BOOCHEVER, Circuit Judge:
Dario Restrepo appeals his forty-six month prison sentence imposed after he was convicted of two counts of distribution of cocaine. The primary issue before us is whether the district court erred in considering conduct that did not result in Restre-[650] po’s conviction in determining his offense level under the Sentencing Guidelines. We also consider the standard of proof to be used to establish a factor enhancing a sentence under the Guidelines, and whether the application of the June 15, 1988 Guidelines to Restrepo violated the ex post facto clause. We affirm.
BACKGROUND
On March 8, 1988, Restrepo was indicted on two counts of distribution of cocaine (counts I and II) under 21 U.S.C. § 841(a)(1) (1988).1 His codefendant, Judith DeMaldo-nado, also was charged with distribution of cocaine in count II. Additionally, she was indicted for possession of cocaine with intent to distribute (counts III and IV) in violation of 21 U.S.C. § 841(a)(1). DeMal-donado pled guilty to counts II, III, and IV and agreed to testify against Restrepo in exchange for a lighter sentence. At trial, DeMaldonado testified that Restrepo provided all the cocaine that she had sold, and an additional amount of cocaine that she had turned over to the police. Restrepo was convicted of counts I and II.
DeMaldonado was the sole witness at Restrepo’s sentencing hearing on August 5, 1988, and repeated her trial testimony. At that time Restrepo challenged the constitutionality of the Guidelines on due process and separation of powers grounds. Restrepo also objected to the district court’s application of §§ 1B1.3 (the relevant conduct section) and 3D1.1 (the multiple counts section) of United States Sentencing Commission, Guidelines Manual (June 15, 1988) (hereinafter Guidelines) in determining the appropriate guideline range for the offenses of which he was convicted. The court over-ruled the objections.
The court then found that all the drugs involved in the charges against DeMaldona-do in counts III and IV and the drugs she turned in were part of a common scheme in which Restrepo was a participant. Relying on this finding, the court added the quantity of drugs involved in counts III and IV and the additional amount DeMaldonado had turned in to the quantity of drugs involved in the charges against Restrepo (counts I and II), for the purpose of fixing the base offense level of Restrepo’s sentence.2 As a result, the court adopted the guideline range of forty-one to fifty-one months imprisonment. The court then sentenced Restrepo to a forty-six month prison term with six years supervised release. Had the district court not aggregated the drugs involved in counts III and IV and the drugs DeMaldonado turned in with the drugs involved in counts I and II, the guideline range for Restrepo’s sentence would have been twenty-seven to thirty-three months.
On appeal, Restrepo challenges the district court’s inclusion of the drugs in counts III and IV and the amount turned in by DeMaldonado in determining his base offense level. He also raises constitutional challenges to the Guidelines, charging a violation of due process in the use at sentencing of a preponderance of the evidence standard of proof.3 In briefs filed after [651] oral argument, Restrepo alleges a violation of the ex post facto clause in the application to him of the version of the Guidelines in effect at the time of his sentencing rather than at the time of his behavior.
STANDARD OF REVIEW
This court reviews de novo the district court’s interpretation of the Sentencing Guidelines. United States v. Howard, 894 F.2d 1085, 1087 (9th Cir.1990). Whether application of the Guidelines violates constitutional requirements is a question of law which we review de novo. United States v. Brady, 895 F.2d 538, 539 (9th Cir.1990).
