Vance White participated in a wire fraud scheme and pleaded guilty to one count of wire fraud, 18 U.S.C. § 1343, and one count of aggravated identity theft, 18 U.S.C. § 1028A(a)(1). The district court calculated White's Sentencing Guidelines range based on the amount of loss caused by the entire scheme over four years. During most of that time, though, White was in prison. We conclude that White's guilty plea did not admit his involvement from the outset of the scheme. No other evidence in the record provides sufficient support to hold White responsible for the entire duration. We therefore vacate his sentence and remand for resentencing.
I. Factual and Procedural Background
White and his co-schemers bought merchandise in retail stores with fake checks and then returned the merchandise for cash. Over about four years, the group targeted 32 stores and inflicted actual losses of approximately $627,000. Posing as representatives of a third-party check-processing company, the schemers contacted retail stores and obtained customers' bank account information from the most recent personal checks used at the stores. The schemers used the account information to make counterfeit checks. They then used *986the checks to buy merchandise that they would later return for cash.
In his plea agreement, White admitted to a key paragraph of the government's factual basis for the plea:
Beginning no later than in or around the fall of 2009 and continuing until at least in or around the summer of 2013 , in the Northern District of Illinois, Eastern Division, and elsewhere, ... VANCE WHITE ..., together with other individuals known and unknown to the Grand Jury (the "co-schemers"), knowingly devised, intended to devise, and participated in a scheme to defraud and to obtain money by means of materially false and fraudulent pretenses, representations, and promises.
The problem is that White was in prison for most of that time. He entered state custody on September 18, 2009 and was not released until nearly two years later, on August 19, 2011. He went back into custody on August 20, 2012, leaving him at liberty to pursue the fraud for only one year during the four-year scheme.1
In calculating a guideline sentencing range, the district court found that White's offense level was 22. White's criminal history category was VI, already the highest level at age 30, based on numerous fraud, theft, and forgery convictions. The guideline range was 84 to 105 months in prison. The court imposed a total sentence of 59 months, giving White credit for 24 months served on a related Illinois forgery conviction. See U.S.S.G. §§ 5G1.3(b), 5K2.23. The court structured the sentence in two parts: 35 months for the wire fraud count, plus a mandatory, consecutive 24 months for the identity theft count. The court also ordered that the 59-month sentence run concurrently with sentences from two different Illinois cases. White is due to be released in August 2018.
II. Analysis
A. Loss Amount
White's principal argument is that the district court used the wrong guideline offense level, holding him responsible for losses imposed by co-schemers while he was in prison before he joined the scheme. The guideline issue is governed by U.S.S.G. § 1B1.3(a)(1), which offers guidance for when a particular defendant should be held responsible for actions of co-schemers. According to White, the district court used an offense level that was two levels too high. We review de novo legal interpretations and applications of the Guidelines, United States v. Sykes , 774 F.3d 1145, 1149 (7th Cir. 2014), citing United States v. Wright , 651 F.3d 764, 774 (7th Cir. 2011), and we review findings of loss amounts for clear error. United States v. Orillo , 733 F.3d 241, 244 (7th Cir. 2013), citing United States v. Littrice , 666 F.3d 1053, 1060 (7th Cir. 2012).
1. Harmless Error?
Since the Sentencing Guidelines are advisory rather than binding, Beckles v. United States , 580 U.S. ----, ----, 137 S.Ct. 886, 894, 197 L.Ed.2d 145 (2017) ; United States v. Booker , 543 U.S. 220, 245, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005), and since the district court imposed a sentence *987that was in fact below the calculated guideline range, we have looked first for signs as to whether the disputed loss amount actually made a difference in the defendant's final sentence.
