After a six-day trial, appellants Emilio Correa-Alicea and Geraldo Santiago-Torres were convicted of conspiracy to possess with intent to distribute certain narcotics as part of a drug point operating in the Aristedes Charier public housing project in Ponce, Puerto Rico. 1 See 21 U.S.C. §§ 841(a)(1), 841(b)(1)(A), 846, 860. Correa-Alicea was sentenced to a 360-month term of imprisonment, and Santiago-Torres was sentenced to a 324-month term. In this consolidated appeal, Correa-Alicea raises several challenges to his sentence, and Santiago-Torres argues that the cumulative effect of a number of triаl errors requires a new trial. We affirm in all respects.
I.
We recite the facts in the light most favorable to the verdict.
United States v. Flores-de-Jesús,
Between November 2005 and November 2006, approximately six drug points operated at the Aristedes Chavier Housing *487 Project. Appellant Correa-Alicea was “in charge” of one of the drug points, and appellant Santiago-Torres was a runner at that point, although he also sold drugs on occasion. Correa-Alicea’s drug point operated every day of the year, from 6:00 or 7:00 a.m. until 11:00 p.m., and had a large number of customers daily. The drug point sold cocaine base as well as othеr narcotics.
At trial, two government informants testified as to controlled purchases they had made from Correa-Alicea’s drug point, and the court admitted into evidence the audio recordings of those purchases. Angélica Colón-González, a lifelong resident of the housing project, testified that she had seen appellants selling drugs to others behind her house in the housing project. She stated that she had known appellants her entire life, although on cross-examination, she clarified that she had known Santiago-Torres for three years. She began cooperating with the DEA in early 2006, and on February 16, 2006, she made a controlled drug purchase of six large packages, each of which contained twenty-five to twenty-six individual packages of cocaine base. Although she and the seller, Sergio Martinez, had agreed the previous day that she would purchase fifteen large packages, he had only four packages available on February 16. Martinez then called appellant Santiago-Torres to see whether Santiago-Torres had any additional drugs, and later that day Santiago-Torres brought ColonGonzález two more packages of cocaine base. The parties stipulated that the net weight of the cocaine base purchased in the February 16 transaction was 17.1 grams.
Another long-time resident of the housing project, Javier Ortiz-Cruz, had grown up with Correa-Alicea and had known him for most of his life, and had known Santiago-Torres for more than fifteen years. Ortiz-Cruz sold heroin and crack at Correa-Alicea’s drug point in the fall of 2005, during which time Santiago-Torres also acted as a drug runner and seller. Ortiz-Cruz began cooperating with the DEA in 2006, and, on April 12, 2006, he made a controlled purchase of fifteen packets of heroin. 2 On May 4, 2006, Ortiz-Cruz made a purchase of eight packets of cocaine base from Santiаgo-Torres, whom he identified as one of Correa-Alicea’s sellers. Correa-Alicea was also present at this purchase, and the witness identified both Correa-Alicea and Santiago-Torres on the audio recording of the purchase. The parties stipulated that the net weight of the cocaine base purchased in the May 4 transaction was 24.3 grams.
The government also presented the testimony of Eddie Vidal-Gil, a Puerto Rico Police Department agent in charge of the investigation conducted at the housing project. The district court accepted Agent Vidal-Gil as an expert оn drug trafficking. Vidal-Gil testified that Correa-Alicea’s drug point sold cocaine base in small plastic bags, each with a net weight of .07 grams. He further testified, over defense counsel’s objection, as to the quantity of drugs sold during his surveillance of the drug point:
*488 Q Okay. And during the times that you actually performed surveillance at the Defendants’ drug point, how many buys of those little baggies did you see occur during the time period that you were looking at the drug point?
A Well, so many that I couldn’t really count them. I would say in a period of 25 minutes or half an hour that I would be surveilling the drug point, many more than 10, 15, of these small bags containing crack would be sold in thаt period of time.
The jury found appellants guilty of conspiracy to possess with intent to distribute fifty grams or more of cocaine base and detectable amounts of cocaine and heroin in the housing project, within 1,000 feet of a public school. See 21 U.S.C. §§ 841(a)(1), 841(b)(1)(A), 846, 860. At sentencing, the district court found Correa-Alicea accountable for in excess of 4.5 kilograms of cocaine base, and sentenced him to a prison term of 360 months. In a separate sentencing proceeding, the court found Santiago-Torres accountable for in excess of 1.5 kilograms of cocaine base, and sentenced him to a 324-month term.
