Appellant Levi Culps ("Culps") and others sold marijuana from the Culps home in rural Washington State. A jury convicted Culps of three counts of distributing and possessing marijuana and one count of maintaining a drug house. The district court sentenced Culps to 88 months in prison based upon the court's approximation of how much marijuana was sold at Culps' house over a three-year period. Culps appeals his sentence. We hold that Culps' sentence was based on an approximated drug quantity that was not supported by sufficiently reliable information, vacate his sentence and remand for resentencing.

This appeal arises out of a lengthy and intermittent investigation into sales of marijuana at the Culps residence, home of Culps, his brother Roy Culps, their mother and James Scott Lewis. The Culps residence is located on Progressive Road in a rural area of Yakima County lying within the Yakama Nation Reservation. Only two other occupied houses are located on the adjacent stretch of Progressive Road. Progressive Road is intersected by Hinman Road, on which several other occupied residences are located.

Over a period of three years and four months between February 1996 and June 1999, undercover law enforcement agents and confidential informants attempted 12 marijuana purchases from individuals at the Culps home, achieving success on nine of those occasions. The size of the purchases ranged from seven to 96.9 gross grams, for which the officers paid between $20 and $200.1 Two of the controlled buys were made from Culps and the remainder were made from Roy Culps, Lewis or a fourth individual, Glenn Burnside. Agents' attempted purchases of marijuana were not always blessed with success. In May 1999, agents tried to purchase a quarter-pound of marijuana from Roy Culps, but he told them he did not have any marijuana to sell. The next month, agents attempted to make another purchase, but Roy Culps told the agents he did not sell marijuana anymore. That same month, agents also tried to arrange a purchase from Lewis, but he declined to sell the agent any marijuana.

The law enforcement investigation of Culps' marijuana operation featured two lengthy hiatuses. After making two controlled buys from Culps in February and April 1996, agents undertook no further activity at the home for more than two years, until August 1998, when they completed two undercover purchases from Roy Culps. There was another lull in the investigation for nine months, until May and June 1999, when the government attempted several more controlled buys and accomplished the remaining five purchases.

The investigation ended in June 1999, when agents executed a search warrant at the Culps residence and arrested Culps and his brother. The search netted 134.4 net grams and 58.4 gross grams of marijuana, 25 tiny plastic bags of marijuana, scales, plastic baggies, various drug paraphernalia and 18 firearms. Culps was among those at the house at the time.

During Culps' trial, three of Culps' neighbors testified about the extent of vehicle traffic on the road leading to the Culps home, testimony that proved integral at sentencing when the district court approximated the quantity of marijuana attributable to Culps. Each neighbor compared the level of traffic in Culps' neighborhood before execution of the June 1999 search warrant with the volume of vehicular traffic after that date. They gave varying estimates of the vehicle traffic before the Culpses' arrests, perhaps reflecting their different geographic vantage points and work schedules. The first neighbor, Dennis Balch, lived on Progressive Road, about an eighth of a mile from the Culps residence. When Balch, who worked during the day, was home, "there would be anywhere from 30 to 50 [or] above cars a night" on the road. The second neighbor, Dave Dorais, lived on Hinman Road, near its intersection with Progressive. Like Balch, he generally worked away from home during the day, although he also worked in his fields on a part-time basis. Dorais saw 50 to 60 cars or more per day on Hinman Road before the Culpses were arrested. Bill Broderson, the third neighbor, also lived on Hinman Road, about a quarter-mile south of the intersection with Progressive Road. He estimated that there were 75 to 125 cars per day on Progressive and Hinman Roads.

The neighbors reported that the traffic level varied based on determinants such as the time of day and the weather. For instance, Balch said the traffic came to a halt when deep snow covered the ground. Dorais said traffic peaked during school lunch hours and holidays. According to Broderson, traffic was heaviest right after school.