In federal sentencing, the advisory Guidelines are the "starting point and ... initial benchmark," and serve to "anchor ... the district court's discretion." Molina-Martinez v. United States , 578 U.S. ----, ----, 136 S.Ct. 1338, 1345, 194 L.Ed.2d 444 (2016), quoting Gall v. United States , 552 U.S. 38, 49, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007) (omission in original), and Peugh v. United States , 569 U.S. 530, 549, 133 S.Ct. 2072, 186 L.Ed.2d 84 (2013) (omission in original). After calculating an advisory guideline range, the district court must consider the final sentence under 18 U.S.C. § 3553(a), and it must do so without presuming that a guideline sentence will be reasonable. Rita v. United States , 551 U.S. 338, 351, 127 S.Ct. 2456, 168 L.Ed.2d 203 (2007). Still, a judge imposing sentence must calculate the applicable Sentencing Guidelines range correctly; an error is "a procedural error that we presume influenced the judge's choice of sentence, unless the judge said otherwise." United States v. Marks , 864 F.3d 575, 582 (7th Cir. 2017) ; see generally Molina-Martinez , 578 U.S. at ----, 136 S. Ct. at 1347-48. At the same time, we have often encouraged district judges facing a tricky guideline issue to ask themselves whether the answer actually makes a difference to them. Marks , 864 F.3d at 576 ("when an arcane and arbitrary issue arises under the Sentencing Guidelines, the sentencing judge should ask, 'Why should I care?' "). When a judge explains that a disputed guideline issue ultimately did not matter for the exercise of sentencing discretion under § 3553(a), we will treat an arguable error in the guideline calculation as harmless. United States v. Snyder , 865 F.3d 490, 500 (7th Cir. 2017).
In this case, we have no signals that might support a finding that any error was harmless. The district court explained, quite properly, that White's sentence was below the calculated guideline range to give him credit for a state sentence that he had already served, as provided in U.S.S.G. §§ 5G1.3(b) and 5K2.23, and to account for § 3553(a) factors, like his "tough life" and the non-violent nature of his crimes. The judge did not otherwise signal that the guideline loss calculation did not affect the final sentence, so we must address the issue on the merits.
2. Loss Amount Merits
We begin with a roadmap of the applicable guideline provisions to determine the correct offense level. For fraud crimes, the most important offense characteristic is often the amount of the actual or intended loss resulting from the scheme. See U.S.S.G. § 2B1.1(b)(1) and cmt. n.3. Specific offense characteristics depend on both the offense of conviction and "relevant conduct," which is a critical concept in the entire Sentencing Guidelines structure and which can cover conduct much broader than the offense of conviction. See U.S.S.G. § 1B1.3. The loss amount calculation includes losses based not only on the defendant's own actions but also the actions of co-schemers, if those actions were "within the scope of," "in furtherance of," and "reasonably foreseeable in connection with" the jointly undertaken criminal activity, § 1B1.3(a)(1)(B), and "occurred during the commission of the offense of conviction, *988in preparation for that offense, or in the course of attempting to avoid detection or responsibility for that offense," § 1B1.3(a)(1) ; see also Sykes , 774 F.3d at 1150. The notes to § 1B1.3 explain that in joint criminal activity, the scope of different defendants' relevant conduct may be different. Relevant conduct "does not include the conduct of members of a conspiracy prior to the defendant joining the conspiracy, even if the defendant knows of that conduct." § 1B1.3 cmt. n.3(B).
When the issue of individual responsibility for conduct of others is contested, a district court should make a finding on each element of the relevant conduct test. See, e.g., Sykes , 774 F.3d at 1150 (requiring "two-step analysis" under previous version of § 1B1.3(a)(1)(B) );2 United States v. Salem , 597 F.3d 877, 886 (7th Cir. 2010) (requiring findings on scope, in-furtherance, and foreseeability). The problem here is that the indictment alleged that White participated in a scheme to defraud beginning in the fall of 2009 and continuing at least until the summer of 2013, yet White was in prison for most of that time, having been out of prison during that range only from August 19, 2011 until August 20, 2012. It is surely rare for a defendant's criminal history to work this way as a potential mitigating factor, but that is the possible effect here, at least as to loss amount and offense level.
As a general rule, the government must show an aggravating offense characteristic under the Guidelines by a preponderance of the evidence, and this rule applies to the loss amount in a fraud offense. Orillo , 733 F.3d at 244, citing Littrice , 666 F.3d at 1060. In this case, both the evidence and the district court's findings are insufficient to support the full loss amount used in White's sentencing. To meet its burden on the loss amount, the government relied on the admissions in the plea agreement and argued that "our information ... indicates that he was involved prior to his incarceration in 2009." The prosecutor did not elaborate on this information, which turns out to be critical for this point. The district court overruled White's objection: "I will find that the government's dollar amount-it seems to me it's clear that the fact that he's involved at the beginning, he leaves, and then he comes back, I guess you could say so much for the deterrent effect of sentencing on him." The district court made no more explicit finding on the scope of the jointly undertaken criminal activity, whether others' actions were in furtherance of that activity, or whether White could reasonably foresee those actions. See U.S.S.G. § 1B1.3(a)(1)(B). (Still, we certainly understand the district court's "so much for deterrent effect" comment, but that's a matter to consider further on remand.)