ANALYSIS
1. APPLICATION OF THE GUIDELINES
The district judge calculated Restrepo’s sentence as follows. As required by Guidelines § 1B1.1, “Application Instructions,” he first determined that § 2D1.1, “Unlawful Manufacturing, Importing, Exporting, or Trafficking” of drugs, was the offense conduct section in Chapter Two most applicable to Restrepo’s offenses. Under § 2Dl.l(a)(3), the base offense level for a drug offense not resulting in death or serious bodily injury is determined by reference to a Drug Quantity Table. The district judge then set the quantity of drugs in Restrepo’s case by reference to § 1B1.3, “Relevant Conduct (Factors that Determine the Guideline Range).” The relevant conduct section provides that where the guideline specifies more than one base offense level, the court shall determine the base offense level “solely with respect to offenses of a character for which § 3D1.2(d) would require grouping of multiple counts, [on the basis of] all such acts and omissions that were part of the same course of conduct or common scheme or plan as the offense of conviction.” Guidelines § lB1.3(a)(2). Application Note 2 to this section indicates that “[t]his subsection applies to offenses of types for which convictions on multiple counts would be grouped together pursuant to § 3D1.2(d); multiple convictions are not required.” (Emphasis added.) The district judge thus included the quantities of cocaine involved in the counts of which Restrepo was not convicted (counts III and IV) and the cocaine DeMaldonado turned in, as well as the cocaine involved in the counts of which he was convicted (counts I and II), because the four counts were a “common scheme.”
The next step under § lBl.l(d) is the application of the multiple counts section of the Guidelines, Part 3D. When counts involve “substantially the same harm,” they are grouped together into a single Group. Guidelines § 3D1.2. The district judge grouped counts I and II together under § 3D1.2(d), which provides that counts involve substantially the same harm
[w]hen counts involve the same general type of offense and the guidelines for that type of offense determine the offense level primarily on the basis of the total amount of harm or loss, the quantity of a substance involved, or some other measure of aggregate harm_ Offenses covered by [§ 2D1.1] are specifically included under this subsection.
(Emphasis added.) The district judge then followed § 3D1.3(b), assigning an offense level to the group “corresponding to the aggregated quantity” of the drugs involved.4
Restrepo objects to this last step, arguing that the district judge grouped together counts I and II (of which he was convicted) with counts III and IV (of which he was not convicted). The multiple counts section of the guidelines, Restrepo claims, does not allow grouping of counts for which a defendant is not charged and con[652] victed. He quotes the opening sentence of the introduction to the multiple counts chapter, “This Part provides rules for determining a single offense level that encompasses all the counts of which the defendant is convicted,” Guidelines ch. 3 pt. D (emphasis added), and points out that § 3D1.1 applies “When a defendant has been convicted of more than one count_” Guidelines § 3D1.1 (emphasis added).
Restrepo’s argument misunderstands the process by which the district judge calculated his sentence. The district judge did not “group” the four counts under the multiple counts section. Rather, as described above, the judge correctly determined that Restrepo’s offense was the type of offense for which multiple counts would be grouped together. As directed by the relevant conduct section, § lB1.3(a)(2), in setting the base offense level he then took into account the amount of drugs involved in counts III and IV and the amount turned in by DeMaldonado before he applied the multiple counts section of the Guidelines. The commentary to § 1B1.3 specifically provides that “multiple convictions are not required,” (Application Note 2), and adds
in a drug distribution case, quantities and types of drugs not specified in the count of conviction are to be included in determining the offense level if they were part of the same course of conduct or part of a common scheme or plan as the count of conviction.
Guidelines § 1B1.3, commentary at 1.18-1.19. The district judge followed the clearly expressed Guidelines method for determining the quantities involved in a drug distribution case.
The commentary to § 1B1.3 is not inconsistent with the language Restrepo quotes from the multiple counts section of the Guidelines. Section 3D1.1 and the introduction to the multiple counts chapter do not limit the quantity to be considered to the amounts charged in the counts of which the defendant is convicted. Nor do they specifically state that only the counts of which the defendant is convicted may be considered. There is no inconsistency, therefore, when another provision mandates adding quantities of drugs from “the same course of conduct or part of a common scheme or plan as the count of conviction.” See Guidelines § 1B1.3, commentary at 1.19; see also United States v. Ruelas-Armenta, 684 F.Supp. 1048, 1051 (C.D.Cal.1988). The relevant conduct section explicitly indicates that the aggregation is to occur only with respect to offenses that are subject to grouping under the multiple counts section of the Guidelines. This explicit cross-reference demonstrates that the two sections were intended to operate in conjunction, and are not in conflict.
