185 F.3d 765 (7th Cir. 1999)
United States of America, Plaintiff-Appellee,v.Marvin M. Johnson, Defendant-Appellant.
No. 98-2517
United States Court of Appeals, Seventh Circuit
Argued October 9, 1998Decided July 16, 1999

Appeal from the United States District Court  for the Northern District of Indiana, South Bend Division. No. 3:97-CR-56--Robert L. Miller, Jr., Judge.
Before Eschbach, Rovner, and Diane P. Wood, Circuit Judges.
Diane P. Wood, Circuit Judge.


1
Marvin Johnson worked as a truck driver for Worldwide Sales, a small company owned by Ronald Stanley. In 1997, he became mixed up in the shadier part of Stanley's business: transporting cash for major Mexican cocaine dealers from various U.S. cities to drop-off locations in Texas, from which the money made its way into Mexico. In due course, Johnson was caught, tried, and convicted of conspiracy to transport U.S. currency into Mexico with the intent to promote the manufacture, importation, sale, and distribution of cocaine, in violation of 18 U.S.C. sec. 1956(h). This appeal concerns only the sentence he received. Because we are concerned that the information on which the district court based its finding that Johnson was responsible for $3.5 million was not reliable enough, we vacate the sentence and remand for resentencing.


2
* Stanley's illegal activities with the drug money began in 1993, two years before he created Worldwide Sales. Until 1997, he handled the business himself, for his boss Tony Alvarez. The work was reasonably lucrative, earning Stanley some $400,000 for his efforts. Eventually, however, he decided to pass the work along to various employees of Worldwide. In March 1997, he asked Johnson if he would be interested in hauling money for the Mexican Mafia, for a payment of $1,200 to $5,000 per load, depending on the amount involved. Johnson said yes.


3
In all, Johnson transported four shipments of money for Stanley. The first trip, which was arranged by Alvarez, Stanley, and others, originated in Queens, New York. Stanley arranged for Johnson to rendezvous at a motel there with others who were to bring him his first cash shipment. The cash arrived--$1.2 million, wrapped in clear plastic with the amount written on the outside, in two suitcases--and it was loaded onto Johnson's truck. Johnson and another Worldwide driver, Roger James, then drove the truck (without a trailer) down to El Paso, Texas. After they delivered the load, Johnson drove the truck back to Oklahoma, Worldwide's headquarters.


4
A planned second trip for Johnson never took place. Stanley had sent Johnson and James back to Queens to pick up more money, but along the way, Alvarez called with a change of plans. Alvarez wanted Stanley to haul a load of drugs instead, but Stanley refused. Stanley canceled the trip, contacting Johnson and James in Pittsburgh, Pennsylvania, and instructing them to drive back as far as Columbus, Ohio. There was no testimony about the amount of money the parties had expected would be carried during this trip.


5
Around April 15, 1997, Stanley summoned Johnson to Michigan City, Indiana, to pick up a shipment of approximately $800,000 in cash. Johnson again drove it down to El Paso, where he met up with Stanley, and Stanley made the final delivery.


6
Johnson's next trip was again from Michigan City to El Paso, a couple of weeks after the April 15 run. This time he picked up $1 million. Johnson, with James's help, drove the truck as far as Oklahoma, where he dropped off James, and then continued on to El Paso alone.


7
Last, in early or mid-May Johnson drove one more time from Michigan City to El Paso. No evidence was introduced about the amount of money involved in this trip. Whatever it was, Stanley again had it loaded into Johnson's truck at a motel, and Johnson drove via Oklahoma to El Paso. Along the way, he also picked up a tractor and a two ton truck to deliver to Alvarez. After that trip, Johnson left Worldwide.


8
Johnson's delivery of the tractor tipped off Alvarez to the fact that Stanley was not personally handling the money shipments. Angry, Alvarez apparently insisted that Stanley start transporting drugs as well. After one successful trip, James was arrested in El Paso on June 18, 1997, in a motor home carrying 315 kilograms of cocaine. James then agreed to cooperate, the conspiracy unraveled, and eventually Stanley, Johnson, and others were arrested.