To support the loss amount using the beginning of the scheme in 2009, the government relies primarily on White's plea agreement and his admission of the government's factual basis in his guilty plea hearing. The government also relies on White's challenge to another part of the factual basis (but not the dates of the scheme) at the plea hearing, earlier offenses described in the presentence report, the grand jury testimony of a co-schemer, and other information in the presentence report. None of these items can close the evidentiary gap.
*989First, White's guilty plea and his admission in the plea agreement are insufficient because they are too ambiguous on the key point. A plea agreement and admissions in a guilty plea hearing may of course establish a factual foundation for sentencing. The question here is just what White admitted. Our broad holdings about the evidentiary force of admissions in a plea agreement do not hold that a general admission in a plea agreement to a conspiracy or scheme spanning a certain time conclusively establishes individual participation during that entire time. E.g., Sykes , 774 F.3d at 1151-52, 1151 n.7 (admission to participating in scheme foreclosed argument that defendant could foresee only loss amounts caused directly by defendant's own participation); Orillo , 733 F.3d at 245, 247 ("defendant's own admission is, of course, evidence enough of the matter admitted" where defendant did not even try to argue that other people may have been responsible); United States v. Krasinski , 545 F.3d 546, 551-53 (7th Cir. 2008) (affirming estimate of drug quantity calculated using defendant's admission to delivering range of pills on range of occasions because admission established maximum and minimum quantities, but saying nothing about sentencing consequences of admission to date range in plea agreement); United States v. Warneke , 310 F.3d 542, 550 (7th Cir. 2002) (saying nothing about sentencing consequences of agreement to wide date range and holding that admission "removes all contest from the case" where defendant attempted to invoke Apprendi because of his guilty plea).
On this point it is useful to compare White's argument to our decision in United States v. Savage , 891 F.2d 145 (7th Cir. 1989). Savage said in his plea agreement that he could have reasonably foreseen his co-conspirators' actions, but he later argued that he participated in only one drug deal. Like Savage, White argues that his admissions about his own conduct and responsibility were narrower than the scheme charged in the indictment. The problem is one of language and one of scale. Savage separately admitted the existence of a conspiracy during a precise date range and conspiring with others "throughout this period of time," and his agreement also listed discrete transactions. Id. at 146-47. Here, White agreed to a factual basis that tracked almost verbatim the broad language of the indictment. White's admission, then, is no better than a plea to an indictment-which "admits only the essential elements of the offense." United States v. Paulette , 858 F.3d 1055, 1059 (7th Cir. 2017), citing United States v. Dean , 705 F.3d 745, 747 (7th Cir. 2013), and citing United States v. Kilcrease , 665 F.3d 924, 929 (7th Cir. 2012) ; see also United States v. Lawler , 818 F.3d 281, 282-83 (7th Cir. 2016) (plea to single-count indictment charging large-scale conspiracy resulting in five deaths "did not prove that any particular defendant was responsible for any particular death"), citing United States v. Walker , 721 F.3d 828, 836-38 (7th Cir. 2013), judgment vacated on other grounds , Lawler v. United States , --- U.S. ----, 134 S.Ct. 2287, 189 L.Ed.2d 169 (2014) (mem.). The beginning and end dates of a scheme are not essential elements. See Paulette , 858 F.3d at 1059-60 (distinguishing United States v. Tolson , 988 F.2d 1494 (7th Cir. 1993) ).