None of the neighbors saw any of the occupants of these vehicles purchase marijuana. Balch saw that most of the cars went to the Culps residence. Cars pulled up to the Culps house, remained there for a couple of minutes and then returned in the opposite direction. Dorais saw cars go by and, minutes later, return in the reverse direction. Although he could not see where the cars were destined when he was home, he could see that the cars were going to the Culps residence when he tended his fields. From time to time, Balch and Dorais observed signs posted at the Culps property stating "sold out," "closed" or "out of product." Broderson could not identify where the traffic was going to or coming from.

The neighbors agreed that traffic slowed to a trickle following the arrests of Culps and his brother. According to Balch and Dorais, traffic slowed to two or three cars per day. Similarly, Broderson observed virtually no traffic on Progressive and Hinman Roads, other than his neighbors' cars, after execution of the warrant.

By all indications, the neighbors' trial testimony was designed primarily to contrast the vehicular traffic in the neighborhood prior to the June 1999 search with the traffic after that time, for the purpose of establishing circumstantial evidence of drug dealing out of the home. It appears that the government did not envision until after the fact that the neighbors' testimony also could be used at sentencing to establish the daily volume of drug sales at the Culps residence and to prove that the sales occurred continuously throughout the period charged in the indictment, encompassing the three years and four months between the first controlled purchase of marijuana and the arrests. As a consequence, the neighbors' testimony proved vague in several material respects.

First, although the neighbors estimated vehicle traffic per day or per night, they did not identify whether they were referring to an average day or a peak day. Nor, other than Balch, did they describe whether their approximations referred to the traffic observed in a full day or part of a day. Balch said he worked during the day and made clear that his estimate referred only to after-work hours. Although both Dorais and Broderson worked outside the home at least part-time, it is unclear whether their "per day" estimates referred to those days in which they were home and observant all day, or only to those hours of the day that they might have been home and watching the road.

The neighbors' estimates also were vague as to duration. Government attorneys did not ask the witnesses whether the volume of traffic they described applied to the entire period charged in the indictment. That said, the testimony of two of the neighbors provides some evidence of duration. Balch's estimate of 30 to 50 cars per night was in response to the prosecutor's request that he describe the amount of traffic he observed during "at least the two or three years preceding" the execution of the search warrant. Broderson, meanwhile, testified that the traffic had "been heavy for quite a few years," adding, "it's always been heavy." Dorais said only that he had lived in the neighborhood for seven years.

Those ambiguities in the neighbors' testimony were not an obstacle to the prosecution's case for conviction. Based on the evidence of the controlled buys, the search and the neighbors' testimony, the jury convicted Culps of three counts of possession and distribution of marijuana, in violation of 21 U.S.C. § 841(a)(1), and one count of maintaining a building for narcotics trafficking, in violation of 21 U.S.C. § 856(a)(1).

The government contended that Culps should be sentenced based on all of the marijuana sold at the Culps residence from the first controlled buy in February 1996 until execution of the search warrant over three years later in June 1999. The presentence investigation report ("PSR"), upon which the government relied, pegged that total at 186.77 net kilograms of marijuana by multiplying together three factors: the estimated size of the average transaction (quarter-ounce); the estimated average number of transactions per day (50); and the estimated number of days drugs were sold (1205). The PSR explained that it derived the number of days (1205) by calculating the period between the first controlled buy and execution of the search warrant. The PSR did not explain, however, how it arrived at the other two numbers: the quarter-ounce average transaction size and the 50 transactions-per-day estimate. Rather, the PSR promised that "the government plans to present testimony to the Court at the time of sentencing that witnesses have observed at least 50 car trips per day to and from the Culps' residence and during each trip an average of a quarter-ounce of marijuana was distributed." Nor did the PSR provide any information to establish that the Culpses sold drugs continuously, or on a daily basis, over the specified 1205-day period.

Notwithstanding the PSR's promise, the government did not present testimony supporting the quarter-ounce and 50 transactions-per-day estimates during the sentencing hearing. Nor did it offer evidence to establish continuous operation of the drug house or to verify that drugs were sold every day. The pertinent record relating to the estimation of drug quantity for purposes of sentencing, therefore, consisted only of the PSR and the evidence heard at trial, including the testimony of Balch, Dorais and Broderson.