Accepting Restrepo’s interpretation would require us to ignore the commentary to the Guidelines. We decline to do so. As the Guidelines authoritatively declare:
The Commentary that accompanies the guideline sections may serve a number of purposes. First, it may interpret the guideline or explain how it is to be applied. Failure to follow such commentary could constitute an incorrect application of the guidelines, subjecting the sentence to possible reversal on appeal. Second, the commentary may suggest circumstances which, in the view of the Commission, may warrant departure from the guidelines. Such commentary is to be treated as the legal equivalent of a policy statement.
Guidelines at 1.22 (emphasis added) (citation omitted). The commentary to § 1B1.7 goes on to say that:
[I]n seeking to understand the meaning of the guidelines courts likely will look to the commentary for guidance as an indication of the intent of those who wrote them. In such instances, the courts will treat the commentary much like legislative history or other legal material that helps determine the intent of a drafter.
See United States v. Gross, 897 F.2d 414, 416 (9th Cir.1990) (application notes are advisory commentary to assist in the application of the statute); United States v. Anderson, 895 F.2d 641, 645 (9th Cir.1990) (like legislative history, commentary helps to determine Commission’s intent).
[653] The Sentencing Commission’s intent is clear: Amounts of drugs calculated on the basis of conduct of which the defendant is neither charged nor convicted but that were “part of the same course of conduct or common scheme or plan as the offense of conviction” may properly be used to adjust the offense level. Three circuits have so held after explicitly discussing the relationship between the relevant conduct rules and the multiple counts rules. United States v. Alston, 895 F.2d 1362, 1371-72 (11th Cir.1990); United States v. Blanco, 888 F.2d 907, 909-11 (1st Cir.1989); United States v. White, 888 F.2d 490, 496-97 (7th Cir.1989). See United States v. Vopravil, 891 F.2d 155, 157 (7th Cir.1989); United States v. Gerante, 891 F.2d 364, 369 (1st Cir.1989) (drugs also may be aggregated when government alleges only one count). In Blanco, Judge Breyer explained that in the relevant conduct section, the reference to the multiple counts section
is designed only to pick out a certain subset of all crimes, namely the subset of “fungible item” crimes, such as those involving drugs and money, which are listed specifically in the cross-referenced multiple count subsection.... It is these crimes in respect to which the Commission has said that courts should punish convicted defendants by taking into account all the drugs or money that form part of the same conduct, scheme or plan. In respect to other crimes, such as murder or bank robbery, the courts will not use § 1B1.3(a)(2) to look to acts that are part of the “same course or conduct or common scheme or plan” ... unless the government separately charges and obtains conviction for these acts.
Blanco, 888 F.2d at 911 (emphasis in original).
Five other circuits have allowed aggregation of amounts of drugs not included in the count or counts of conviction, without considering any possible conflict with the multiple counts rules of the Guidelines. See United States v. Smith, 887 F.2d 104, 106-08 (6th Cir.1989); United States v. Mann, 877 F.2d 688, 690 (8th Cir.1989); United States v. Sailes, 872 F.2d 735, 738-39 (6th Cir.1989); United States v. Taplette, 872 F.2d 101, 106 (5th Cir.), cert. denied, — U.S. -, 110 S.Ct. 128, 107 L.Ed.2d 88 (1989); United States v. Guerrero, 863 F.2d 245, 250 (2d Cir.1988).