II

9
The jury found Johnson guilty on one count of conspiracy to commit money laundering, in violation of 18 U.S.C. sec. 1956(h). His sentencing hearing took place on June 5, 1998. The court first concluded that his base offense level was 23, under U.S.S.G. sec. 2S1.1(a). That guideline provides that the base offense for money laundering is "(1) 23, if convicted under 18 U.S.C. sec. 1956(a)(1)(A), (a)(2)(A), or (a)(3)(A); (2) 20 otherwise." The court reasoned that, even though Johnson had literally been convicted under the conspiracy statute, sec. 1956(h), the type of money laundering he had conspired to commit was that described in sec. 1956(a)(2)(A), and thus the higher base level applied. The court then added on three levels because Johnson knew the funds were proceeds from the distribution of controlled substances, as required by U.S.S.G. sec. 2S1.1 (b)(1), taking the level up to 26. It subtracted two levels under sec. 3B1.2(b) because Johnson was a minor participant, but then it added two levels back on under sec. 3C1.1 because he had presented perjured testimony. Finally, the court added on additional levels to account for the amount of money Johnson was transporting, as required by sec. 2S1.1(b)(2), because the value exceeded $100,000.


10
Like a number of other guidelines, U.S.S.G. sec. 2S1.1 (b)(2) sets forth a table specifying the number of levels that should be added to a money laundering offense for various amounts of money at issue. In Johnson's case, two of these are relevant. If the offense involved more than $2 million, sec. 2S1.1(b)(2)(G) calls for another 6 levels; and if the value of the funds exceeded $3.5 million, then sec. 2S1.1(b)(2)(H) provides for another 7 levels. The district court found that Johnson had laundered funds in excess of $3.5 million, and accordingly it added 7 levels to the 26 it had already calculated, for a final offense level of 33. Johnson had a criminal history category of I, which led to a sentencing range of 135 to 168 months. The court gave him a sentence near the top of that range, of 160 months.


11
Johnson's only argument on appeal is that the record does not support the court's selection of the $3.5 million level. Had the court found instead that he was responsible only for more than $2 million, his final offense level would have been a 32, and the sentencing range would have dropped to 121-151 months.

III

12
The court's methodology for concluding that Johnson was responsible for more than $3.5 million was simple-- too simple, we believe. It added up the value of the funds in the three trips for which that fact was known ($1.2 million, $800,000, and $1 million), took the total of $3 million, divided it by three for an average value of $1 million per trip, and came up with $1 million. Then, to be conservative, the judge cut that figure in half, and assumed that the last trip (for which no evidence existed) and the aborted second trip both must have involved at least $500,000. Adding the extra million to the $3 million for which evidence existed, the court arrived at $4 million, well over the $3.5 million threshold required by sec. 2S1.1 (b)(2)(H). In addition to this evidence, Stanley had testified that he was responsible for approximately 100 shipments of money totaling about $500 million.


13
Although the district court's findings about the amount of money involved are findings of fact, entitled to deferential review, it remains true that such findings must be supported by reliable evidence in the record. See United States v. Henderson, 58 F.3d 1145, 1151 (7th Cir. 1995). "Nebulous eyeballing" is not good enough, see United States v. Jarrett, 133 F.3d 519, 530 (7th Cir. 1998), nor can the judge pull a number out of thin air. The government asserts that the court here committed neither of those errors. It notes that judges are entitled to make reasonable estimates of quantities, arguing by analogy to cases involving estimated drug quantities. See U.S.S.G. sec. 2D1.1, application note 12, para. 1; United States v. Patel, 131 F.3d 1195, 1203 (7th Cir. 1997); United States v. Rivera, 6 F.3d 431, 446 (7th Cir. 1993). Nothing more than that happened here, it argues, and thus the district court could not have been clearly erroneous.


14
However, courts have taken greater care than this argument suggests to make sure that inferences drawn from a sample of incidents have some support in the record. Thus, for example, this court warned in Henderson that "at some point a court's estimation will seem less like a restrained approximation and more like unsupported evidence." 58 F.3d at 1152. Other courts have looked more specifically at the problems posed when averaging techniques are used. In United States v. Shonubi, 998 F.2d 84 (2d Cir. 1993), the defendant Shonubi had made eight trips to Nigeria for the purpose of obtaining heroin to import into the United States. On the day he was caught, he had in his possession 427.4 grams of heroin. The district court there assumed that this was a typical quantity, multiplied that number by eight, and concluded that Shonubi should be held responsible for the importation of 3,419 grams of heroin. The Second Circuit found this conclusion to be clearly erroneous, because there was no proof in the record that the 427.4 gram quantity was typical or somehow standardized, nor was there any proof about the amounts involved in any of the other seven trips. This left only surmise and conjecture to support the district court's quantity finding, which was insufficient.