The district court embraced the PSR's method of approximating drug quantity by multiplying an average transaction size by an estimated number of transactions per day and an estimated number of days. Without comment, the court adopted the quarter-ounce transaction size from the PSR. It also accepted the government's estimate of 50 transactions per day, stating, "the computation should be based on the testimony of the neighbors about the car traffic up and down the road which was said by Balch and other people to be 30 to 50 cars a day." The district court also accepted the government's estimate of 1205 days, at least as a point of departure. The court reduced the government's estimate of total drug quantity by one half, however, to account for uncertainties in the number of transactions per day and the number of days marijuana was sold:

Of course, the problem with [the government's estimate] is that there isn't any evidence to suggest that this went on every day. Even the neighbors, rightfully offended by this traffic up and down Progressive Road for five years, indicated that they weren't watching the road all the time. Mr. Culps, in consideration of his clients' convenience, even posted signs on occasion saying he was out of product, they should come back another time. We know that he himself was in confinement for a period of time in excess of 40 days.

By halving the government's estimate, the district court determined that Culps was responsible for approximately 80 to 100 net kilograms.2 Under the Sentencing Guidelines, that quantity of marijuana equated to a sentencing range of 78 to 97 months. The district court sentenced Culps to 88 months' imprisonment and three years' supervised release.

The district court's interpretation and application of the Sentencing Guidelines are reviewed de novo. United States v. August, 86 F.3d 151, 153 (9th Cir.1996). Whether the method adopted by the district court to approximate the relevant quantity of drugs is proper under the Guidelines is therefore reviewed de novo. Id. (citing United States v. Williams, 989 F.2d 1061, 1073 (9th Cir.1993)). We review the district court's factual findings for clear error. United States v. Walter, 256 F.3d 891, 894 (9th Cir.2001).

Culps makes three arguments on appeal. First, he contends that the district court erred when it attributed 80 to 100 kilograms of marijuana to the operation of the drug house. Second, he complains that the court failed to make required findings regarding what portion of the marijuana sold at the Culps residence was attributable to him as opposed to his brother and others. Third, he argues under Apprendi v. New Jersey, 530 U.S. 466, 120 S. Ct. 2348, 147 L. Ed. 2d 435 (2000), that all the findings made at sentencing had to be presented to a jury and found beyond a reasonable doubt. We agree with Culps' first challenge, reject his second and decline to reach his third.

The applicable sentence range for both drug trafficking and maintaining a drug house depends upon the amount of drugs involved. See U.S.S.G. §§ 2D1.1(c) (Nov. 1, 2001) & 2D1.8(a) (Nov. 1, 2001). Where the amount of drugs seized does not reflect the scale of the offense, the district court may approximate the quantity of the drugs. Id. § 2D1.1, comment (n. 12); August, 86 F.3d at 154.

Approximations of drug quantity must meet three criteria. First, "as with all factors which increase a defendant's offense level, the government is required to prove the approximate quantity by a preponderance of the evidence." August, 86 F.3d at 154. "The district court must `conclude that the defendant is more likely than not actually responsible for a quantity greater than or equal to the quantity for which the defendant is being held responsible.'" Id. (quoting United States v. Walton, 908 F.2d 1289, 1302 (6th Cir.1990)). Second, "the information which supports an approximation must possess `sufficient indicia of reliability to support its probable accuracy.'" Id. (quoting U.S.S.G. § 6A1.3(a)). Third, "since a defendant's sentence depends in large part upon the amount of drugs attributable to his conduct, and approximation is by definition imprecise, the district court must err on the side of caution" in calculating approximated drug quantity. Id. Because approximation "prescribes punishment for unconvicted conduct," courts must "proceed carefully ... in the estimation of drug quantities." United States v. Scheele, 231 F.3d 492, 498 (9th Cir.2000). A "district court's failure to consider the margin of error when arriving at the quantity of drugs on which the sentence was based constitutes error." Id. at 500.3

This case illustrates the profound impact a determination of drug quantity by the district court can have on a defendant's sentence. The total marijuana actually seized in the entire three-year investigation comprised less than one kilogram. The district court sentenced Culps as if a jury had convicted him of selling 80 to 100 kilograms of marijuana. As a result, Culps' base offense level under the Sentencing Guidelines increased threefold, from 8 to 24, and the applicable sentencing range rose from 10-16 months to 78-97 months.