We hold that the district judge properly added the amount of drugs involved in counts III and IV and the amount that DeMaldonado turned in to the drugs involved in Restrepo’s counts of conviction, counts I and II. Such aggregation reflects the balance struck by the Sentencing Commission between a “real offense” sentencing system — one that takes into account the defendant’s real conduct, rather than simply the conduct for which he or she is charged — and a “charge offense” system, under which only the conduct of which the defendant is charged may be taken into account at sentencing. See Blanco, 888 F.2d at 909-11. It also is consistent with the pre-Guidelines sentencing practice of district judges, who often took into account information regarding other behavior for which the defendant had not been convicted. See White, 888 F.2d at 498; Smith, 887 F.2d at 108 n. 5. Although before the Guidelines the sentencing judge had discretion to decide how much weight to give that information, and under the Guidelines the judge is bound to increase the sentence in a case such as Restrepo’s,5 that does not constitute a violation of due process. See Brady, 895 F.2d at 540 (Guidelines limitations on judicial discretion “do not infringe a defendant’s right to an individualized sentence, whether or not such a right is constitutionally mandated.”).
2. STANDARD OF PROOF
Restrepo objects that the Guidelines violate due process because the government need not prove beyond a reasonable doubt evidence of uncharged conduct used to determine his sentence. He acknowledges that under pre-Guidelines practice sentencing judges could consider conduct proven [654] by only a preponderance of the evidence. But because the Guidelines require that such conduct be given a predetermined effect in fixing a sentence, without allowing the sentencing judge to ignore the conduct or mitigate its effect by considering other factors, Restrepo contends that the lower standard of proof violates due process.
In McMillan v. Pennsylvania, 477 U.S. 79,106 S.Ct. 2411, 91 L.Ed.2d 67 (1986), the Supreme Court held that a preponderance of the evidence standard satisfied due process for the post-conviction determination by a state judge that a firearm was used in commission of a crime, resulting in imposition of a mandatory sentence. Id. at 91, 106 S.Ct. at 2418. The Court rejected the argument that a lack of discretion in the sentencing court required a higher standard of proof. Id. at 92, 106 S.Ct. at 2419. This court has recently indicated that the Constitution requires district courts to make factual determinations at sentencing under the Guidelines only by a preponderance of the evidence. United States v. Wilson, 900 F.2d 1350, 1354-55 (9th Cir.1990). Other circuits agree. See United States v. Frederick, 897 F.2d 490, 492 (10th Cir.1990); United States v. Alston, 895 F.2d 1362, 1372-73 (11th Cir.1990); United States v. Gooden, 892 F.2d 725, 727-28 (8th Cir.1989); United States v. Silverman, 889 F.2d 1531, 1535 (6th Cir.1989); White, 888 F.2d at 499; United States v. McDowell, 888 F.2d 285, 290-91 (3d Cir.1989); United States v. Guerra, 888 F.2d 247, 251 (2d Cir.1989); United States v. Urrego-Linares, 879 F.2d 1234, 1237 (4th Cir.), cert. denied, — U.S. -, 110 S.Ct. 346, 107 L.Ed.2d 334 (1989); United States v. Wright, 873 F.2d 437, 441-42 (1st Cir.1989).
While we as well as other circuits have held that the standard of proof required for factors enhancing a sentence is a preponderance of evidence, none of those cases further defines that standard when used for this purpose. A literal interpretation of this standard would hold that courts must do no more than weigh the evidence for and against the establishment of a factor, and find that evidence preponderated upon a slight tipping of the scales. Even in civil cases, however, the standard has not always been so strictly construed and is generally equated to evidence showing “that the existence of the proposition to be proved is more probably true than not true,” M. Graham, Handbook of Federal Evidence § 301.5 (2d ed. 1986), or even evidence sufficient to satisfy or convince the trier of fact. J. Wigmore, Evidence § 2498 (1940). It is a “ ‘misinterpretation [of the preponderance test] that it calls on the trier of fact merely to perform an abstract weighing of the evidence in order to determine which side has produced the greater quantum, without regard to its effect in convincing his mind of the truth of the proposition asserted.’ ” In re Winship, 397 U.S. 358, 367-68, 90 S.Ct. 1068, 1074-75, 25 L.Ed.2d 368 (1970) (quoting Dorsen & Resneck, In Re Gault and the Future of Juvenile Law, 1 Fam.L.Q. No. 4, 26-27 (1967)).