On appeal, Correa-Alicea challenges his sentence, and Santiago-Torres contends that his conviction should be reversed. We address each appellant’s claims in turn.
II.
A. Correa-Alicea’s Sentence
Correa-Alieea’s Presentence Investigation Report (PSR) recommended that he be held accountable for approximately six kilograms of cocaine base over a one-year period. The PSR did not explain how it reached this drug-quantity determination, but instead merely stated that the finding was based on “the evidence presented at trial, and the testimony of drug expert Eddie Vidal.”
Correa-Aliсea filed objections to the PSR, contending that the drug-quantity finding was incorrect because it was based on unreliable expert witness testimony from Agent Vidal-Gil. At the sentencing hearing, after argument from counsel on this point, the district court adopted the PSR’s recommendation and found that Correa-Alicea was responsible for in excess of 4.5 kilograms of crack cocaine. Like the PSR, the district court did not explain how it reached its drug-quantity determination, but instead simply stated that its finding was based on “the evidence presented at trial.”
Based on the finding that Correa-Alicea was responsible for in excess of 4.5 kilogrаms of cocaine base, the district court assigned him a base offense level of 38. U.S.S.G. § 2D1.1(c)(1). The court applied a one-level enhancement because the offense was committed in a protected location, U.S.S.G. § 2D1.2(a)(2), and a three-level enhancement because Correa-Alicea was a leader in the criminal activity, U.S.S.G. § 3B1.1(b), for a total offense level of 42. Combined with a Criminal History Category of I, this offense level resulted in a guidelines imprisonment range of 360 months to life, and the court sentenced Correa-Alicea to a prison term of 360 months.
B. Calculating Drug Quantity
Under the sentencing guidelines, the base offense level largely depends upon the total drug quantities involved in the offense. U.S.S.G. § 2D1.1(e). If the quantity of drugs seized does not accurately reflect the scale of a drug-distribution conspiracy, the district court must “approximate the [total] quantity of the controlled substance.” U.S.S.G. § 2D1.1, cmt. n. 12. Because Correa-Alicea was convict
*489
ed of conspiring to distribute controlled substances, he is responsible “not only for the drugs he actually handled but also for the full amount of drugs that he could reasonably have anticipated would be within the ambit of the conspiracy.”
United States v. Santos,
A district court’s finding as to drug quantity “need only be by a prepondеrance of the evidence and is not required to be an exact determination but rather only a reasoned estimate.”
Rodríguez,
We review the district court’s factual finding as to drug quantity for clear error.
Rodríguez,
C. Correa-Alicea’s Challenge to the Drug-Quantity Determination
Correa-AIicea argues that the district court erroneously found that he was individually responsible for more than 4.5 kilograms of cocaine base. Relatedly, he challenges the admission of Agent Vidal-Gil’s testimony, which he claims provided the basis for the court’s drug-quantity determination. He argues that Vidal-Gil’s testimony was unreliable and not based on recognized scientific techniques, and therefore was improperly admitted as expert tеstimony. The government responds that, even if Vidal-Gil’s testimony was unreliable, an alternate calculation based on the stipulated quantities of cocaine base purchased in two controlled transactions adequately supports the district court’s 4.5 kilogram finding. We agree with the government’s contention. Because we conclude that the district court’s drug-quantity determination is sufficiently supported by reliable evidence independent of Vidal-Gil’s testimony, we need not reach the question of whether the district court erred in admitting Vidal-Gil’s testimony.
See Barnett,
At trial, the parties stipulated to the quantity of cocaine base recovered from each of two controlled purchases: on February 16, 2006, Colón-González purchased cocaine base with a net weight of 17.1 grams, and on May 4, 2006, Ortiz-Cruz purchased cocaine base with a net weight *490 of 24.3 grams. 3 These controlled purchases were recorded on audio tape, and the audio recordings were admitted as evidence at trial. According to the testimony of Ortiz-Cruz and Colón-González, longtime residents of the housing project, Correa-Alicea was “in charge” of the drug point and was involved in the conspiracy from November 2005 until November 2006. The drug point operated for at least sixteen hours every day, and a large number of people visited the drug point daily.