The aforementioned criteria apply to any method of approximation, including the "multiplier" method used here. Under the multiplier method, the district court accounts for the defendant's behavior over time by determining a daily or weekly quantity, selecting a time period over which it is more likely than not that the defendant was dealing in that quantity and multiplying these two factors together. See August, 86 F.3d at 155. Although other circuits have approved of the multiplier method, United States v. Paulino, 996 F.2d 1541, 1548 (3d Cir.1993); United States v. Walton, 908 F.2d 1289, 1302 (6th Cir.1990), and we have cited those cases with approval, Scheele, 231 F.3d at 498; August, 86 F.3d at 154, we have not previously had occasion to hold that the multiplier method is one permissible method of approximating drug quantity.4 We do so now. Provided that the approximation has a reliable evidentiary basis and that the court proceeds with caution, a court may approximate drug quantity for sentencing purposes by multiplying an estimated daily or weekly quantity by an applicable period of time. The district court did not err by choosing to employ the multiplier method here. We thus consider whether the three numbers the court plugged into the formula are clearly erroneous.

The first of those numbers, one quarter-ounce as the average transaction size, cannot be sustained. The district court did not identify the information upon which it relied in adopting the quarter-ounce estimate. We see two possible sources of that information — the PSR and the government's nine controlled purchases. Whether the district court relied on either of these sources of information or both, we conclude that the quarter-ounce estimate lacks a reliable evidentiary basis and must therefore be rejected as clearly erroneous. The information supporting that estimate was either not sufficient or was not sufficiently reliable.

1. Adoption of Findings of Fact from the PSR

The first possibility is that the district court adopted the quarter-ounce estimate directly from the PSR. If it did so, the court's finding cannot be sustained. Although the "court may adopt the factual findings of the presentence report ... [i]t may not ... adopt conclusory statements unsupported by facts or the Guidelines." United States v. Navarro, 979 F.2d 786, 789 (9th Cir.1992); see United States v. Garcia-Sanchez, 189 F.3d 1143, 1149 (9th Cir.1999) (reversing estimate of conspiracy's weekly drug sales where government offered only agent's unexplained conclusions that did not contain sufficient indicia of reliability to support its probable accuracy). The PSR contained only a conclusory statement that the average transaction size was one quarter of an ounce. The factual underpinning for that assertion, if any, was not explained. Rather, the PSR promised that "the government plans to present testimony to the Court at the time of sentencing that ... an average of a quarter-ounce of marijuana was distributed" per transaction. The government failed to deliver on that promise.

In the alternative, we can assume the district court adopted the quarter-ounce estimate based on the quantities associated with the nine marijuana purchases controlled and executed by government agents and informants. Although it is not clear what evidentiary basis the government advanced below, on appeal the government emphasizes the controlled buys as the basis upon which we could sustain the estimate. We disagree that these few buys do so.