We believe that the more demanding interpretation of the preponderance standard is particularly appropriate for enhancement of a sentence under the Guidelines. See Addington v. Texas, 441 U.S. 418, 423-25, 99 S.Ct. 1804, 1808-09, 60 L.Ed.2d 323 (1979) (quantum of proof required increases with relative importance of ultimate decision). As this case illustrates, under Guidelines § 2D1.1 the quantity of cocaine involved in a defendant’s relevant conduct determines the offense level. The sentencing judge’s finding of the amount of drugs involved thus can drastically affect a defendant’s sentence. Depending on the amount of cocaine, the offense level can range from level 12 to level 36. See Guidelines at 2.38-39 (Drug Quantity Table). For a defendant with a criminal history category of I, the sentence that results can be as few as ten to sixteen months, or as many as 188 to 235 months. See id. at ch. 5 pt. A (Sentencing Table). Because the consequences can be severe, we hold that when a preponderance of the evidence standard is used in criminal sentencing to increase the period of confinement, it means a sufficient weight of evidence to convince a reasonable person of [655] the probable existence of the enhancing factor.
This conclusion is supported by analogy to Guidelines § 6A1.3(a), which indicates that at sentencing a “court may consider relevant information ... provided that the information has sufficient indicia of reliability to support its probable accuracy.” Although this section does not specify the quantity of evidence required before a court may enhance a sentence, it does require that the quality of the evidence be such that the information is probably accurate before the judge may consider it. That requirement is consistent with requiring that the sum of the evidence be of sufficient weight to convince a reasonable person of the probable existence of the fact relied upon to increase the sentence.
It appears that in Restrepo’s case, the district court found that the government had proved Restrepo’s and DeMaldo-nado’s participation in a common scheme by convincing evidence. Transcript of Sentencing Proceedings at 65 (“I’m satisfied certainly by a preponderance of evidence and in fact, I think, by clear and convincing evidence that Dario Restrepo supplied the cocaine that Judith Maldonado [sic] had at her house and that she sold on March 1, the other cocaine that he wasn’t convicted of.”). The court also stated: “Now, in this case, the facts plainly support the conclusion and no other conclusion that the drugs which Judith Maldonado [sic] sold in Count Three and the drugs which she possessed in Count Four and the drugs that were found at her house late when she turned them in, were all part of the common scheme.” Id. at 64. We conclude that the district court applied a proper standard of proof.
3. EX POST FACTO
Restrepo claims that the district court violated the ex post facto clause of the United States Constitution (art. I, § 9, cl. 3) by applying the Guidelines as amended after the date of his conduct. At the time of Restrepo’s sentencing in August 1988, the district judge applied the June 15, 1988, version as mandated by 18 U.S.C. §§ 3553(a)(4) (1988) (providing that the sentencing court is to apply the version of the Guidelines “in effect on the date the defendant is sentenced”). Restrepo committed the offenses for which he was committed on January 8, 1988, and January 13, 1988. It is not clear when the additional conduct of supplying drugs to DeMaldonado took place. The government submits that the wrongdoing for which Restrepo was not charged occurred at or after the time of his offenses of conviction. It is thus possible that all of Restrepo’s wrongdoing occurred before the effective dates of the January 15 and June 15, 1988, amendments to the Guidelines.6 It is certain that the acts for which he was convicted preceded the amendments. See United States v. Allen, 886 F.2d 143, 146 (8th Cir.1989) (only dates of offenses of conviction are relevant for ex post facto analysis).
