurence H. Tribe, “Trial by Mathematics: Precision
and Ritual in the Legal Process,” 84 Harv. L. Rev. 1329 (1971);
Charles Nesson, “The Evidence or the Event? On Judicial
Proof and the Acceptability of Verdicts,” 98 Harv. L. Rev.
1357, 1378-85 (1985); Craig R. Callen, “Adjudication and
the Appearance of Statistical Evidence,” 65 Tul. L. Rev.
457 (1991), and toward decisions, such as Smith v. Rapid
Transit, Inc., 

(Mass. 1945), that refuse to per-
mit a case to go to a jury on purely statistical evidence. In
Smith the court held that it “was not enough” “that mathe-
No. 01-4208                                                  9

matically the chances somewhat favor the proposition
that a bus of the defendant caused the accident.” 

   Suppose, to consider a well-known hypothetical variant
of Smith, that a person is hit by a bus, and it is known that
51 percent of the buses on the road where he was hit
are owned by Bus Company A and 49 percent by Bus Com-
pany B. He sues A and asks for judgment on the basis of
this statistic alone; he presents no other evidence. If the
defendant also presents no evidence, should a jury be
permitted to award judgment for the plaintiff? See, e.g.,
Gary L. Wells, “Naked Statistical Evidence of Liability:
Is Subjective Probability Enough?” 62 J. Personality & Soc.
Psych. 739 (1992). The law answers “no.” Richard W. Wright,
“Causation, Responsibility, Risk, Probability, Naked Sta-
tistics, and Proof: Pruning the Bramble Bush by Clarify-
ing the Concepts,” 73 Ia. L. Rev. 1001, 1050-51 (1988). But
this is not because of doubt about the evidentiary value
of statistical evidence. The true source of disquiet in the
example, we believe, is the tacit assumption that the sta-
tistic concerning the ownership of the buses is the only
evidence the plaintiff can obtain. Howard v. Wal-Mart Stores,
Inc., 

, 360 (7th Cir. 1998). If it is his only evi-
dence, the inference to be drawn is not that there is a
51 percent probability that it was a bus owned by A that
hit him but that he either investigated and discovered
that it was actually a bus owned by B (which might be
judgment-proof and so not worth suing), or that he has
simply not bothered to conduct an investigation. In either
event he should lose, in the first case obviously and in
the second because a court should not be required to ex-
pend any of its scarce resources of time and effort on a
case until the plaintiff has conducted a sufficient search
to indicate that an expenditure of public resources is
reasonably likely to yield a social benefit.
10                                                No. 01-4208

  But if both bus companies had been determined to be
negligent, so that the only issue was which had hit the
plaintiff, then in many states the 51/49 ratio of A’s to B’s
buses would be enough for a judgment against A—indeed
against A and B. See Sindell v. Abbott Laboratories, 

(Cal. 1980); Summers v. Tice, 

(Cal. 1948), Krist
v. Eli Lilly & Co., 

, 300 (7th Cir. 1990). Or if
the ratio of buses owned by A to those owned by B were
much higher than 51/49, the case against allowing “naked”
statistical evidence to carry the plaintiff’s burden of pro-
duction on the issue of liability (rather than only causation)
would be weakened. The law recognizes this not only in
the obvious cases of fingerprint and DNA evidence, the
admissibility of which depends on the improbability that
two different people would have the same fingerprint
or DNA signature, Branion v. 

, 855 F.2d at
1265, but also in the law’s adoption of such presumptions
as that a properly addressed, stamped, and mailed letter
will reach the addressee. This is a purely statistical pre-
sumption because it is applied without regard to the
particulars of the case beyond those required to satisfy
the conditions of the presumption; and yet it can deter-
mine the outcome.
   “All evidence is probabilistic—statistical evidence mere-
ly explicitly so,” Riordan v. Kempiners, 

, 698
(7th Cir. 1987); see also Howard v. Wal-Mart Stores, 

, 160 F.3d at 360; Milam v. State Farm Mutual Automobile
Ins. Co., 

, 170 (7th Cir. 1992); United States
v. Chaidez, 

, 1200 (7th Cir. 1990), because
nothing with which the law deals is metaphysically certain.
Statistical evidence is merely probabilistic evidence coded
in numbers rather than words. “Nothing about the nature
of litigation in general, or the criminal process in par-
ticular, makes anathema of additional information, wheth-
er or not that knowledge has numbers attached. After
No. 01-4208                                                11

all, even eyewitnesses are testifying only to probabilities
(though they obscure the methods by which they generate
those probabilities)—often rather lower probabilities
than statistical work insists on.” Branion v. 

,
855 F.2d at 1264. An eyewitness does not usurp the jury’s
function if he testifies that he is positive that he saw the
defendant strike a match, and it would make no differ-
ence if he said that he is “99 percent” positive. The sig-
nificant question would be the accuracy of the estimate.
The actuary’s one in 1.7 trillion estimate in this case prob-
ably was inaccurate, but not because it was a statistic. The
issue of its accuracy has been waived, however, and in
any event the error in its introduction was harmless; the
other evidence against the defendant was overwhelming.
  We wish to remark finally the apparent carelessness of
the insurance companies, particularly the fire-insurance
companies, in failing to pool information concerning fire
claims. As a result of this failure, the insurers who in-
sured Veysey against the last three fires were unaware of
his previous claim or claims. This is a matter deserving
of the industry’s attention—and, with recent improve-
ments in electronic storage and retrieval, beginning to
receive it. Bruce R. Fox, “Technology: The New Weapon
in the War on Insurance Fraud,” 67 Def. Couns. J. 237, 241-
42 (2000).
                                                  AFFIRMED.

A true Copy:
       Teste:

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

                    USCA-02-C-0072—6-26-03