The use of nine buys to estimate the 60,250 transactions the government says took place is statistically and legally unreliable. Without information showing that the sample purchases are representative of the larger conduct, there is an inadequate evidentiary basis for the quarter-ounce estimate. See United States v. Rivera-Maldonado, 194 F.3d 224, 231 (1st Cir.1999) (holding that estimating the average drug transaction size of 86,400 transactions by using a sample of 12 controlled buys was improper); see also United States v. Shonubi, 103 F.3d 1085, 1092 (2nd Cir.1997) (holding it was error to use a sample of four balloons to estimate the total weight of heroin found in 103 balloons); United States v. Butler, 41 F.3d 1435, 1447 (11th Cir.1995) (rejecting average of 66 transactions per day based solely on a single day's 66 transactions where there was no evidence that single day was "typical" or "average" or otherwise "a valid indicator of drug activities on other days"); United States v. Collado, 975 F.2d 985, 998 (3d Cir.1992) (overturning a finding that telephone calls regarding heroin transactions must have referred to a sale of at least 62.5 grams because the defendants dealt in quantities of at least that amount on other occasions); United States v. Hewitt, 942 F.2d 1270, 1274 (8th Cir.1991) (disapproving of using defendant's admission that he brought 112 grams during certain trips to conclude that other trips also involved 112 grams); cf. U.S.S.G. § 2D1.1, comment (n.12) (permitting district court to consider "similar transactions in controlled substances by the defendant" to approximate drug quantity (emphasis added)). The government presented no evidence that the nine controlled transactions typified the alleged 60,241 other marijuana purchases. Indeed, other evidence at trial and in the PSR undercut the quarter-ounce estimate. One of the government's confidential informants testified that he bought marijuana from Culps five times in amounts less than a quarter-ounce. Further, during the search of the residence, the government found 25 small, prepackaged bags of marijuana with an amount of marijuana that apparently was too small to weigh.

That the sample represents buys controlled by the government, in which the government established the quantity, amplifies our misgivings. See Rivera-Maldonado, 194 F.3d at 232 (holding there was insufficient evidence to conclude that controlled buys by government agents were representative of the average drug purchaser); cf. U.S.S.G. § 2D1.1, comment (n.14) (recognizing that the use of quantities "controlled by the government" to approximate drug quantity may not accurately reflect a defendant's culpability). The government possesses considerable monetary resources and an incentive to buy as much marijuana as it can from the targets of its investigation. Indeed, on several occasions, undercover officers attempted to buy much larger, quarter-pound quantities of marijuana from the Culps residence. "Although we do not suggest that the respective drug-type quantities indicated in these controlled buys must be disregarded merely because they were controlled by the government, we do say that the necessary factual inference — that these controlled buys were reasonably representative of the uncontrolled drug transactions ... — should find discernible record support" that is lacking here. Rivera-Maldonado, 194 F.3d at 232.5

We therefore hold that the district court's use of a quarter-ounce of marijuana as an average transaction size constituted clear error. Culps' sentence must be vacated and the case remanded to the district court. Because additional issues raised by Culps' appeal may arise on remand, we address them next.

The remaining two numbers plugged into the multiplier formula were 50 transactions per day and 1205 days. The district court adopted each of these estimates from the PSR, but halved the resulting approximation — the total quantity produced by multiplying the three factors — before designating a final drug quantity of 80 to 100 kilograms. In determining whether the 50-transactions-per-day and 1205 days estimates can be sustained, we take into consideration the district court's application of a 50% discount to account for evidence indicating that the government's estimate was excessive. We begin with the 50 transactions per day estimate.

We conclude that the estimation of 50 transactions per day was supported by sufficient and reliable information. Although the neighbors gave varying estimates of the numbers of cars in the neighborhood, much of the deviation can be explained by the neighbors' differing vantage points and schedules. Balch's estimate of 30 to 50 vehicles per night is not inconsistent with the testimony of Dorais and Broderson, each of whom observed a somewhat greater number of cars per day — 50 to 60 trips in the case of Dorais and 75 to 125 trips in the case of Broderson. Considering that Balch's testimony referred only to a portion of the day, and that the district court reasonably could have inferred that the higher estimates represented full-day activity, it was reasonable to adopt the 50 transactions per day figure.

Given the unusual circumstances of this case — in particular, the sparsely populated rural setting — the district court also reasonably relied on vehicular traffic in the neighborhood as a proxy for the number of marijuana transactions occurring at the Culps residence. The neighbors' testimony created an adequate link between the cars in the neighborhood and the Culps residence, and motorists' brief layovers at the Culps residence supported a reasonable inference that they were buying drugs. As all three witnesses agreed, the automotive traffic in the neighborhood slowed to a trickle after Culps and his brother were arrested.