15
The First Circuit faced a similar problem in United States v. Sepulveda, 15 F.3d 1161 (1st Cir. 1993). There, a witness had testified that he made approximately 80 drug-buying trips. The smallest amount of drugs he recalled buying was four ounces, or about 110 grams, and the largest amount was one kilogram. Defendant Wallace had accompanied him on 10-15 of the trips. The district court took the average of 10 and 15, called it 12, and used that for the number of trips Wallace made. The court then averaged the 110 grams and the 1,000 grams, came up with 556, and called that the amount of drugs per trip. That yielded a total of about 6.68 kilograms, which was the amount on which Wallace's sentence was based.


16
The court of appeals, while acknowledging the value and legitimacy of estimates, found this methodology fatally flawed. As the court explained:


17
To say that the minimum amount carried on a single trip was four ounces and that the maximum was one kilogram provides no rational basis for presuming that the average amount carried on a given number of trips was the mathematical midpoint between the high and low figures. Cf. United States v. Hewitt, 942 F.2d 1270, 1274 (8th Cir. 1991) (condemning use of a "far reaching" averaging assumptions [sic] in estimating drug quantity). Similarly, while the distortions are mathematically less serious, the selection of a midpoint in estimating the number of trips is also without evidentiary support.


18
Id. at 1198. The court was at pains to point out that there was no testimony from a witness suggesting what the average amount might have been, nor had any witness suggested a range relating to amounts or trips. With no evidentiary basis for the average figures selected, the court concluded that they were unreliable and that the defendant was entitled to resentencing.


19
In our view, the same type of problem afflicts the government's case against Johnson. Even though it is possible to calculate the average amount of money Johnson carried on the three trips for which information exists ($1 million), or the average amount of money Stanley moved ($5 million), we have no information at all about either the maximum or the minimum amounts involved. Nor is there anything in the record to support the judge's decision to assume that at least $500,000 was on the truck during the last trip, and that at least $500,000 would have been on the truck for the second, canceled trip, if it had involved money instead of drugs and if it had taken place at all. This is not a case like Jarrett, in which a large number of sales were at issue, evidence was before the court about the typical purity of the drug in question, and a sample of six undercover purchases was used as a baseline for calculations supported by substantial corroborating evidence. To the contrary, here there were just four shipments, and the government offered no reason whatever to explain its failure to elicit testimony about the amount of money involved in the fourth one.


20
Put more technically, the problem with the government's case has less to do with what statisticians call the point estimate, which in this case was a variant of the mean, than it has to do with the lack of any information that would permit calculation of a reliable confidence interval. See generally Richard A. Wehmhoefer, Statistics In Litigation 56-59 (1985); David W. Barnes, Statistics As Proof: Fundamentals of Quantitative Evidence 232-40 (1983). As Barnes explains, "[t]he limits of likely deviation of the estimate from the true (population) value form a confidence interval around the estimate." Id. at 232 (emphasis in original). Confidence intervals are particularly difficult to calculate when the sample used is very small (i.e. less than 30). Wehmhoefer at 57. Other techniques are available, but it is enough to say that nothing like the rigor required for them was used here. Furthermore, the samples themselves (Johnson's three trips) are problematic. They were not selected randomly from a larger pool of subjects; thus, this was an instance of nonprobability sampling. That makes it especially inappropriate to extrapolate from the three known values to the fourth unknown one, as Wehmhoefer again explains: "While this type of sampling [i.e. nonrandom] has definite uses and usually is less complicated and cheaper to complete than random sampling, it can only be justified if there is no need to generalize the findings beyond the specific sample studies." Id. at 50.


21
In Johnson's case, the record shows only how little we know about the amount of money involved in the last trip. Johnson's three trips obviously involved much less than the average of all of Stanley's runs ($5 million), assuming for the sake of argument that the information about Stanley's average is itself reliable. Indeed, Johnson's largest run ($1.2 million) was a little less than 25% of Stanley's average, and his smallest ($800,000) was only 16% of Stanley's average. Nothing in the record supports the assumption that any money at all would have been carried during the canceled run, because it turned out that Alvarez or Stanley wanted to use that one to move product, not proceeds. Furthermore, if Stanley thought it was worth sending someone across the country for $800,000, then why not for $490,000? There is simply no reliable evidence that would show that the last trip involved more than $500,000, and if it did not, then the value of the funds attributable to Johnson did not exceed $3.5 million.

IV

22
Johnson concedes that the evidence before the court supported a finding that more than $2 million was involved, and that the enhancement of six levels pursuant to U.S.S.G. sec. 2S1.1(b)(2)(G) was appropriate. As we pointed out earlier, this leaves him with an adjusted offense level of 32 and a sentencing range of 121-151 months. We therefore Vacate his sentence of 160 months and Remand his case to the district court for resentencing within that range.