Based on this evidence, it is reasonable to conclude that, over the course of the year-long conspiracy, Correa-Alicea’s drug point made
at least
one cocaine base sale per day in an amount comparable to the controlled purchases. Using the smaller controlled purchase of 17.1 grams as a sample, 6.2415 kilograms of cocaine base are reasonably attributable to Correa-Alicea over the one-year conspiracy (17.1 grams of cocaine base sold per day, multiрlied by 365 days per year). Using the larger controlled purchase of 24.3 grams, he is accountable for 8.8695 kilograms (24.3 grams of cocaine base sold per day, multiplied by 365 days per year). Even the more conservative estimate of 6.24 kilograms is significantly more than the 4.5 kilograms of cocaine base attributed to Correa-Alicea by the district court. The court’s finding as to drug quantity was not a mere “hunch or intuition,”
see MarreroOrtiz,
Relying on our decision in
Riverar-Maldonado,
In
Riverar-Maldonado,
we recognized that “[generally speaking, the smaller the sampling, the less reliable the resulting probability estimate,” and an estimate of drug quantity may be unreliable if based on an extrapolation from too small a sample.
Id.
at 231. We held that it was improper for the sentencing court to estimate the average drug transaction size using a very small sample of controlled buys over the course of a six-month invеstigation. Id. at 233. The sampling in that case was “minuscule,” “twelve controlled buys drawn from a set of 86,400 transactions (20 transactions per hour, times 24 hours per day, times 180 days),” and there was no evidence that the twelve controlled buys were representative of ordinary drug transactions at the drug point. Id. at 231-32. Furthermore, the other estimates upon which the total drug-quantity finding was based, including the average number of transactions per hour and average operating hours per day, were also unreliable, and therefore “the risk of error was compounded by pyramiding unreliable inferences.” Id. at 233. We concluded that the sеntencing court’s drug-quantity determination was not based on sufficiently reliable information, and remanded the case for resentencing. Id. at 233;
see also United States v. Culps,
In this case, however, the sample used for calculating average drug transaction size is proportionately much larger, and therefore more reliable, than in
RiverarMaldonado:
two controllеd buys drawn from a set of 365 transactions (one per day for a year), rather than twelve buys drawn from 86,400 transactions. Furthermore, unlike in
Riverar-Maldonado,
the other estimates upon which the total drug-quantity finding is based are reliable, even conservative. The estimate of one transaction per day, or 365 transactions per year, is highly conservative in light of testimony that the drug point operated for sixteen to seventeen hours per day, 365 days per year, and had a large number of customers daily. The district court’s ultimate finding that Correa-Alicea was accountable for in excess of 4.5 kilograms of cocaine base is likewise conservative, given that even calculations based on the smaller of the two controlled buys would yield a figure of 6.24 kilograms. The court’s finding, although not an “exact determination” of drug quantity,
see Rodríguez,
In sum, because there is clear record support for the district court’s finding that Correa-Alicea was accountable for more than 4.5 kilograms of cocaine base during the charged conspiracy, we affirm the sentence imposed.
III.
Santiago-Torres contends that the cumulative effect of several еrrors requires a new trial. We disagree and affirm his conviction.
A. Voice Identification Expert
Santiago-Torres’s principal argument is that the district court erred in denying his request to retain a voice identification expert and his related motion for a continuance to secure that expert’s presence at trial. We review a denial of a request to fund expert services for abuse of discretion.
United States v. Quñones-Medina,
Prior to trial, upon defense counsel’s request, the district court ordered that the defendants and their counsel be permitted to listen on March 6, 2007, to the audio recordings of the controlled purchases. Nearly two months later, on April 30, Santiago-Torres and other defendants filed a motion to continue the trial date set for May 14, citing ongoing investigations and plea negotiations. On May 1, Santiago-Torres submitted a sealed, ex parte motion requesting funds to retain a voice identification expert, asserting that it was not his voice on the incriminating audio recordings, and the only way he could present a defense against the evidence contained in the audio recordings was through such an expert. Two days later, in an order deny *492 ing the April 30 motion for cоntinuance of trial, the court referenced, but did not expressly rule on, Santiago-Torres’s ex parte request for a voice identification expert: “Furthermore, defendants’ counsel listened to the United States’ evidence on March 6, 2007 and only now request[s] an expert on voice identification.” 5
Santiago-Torres renewed his request for a voice identification expert in a second sealed ex parte motion on May 7. The following day, the court issued sealed orders denying both ex parte motions without prejudice pending completion of the government’s case in chief. The district court did not further explain the basis for its denial. On May 14, the day trial was scheduled to start, Santiago-Torres filed a motion again requesting funds to retain a voice identification expert and a continuance to ensure the expert’s availability for trial. The court orally denied the motion. At trial, audio recordings of the February 16 purchase by government witness Colón-González and the April 12 and May 4 purchases by government witness Ortiz-Cruz were admitted into evidence over defense counsel’s objections.