The court's application of a 50% discount — a portion of which was allocated to uncertainties in the number of transactions per day — properly erred on the side of caution. The discount accounted for the margin of error in each neighbor's estimate and for the fact that not every prospective customer would have been successful. Narcotics officers attempting to purchase marijuana were unable to consummate controlled buys in one-quarter of their attempts. As the district court acknowledged, two of the neighbors also recalled seeing signs stating "out of product," "closed" or "sold out" on some occasions.

When the multiplier method is used to approximate drug activity over time, the court must select a time period over which it is more likely than not that the defendants were dealing in the average daily or weekly quantity. See August, 86 F.3d at 155. To establish that illegal activity was continuous between Point A and Point B, it is not enough simply to establish that drug sales occurred at Points A and B, at least where A and B are not "close enough in time to infer [that the defendants] were dealing on a regular basis in the interim." Walton, 908 F.2d at 1302. This principle is illustrated by Walton, where the Sixth Circuit reversed a drug approximation using the multiplier method because the government had failed to establish continuous illegal activity between drug sales that took place in 1986 and drug paraphernalia found during a search of defendants' home in 1988. Without evidence filling the two-year gap, the evidence was "simply insufficient to support a finding of continuous drug dealing during this period." Id. at 1303.

As in Walton, the investigation here involved extended intervals between controlled buys — an extraordinary 28 months in one instance and nine months in another. To overcome these gaps, the government once again presses the neighbors' trial testimony into service. The neighbors' reports constitute some evidence that the Culpses regularly sold marijuana during the 1205-day period. Balch was asked to describe the traffic "at least for the two or three years preceding" execution of the warrant. His answer of 30 to 50 cars per night spans a period of time corresponding to a portion of the period charged in the indictment. Broderson's testimony that the traffic had "been heavy for quite a few years" and that "it's always been heavy" furnishes some underpinning for the district court's finding of continuous operation. The direct evidence of continuous dealing also was stronger here than it was in Walton. Agents' contacts with the Culps residence, although marked by large intervals, were nonetheless numerous. The search, moreover, turned up not just drug paraphernalia, but tell-tale signs of large-volume marijuana dealing. The controlled buys occurring in 1996 and 1998-99 and the physical evidence seized in June 1999 bolster the district court's conclusion.

Nonetheless, we must conclude that the evidence was insufficient to establish continuous operation during the period charged in the indictment. Even if Balch's testimony is read in the light most favorable to the government, it does not fully bridge the gap in the government's investigation. Broderson's testimony was simply too vague to establish a reliable evidentiary basis for the district court's conclusion. The direct evidence of drug sales in 1996 and 1998-99 is not sufficient to establish continuous operation in the intervening two years. In short, the neighbors' trial testimony was not tailored to sentencing and the evidence that the government produced at sentencing did not establish continuous operation. On this record, we cannot sustain the district court's finding that Culps' drug business operated for 1205 days.

The district court's use of a 50% discount cannot cure the approximation's evidentiary defects. As a general matter, we follow the Third and Sixth Circuits and approve of the use of a discount in multiplier cases to account for uncertainties and satisfy the district court's duty to err on the side of caution. The 50% discount is an appropriate tool in the right case. See Walton, 908 F.2d at 1302 (approving of the district court's halving of the government's estimate as necessary to give effect to the court's duty to "err on the side of caution" and as "constitutionally required to prevent excessive sentences"); Paulino, 996 F.2d at 1548 ("The halving of [the government's proposed amount], rather than being arbitrary, is, instead a reasonable calculation by the district court, erring on the side of caution, to take into consideration `off' days and days in which perhaps lesser sales occurred."). If the evidence here had supported continuous operation, the 50% reduction would have been an appropriate mechanism to account for the margin of error in the number of days drugs were sold, including "off days," days in which the Culpses were "out of product," snow days, days Culps was in custody and other uncertainties. The district court's 50% reduction, however, cannot substitute for sufficient and reliable evidence that marijuana more probably than not was sold on 1205 days, an estimate that presumes, without an adequate evidentiary foundation, continuous operation during the extraordinary investigatory lapses. See Walton, 908 F.2d at 1302-03 (approving of the district court's 50% discount but nonetheless vacating its approximation where the government failed to establish continuous drug dealing).