With respect to the timing of his participation in the scheme, White's admission in the agreement tracked the language of the indictment. He admitted that the scheme existed for four years, and he admitted that he was a part of the scheme. He did not admit that he was part of the scheme for the entire four years, and he was not asked whether he was. Again, a guilty plea admits only the essential elements of the offense, and dates are not elements of the *990offense. Paulette , 858 F.3d at 1059 ; cf. United States v. Wang , 707 F.3d 911, 916 (7th Cir. 2013) (affirming foreseeability finding and noting that "there is no evidence that the court held Wang accountable for documents that predated his involvement in the conspiracy"); United States v. Kopshever , 6 F.3d 1218, 1222 (7th Cir. 1993) (rejecting government's argument that guilty plea to conspiracy during date range preceded by "on or about" admitted that fraudulent conduct continued after end date of range), abrogated on other grounds , United States v. Vizcarra , 668 F.3d 516 (7th Cir. 2012). The analysis (but not the outcome here, because of a lack of evidence) would be different if White had expressly and separately admitted his own participation over the entire duration of the scheme. See Savage , 891 F.2d at 146 (admission to participation "throughout this period of time").
A defendant may admit more than just the essential elements of an offense by stipulating to facts in a plea agreement or by agreeing with the government's factual basis. Paulette , 858 F.3d at 1060. White did that: he admitted to specific activities like contacting stores to get customer information, using the fraudulently obtained information to create counterfeit checks, making purchases with the counterfeit checks, and then returning the fraudulently obtained merchandise for cash. But none of those admissions speaks to the timing problem. The defendant's admission to the general duration of the scheme does not conclusively establish his own participation in the entirety of the scheme with others, at least where the defendant was in prison for much of that time. At sentencing, the judge asked the government specifically whether it was charging White for any conduct before his release from prison in August 2009, and the prosecutor said no. While the prosecutor contradicted that position at other points, we think that was the correct answer. Still, the confusion on the point underscores the problem with the scope of White's admission. And since the ambiguous admission in the plea agreement is not sufficient, it makes no difference whether he challenged other aspects of the factual basis at his change of plea hearing.3
The government's remaining three points fare no better. On this record, a connection between White's 2007 and 2009 forgery convictions and this scheme is speculative. The presentence report contains no details relating to the factual basis for the 2007 conviction. The 2009 conviction involved fraud but by a different method: White tried to buy merchandise with a fraudulent traveler's check and fake identification. The government offers no other evidence to corroborate any circumstantial connection to the scheme charged and admitted here, using checking account information and involving others. Cf. United States v. Patel , 131 F.3d 1195, 1204 (7th Cir. 1997) ("participation in other drug transactions does not itself establish the required relationship between those earlier transactions and the offense of conviction"). Perhaps the government can establish the link on remand, but it did not do so in this record.
As for co-schemer Ayanna Armstrong's grand jury testimony, the records of White's imprisonment show it was not accurate. Armstrong testified that White began participating in 2010, made purchases and returns in 2010, and began making fake identification cards in 2010. White spent all of 2010 in state custody.
*991Other information in the presentence report also falls short. White's statement that he learned how to commit check fraud after being discharged from a group home does not prove that he participated in the charged scheme before he went to prison in September 2009. And the statement that White "relied on funds from the instant offense and from other criminal activities" from 2007 to 2012 is also too vague to prove that the scheme of the offense of conviction or its relevant conduct began in 2007. After all, White had earned a criminal history category of VI by the time of the offense of conviction, primarily through a long history of other frauds, thefts, and forgeries. That history counts toward the criminal history calculation, but not all of those prior offenses can be treated as relevant conduct under the Guidelines for this sentence.4
To be sure, the district court might well impose the same sentence on remand. Perhaps the government can fill in the evidentiary gaps. The court's discretion under § 3553(a) is substantial and may take into account White's terrible record of recidivism. And even on White's own terms, the guideline issue itself may be very close. The key threshold under U.S.S.G. § 2B1.1(b)(1)(H) is whether the loss amount exceeds $550,000. White argues that the first evidence of his involvement in the charged scheme is a fake check he passed in December 2011. Calculating the loss amount from the date of that check results in a loss of $453,923.55, which corresponds to a 12-level enhancement under § 2B1.1(b)(1)(G), instead of the 14-level enhancement White received under § 2B1.1(b)(1)(H). That two-level difference would have reduced White's offense level to 20, which would have reduced his guideline range from 84 to 105 months to 70 to 87 months. U.S.S.G. ch. 5, pt. A.