As an indigent, Santiago-Torres was entitled to the benefits of the Criminal Justice Act (CJA), 18 U.S.C. § 3006A. The CJA provides that “a person who is financially unable to obtain ... expert ... services necessary for an adequate defense” may obtain them after demonstrating in an ex parte hearing that such services are “necessary.” 18 U.S.C. § 3006A(e)(l). “Generally, expert services have been found necessary when the proffered expert testimony was pivotal to the indigent defendant’s defense.”
United States v. Manning,
We discern no abuse of discretion in the district court’s denial of Santiago-Torres’s ex parte motion for funds to retain a voice identification expert, or his related motion for a continuance to secure that expert’s presence at trial. Santiago-Torres’s proffered expert testimony was not pivotal to his defense. The audio recordings were not the “primary means of connecting [Santiago-Torres] to the crime,” see id., but instead merely served as corroboration for the ample eyewitness testimony that Santiago-Torres had acted as a runner and seller for the drug point.
Cоlón-González testified that she had known Santiago-Torres for three years, and had seen him acting as the runner at the drug point and selling drugs to others behind her house. She further testified that during the February 16 controlled transaction, the seller, Martinez, called Santiago-Torres to see whether he had any additional drugs, and Santiago-Torres brought her two more packages of cocaine base later that day. Ortiz-Cruz testified that he had known Santiago-Torres for more than fifteen years, and had sold drugs at Correa-Alicea’s drug point in late 2005, during which time Santiago-Torres also worked as a drug runner and seller. Ortiz-Cruz also testified that he purсhased cocaine base directly from Santiago-Torres in the May 4 controlled transaction. In light of this eyewitness testimony, none of which depended on identification of San *493 tiago-Torres’s voice on the audio recordings, the voice identification expert services were not critical or necessary to his defense.
Moreover, as the district court noted, Santiago-Torres’s counsel had the opportunity to listen to the audio recordings at issue on March 6, but did not request a continuance until April 30 and did not request funds to retain a voice identification expert until May 1, less than two weeks before his trial was scheduled to begin. Santiago-Torres contends on appeal, as he did in his motion to the district court, that his requests were delayed because he spent weeks trying to locate a voice identification expert available to come to Puerto Rico. However, he does not explain why he could not have made his requests for expert services and for a continuance prior to locating an available expert, and the district court could reasonably have found that the requests were unreasonably dilatory. In light of these facts, we cannot conclude that the court abused its discretion in denying Santiago-Torres’s requests for a continuance and for funds to retain the proffered expert.
Santiago-Torres further contends that the district court erred in disclosing his ex parte request for a voice identification expert in its May 3, 2007 denial of his motion for a continuance. The government correctly concedes error on this point.
See United States v. Abreu,
B. Alleged Discovery Violations
Santiago-Torres further contends that the district court failed to remedy two alleged discovery violations by the government.
1. Disclosure of Photograph
First, Santiago-Torres contends that the court erred in not ordering the government to produce a photograph shown to Colón-González prior to trial, which he argues was subject to disclosure under Rule 16 of the Federal Rules of Criminal Procedure. We review the court’s determination under Rule 16 for abuse of discretion.
United States v. Caro-Muñiz,
Colón-González testified that she had personally identified both defendants to DEA agents while she and the agents were riding in an undercover car, and she had later identified Santiago-Torres in a photograph shown to her by DEA agents. Santiago-Torres objected on the ground that, during discovery, he had asked the prosecution for information about any identification procedures used in the investigation, such as photographic line-ups, and the government had responded that no such procedures had occurred. Santiago-Torres contended that the government should have disclosed the photograph during discovery so that he could cross-examine Colón-González about her identification, and requested that the court order production of the photograph. The government argued that the photograph was irrelevant because Colón-González knew Santiago-Torres from personal interac *494 tions, and did not identify him based on the photograph. The court denied Santiago-Torres’s request, accepting the government’s assertion that the photograph was not the basis for her identification of Santiago-Torres because she knew him personally.