A criminal law is ex post facto if it satisfies two requirements: it must apply retrospectively to events occurring before its enactment, and it must disadvantage the defendant affected by it. Miller v. Florida, 482 U.S. 423, 430, 107 S.Ct. 2446, 2451, 96 L.Ed.2d 351 (1987). Additionally, “no ex post facto violation occurs if a change does not alter 'substantial personal rights,’ but merely changes ‘modes of procedure which do not affect matters of substance.’ ” Id. (citation omitted).
The amendments to the Guidelines of which Restrepo complains include the sections of the commentary to § 1B1.3 cited above. Both Application Note 2, indicating that “[t]his subsection applies to offenses of types for which convictions on [656] multiple counts would be grouped together pursuant to § 3D.2(d); multiple convictions are not required,” and the portion of the background that states “in a drug distribution case, quantities and types of drugs not specified in the count of conviction are to be included in determining the offense level if they were part of the same course of conduct or part of a common scheme or plan as the count of conviction,” were effective as of January 15, 1988, and remained in effect when the Guidelines were amended again on June 15, 1988.
The Commentary to the amended § 1B1.3 (Relevant Conduct) states that the amendments “clarify the intent underlying § 1B1.3 as originally promulgated.” Guidelines at 1.20. If we defer to the Sentencing Commission’s interpretation of these amendments as not substantive changes but rather clarifications of the Commission’s intent in the Guidelines before January 15, 1988, then their retrospective application presents no ex post facto issue. See Frederick, 897 F.2d at 494 (changes were “a permissible clarification of an existing guideline”); Smith, 887 F.2d at 106-08 (amendment to § 1B1.3 was mere clarification of original version); United States v. Scroggins, 880 F.2d 1204, 1211 n. 19 (11th Cir.1989) (“no substantive difference between the October 1987 and January 1988 versions of guideline 1B1.3”); Guerrero, 863 F.2d at 250 (“we agree with the Commission that its change in the commentary ... only clarifies] a meaning that was fairly to be drawn from the original version”); but see Taplette, 872 F.2d at 106 (“it is not absolutely plain to us that under the pre-January 1988 guidelines relevant conduct could be considered in determining [the defendant’s] applicable guideline range”). It would then be irrelevant whether any or all of Restrepo’s acts occurred before the guideline amendments.
We find that the October 1987 version of the Guidelines, in effect at the time that Restrepo committed the offenses for which he was convicted, directed that behavior for which he was not charged and of which he was not convicted was “relevant conduct” that could be used to select a base offense level under § 1B1.3. The original version of § 1B1.3 directed the sentencing judge to consider acts that are part of a common scheme as “conduct relevant to the offense of conviction” to determine the seriousness of the defendant’s offense. Guidelines § 1B1.3 (October 1987). Restrepo’s distribution of drugs to DeMaldonado qualified as relevant conduct under that earlier version. The 1988 amendments made that more explicit. See United States v. Ykema, 887 F.2d 697, 700 (6th Cir.1989) (no violation of ex post facto clause where amounts of cocaine distributed before Nov. 1, 1987 effective date of Guidelines used to determine base offense level), cert. denied, — U.S. -, 110 S.Ct. 878, 107 L.Ed.2d 961 (1990). Because Restrepo was not disadvantaged by the application of the January 15, 1988, amendments to him, and because the amendments did not alter substantial personal rights, Miller, 482 U.S. at 430, 107 S.Ct. at 2451, no ex post facto violation occurred.
CONCLUSION
We find that the Guidelines allow the district court to consider conduct of which Restrepo was not convicted in determining his base offense level. The preponderance of the evidence standard of proof used at his sentencing hearing did not violate due process. When it is used to establish a factor enhancing a sentence, we define the preponderance standard as sufficient evidence to convince a reasonable person of the probable existence of the enhancing factor. Judge Kleinfeld applied the proper standard. There was no ex post facto violation in the application to Restrepo of guideline amendments that went into effect after he committed the offenses of which he was convicted. We therefore AFFIRM his sentence.