But White admitted to participating in the scheme as early as September 2011 by requesting (and receiving) credit for time served on an Illinois forgery conviction that stemmed from an arrest on September 13, 2011. At sentencing, White argued that offense was "all part of the scheme." Using the government's loss spreadsheet, the earlier date leads to a loss amount of $548,353.71, just shy of the $550,000 that would require the same guideline range that the district court used. White thus narrowly avoids a harmless error finding, see United States v. Crockett , 82 F.3d 722, 730 (7th Cir. 1996) (mistaken calculation of drug quantity "harmless" because correct quantity would result in same base offense level), but sentencing judges are free to consider where relevant fraud losses (or robbery losses or drug quantities, etc.) fall in the relevant ranges under the Guidelines.
Without a more specific and supported finding on when White's participation in the scheme began, we cannot assume that his participation began any earlier than the September 13, 2011 arrest.5 We must therefore vacate the sentence and remand.
*992Compare United States v. Locke , 643 F.3d 235, 244-45 (7th Cir. 2011) (rejecting inclusion of dismissed counts as relevant conduct where "both the findings and supporting evidence are deficient," and collecting cases), with United States v. Bogdanov , 863 F.3d 630, 634 (7th Cir. 2017) (affirming loss calculation because "abundant circumstantial evidence" and "direct evidence" corroborated admissions in plea agreement and supported finding that defendant stole goods), and Paulette , 858 F.3d at 1060 (admission in plea agreement that conspiracy involved methamphetamine was "conclusive" proof that defendant participated in conspiracy before 2013 because evidence showed that defendant's only methamphetamine transactions occurred before 2013).
B. Restitution
White has also objected to the restitution ordered as part of his sentence. The restitution issue is similar but not identical to the loss amount issue. The Mandatory Victim Restitution Act, 18 U.S.C. § 3663A, applies to a victim's losses from the offense of conviction, which is narrower than relevant conduct under the Guidelines. The amount of restitution is "limited to the actual losses caused by the specific conduct underlying the offense, and, like the loss amount, the government must establish that by a preponderance of the evidence." United States v. Orillo , 733 F.3d 241, 244 (7th Cir. 2013), citing United States v. Kennedy , 726 F.3d 968 (7th Cir. 2013) ; see also United States v. Burns , 843 F.3d 679, 689 (7th Cir. 2016) ("The MVRA has a proximate cause requirement."); Locke , 643 F.3d at 247 n.7 (noting that " 'relevant conduct' is not within the scope of the MVRA"). We ordinarily review restitution amounts for abuse of discretion, but because White failed to object to the restitution calculation at the sentencing hearing, he and the government agree that we should review the restitution amount for plain error. See Locke , 643 F.3d at 246.
The restitution amount is plainly erroneous. In calculating restitution, the district court should " 'adequately demarcate the scheme.' " Id. at 247-48 (vacating restitution order under plain error review because district court "never discussed its restitution decision" and made no findings on scope of scheme or victims harmed), quoting United States v. Smith , 218 F.3d 777, 784 (7th Cir. 2000). In this case, the district court did not do so. It imposed the restitution without explaining how White was responsible for that amount and without evidence to support the full amount. The lack of a finding is not necessarily fatal, but the lack of evidentiary support that would have supported a finding is. See, e.g., Burns , 843 F.3d at 689-90 (finding plain error in restitution amount where defendant failed to object); id . at 691 (Hamilton, J., dissenting) ("We should not find 'plain error' for the mere lack of a finding that the judge was not asked to make, at least when the evidence will support such a finding ." (emphasis added) ).
We vacate the restitution amount for the same reason as the loss amount. See Orillo , 733 F.3d at 244 (resolving restitution and loss amount issues together because defendant raised "one challenge applicable equally to both determinations"), citing United States v. Ali , 619 F.3d 713, 720 (7th Cir. 2010). Also, we must remand because the evidence actually contradicts the restitution award. The restitution amount includes about $25,000 in losses that predate the "fall of 2009." The government argues that the loose language in the plea agreement (i.e., "no later than in or around" the fall of 2009) "does not necessarily exclude" pre-2009 losses. That argument stretches too far-especially because the prosecutor expressly stated at sentencing that the *993government did not charge White with any conduct before his release from prison in August 2009. To hold White responsible for a restitution amount, the government must prove that amount by a preponderance of the evidence. This record falls short of that standard.
We VACATE White's sentence and the restitution order and REMAND for resentencing consistent with this opinion. Because White is due to be released in August 2018, the district court should expedite his resentencing. Our mandate shall issue immediately.