II. Attribution of All the Drugs to Defendant

Culps argues that the district court failed to determine how much of the marijuana sold at the drug house was attributable to him as opposed to his brother, Roy Culps, Lewis and the others. A defendant convicted of maintaining a drug house is sentenced pursuant to U.S.S.G. § 2D1.8, which provides that a defendant is sentenced for the amount of drugs involved in the underlying offenses that took place at the drug house as calculated pursuant to U.S.S.G. § 2D1.1, unless the defendant did not participate in the underlying offenses.6 U.S.S.G. § 2D1.8(a)(2). A defendant does not participate in the underlying offenses when his role is limited to "allowing the use of the premises." Id. § 2D1.8, comment (n.1). The burden is on the defendant to establish that he did not participate personally in the underlying offenses. See United States v. Dickerson, 195 F.3d 1183, 1189-90 (10th Cir.1999).

Culps did more than allow his home to be used to sell drugs; he actually sold drugs himself. Indeed, he was convicted of two counts of distributing marijuana and one count of possession with intent to distribute marijuana. Additionally, the government points out that in several of the other controlled buys, Roy Culps and the others would go into Culps' bedroom to retrieve the marijuana. Culps, therefore, failed to establish that he did not participate in the underlying offenses that took place at the residence. See id. (upholding district court's finding that defendant participated in underlying offenses where defendant was found to be in possession of drugs and additional drugs were found in his bedroom). Accordingly, Culps can be sentenced based upon the total amount of drugs sold at the drug house.

Culps maintains that his sentence violates Apprendi v. New Jersey, 530 U.S. 466, 120 S. Ct. 2348, 147 L. Ed. 2d 435 (2000), because neither the amount of drugs attributed to him nor his possession of a gun was proven to a jury beyond a reasonable doubt. Because we vacate Culps' sentence and remand for resentencing, we decline to reach these issues.

We have held that the average transaction size of one quarter ounce and the estimate of 1205 days are not supported by sufficient and reliable evidence. We also have held that neither the nine controlled buys nor the conclusory assertions in the PSR, standing alone, can establish any average transaction size. Although we approve of the multiplier method, this method necessarily fails when any single variable cannot be ascertained by a preponderance of the evidence. Here, two variables were not successfully established. We therefore hold the approximation to be erroneous, vacate the sentence imposed and remand.

It remains for us to determine whether we should limit the district court's discretion on remand. Under United States v. Matthews, 278 F.3d 880 (9th Cir.2002) (en banc), "if a district court errs in sentencing, we will remand for resentencing on an open record — that is, without limitation on the evidence that the district court may consider." Id. at 885 (citations omitted). We may limit the district court's discretion to consider new evidence on remand only in certain cases — including those that "involve circumstances in which either additional evidence would not have changed the outcome or where there was a failure of proof after a full inquiry into the factual question at issue." Id. at 886 (citations omitted). The case before us was briefed and argued before Matthews was decided. Neither party has addressed whether the exceptions recognized in Matthews apply here. Similarly, neither party has addressed whether, assuming one of the Matthews exceptions does apply, we should exercise our discretion to constrain the district court on remand.

Given this procedural posture, we follow Matthews' default rule. The district court is in a better position to determine whether evidence in the existing record, or additional evidence that might be offered, could establish an approximated quantity. In the event that the district court decides not to consider such evidence, or in the event that such evidence is offered but proves inadequate, the district court may sentence Culps only for the marijuana seized in the nine controlled buys and in the search of the Culps home.

For the foregoing reasons, we VACATE the sentence and REMAND to the district court for resentencing consistent with this opinion.

SENTENCE VACATED AND CASE REMANDED FOR RESENTENCING.