The district court did not abuse its discretion in refusing to order production of the pretrial photograph. Rule 16 requires disclosure of documents and objects within the government’s possession, custody or control upon a defendant’s request if “(i) the item is material to preparing the defense; (ii) the government intends to use the item in its case-in-chief at trial; or (iii) the item was obtained from or belongs to the defendant.” Fed.R.Crim.P. 16(a)(1)(E). Santiago-Torres contends that the photograph was matеrial to his defense because it could have been used during cross-examination of Colón-González and could have formed the basis for a “pretrial motion to suppress the reliability of her identification.” However, nothing in the record indicates that Colón-González identified Santiago-Torres on the basis of the photograph. To the contrary, she testified that she had known Santiago-Torres for three years and purchased drugs from him, and that, before being shown the photograph, she had identified him in-person while riding in an undercover car with DEA agents. Thus, the photograph was not material and the government was not required to disclose it.
2. Disclosure of Audio Recording
Santiago-Torres contends that the district court erred in denying his request for a mistrial based on the government’s alleged failure to produce the April 12, 2006 audio recording during pretrial discovery. We review the court’s denial of a mistrial motion for a manifest abuse of discretion.
United States v. Van Anh,
At trial, after the audio recording of Ortiz-Cruz’s April 12 controlled purchase was played for the jury, defense counsel moved for a mistrial, claiming that he had not received the recording during discovery. He stated that during pretrial discovery he had received a recording marked “April 12” along with a transcript, but the recording was inaudiblе. He then requested and received a second copy of the recording and transcript from the government, also marked “April 12,” but he claimed that this was not the recording played at trial. The government maintained that it had provided defense counsel with copies of the April 12 recording and the transcript on two occasions well in advance of trial, and defense counsel should have notified the government if the recording did not match the transcript. The district court then listened to the recording at issue and denied Santiago-Torres’s motion, explaining that “whatever the CD was — that was provided — I meаn, it was easily determined that it — it wasn’t the proper CD by just looking at the transcript.”
We find no abuse of discretion in the court’s ruling. The court reasonably concluded that, even if the incorrect recording was mistakenly provided, defense counsel could have easily discovered the error and requested the correct recording from the government. Moreover, Santiago-Torres has not shown that he was prejudiced by the government’s alleged failure to produce the correct recording prior to trial.
See United States v. Devin,
Santiago-Torres’s claims of prejudice are not plausible. Defense counsel conceded to the district court that after receiving the first recording, which he claimed was inaudible, he requested and received a second copy of the recording from the government. He did not claim that this second recording was inaudible; instead, he conceded that he listened to the recording and “understood that this transcript was not really right, that you could not really read — you could not really hear what is in the transcript.” In addition, defense counsel was permitted to listen to the government’s аudio recordings in court on March 6, 2007, prior to trial. Defense counsel admitted to the district court that he “wasn’t present for the whole session.” Finally, although Santiago-Torres claims that his trial strategy was to file a motion to suppress the audio recording, he did not file any such pretrial motion. Santiago-Torres has failed to credibly demonstrate that the alleged discovery failure caused him to adopt a less effective defense strategy, and we are therefore satisfied that any discovery failure was harmless.
Affirmed.
Notes
. Correa-Alicea and Santiago-Torres were indicted along with six co-defendants. The six сo-defendants entered into plea agreements, while Correa-Alicea and Santiago-Torres proceeded to a joint trial.
. The government acknowledges in its brief that Ortiz-Cruz provided inconsistent testimony as to whom he purchased heroin from on April 12. On direct examination, he stated that he bought drugs from "Colin [Correa-Alicea] and Geraldo [Santiago-Torres]” on or about April 12. However, he subsequently claimed that he had purchased the drugs on April 12 "[f]rom Colin,” which he then repeated on cross-examination. The government now takes the position that the April 12 purchase did not involve Santiago-Torrеs at all, noting that the transcript of the audio recording of this purchase does not list Santiago-Torres as a speaker.
. The third controlled purchase, made by Ortiz-Cruz on April 12, 2006, was for heroin rather than cocaine base, and therefore is not relevant to this calculus.
. Although Correa-Alicea does not raise the argument, it could be contended that an estimate of drug quantity based on controlled buys arranged by government agents is particularly unreliable, as there is no evidence that these buys are representative of sales by ordinary customers.
See Rivera-Maldonado,
. Santiago-Torres also contends on appeal that the district court erred by stating in this order that Santiago-Torres "requests] an expert on voice identification,” thereby disclosing his ex parte request for a voice identification expert. We discuss this claim of error below.