Kash Lee appeals the sentence he received when his supervised release was revoked. He faults the district court for not addressing what he now characterizes as his principal argument in mitigation: that a longer sentence would unjustifiably subject him to harsher treatment than similarly situated defendants. But Lee did not make this argument in the district court, so the district court had no obligation to address it. Lee also complains that the district court failed to fill out a form stating the reasons for his sentence. It is not clear that a district court has an obligation to fill out such a form when revoking supervised release. Even if it does, however, Lee suffered no prejudice *872from the district court's failure to complete this administrative task.

I.

Kash Lee was sentenced to life imprisonment and ten years of supervised release for several drug-trafficking convictions. His term of imprisonment was reduced to 312 months in prison in return for his substantial assistance to the government, and it was later reduced still further-to 112 months-because of a retroactive change in the Sentencing Guidelines. After he was discharged from prison, he moved to Iowa, where he began serving his term of supervised release.

But Lee did not adopt a law-abiding lifestyle. He violated conditions of his supervised release by missing numerous scheduled drug tests and meetings with his probation officer. And more seriously, he battered his girlfriend, Delisa Roland, by chasing her down a flight of stairs and repeatedly kicking her after she fell. Lee fled, but he was ultimately arrested. He then called several friends and relatives from jail, cajoling them to get Roland to change her story. Roland testified anyway, and the district court found that Lee had violated the conditions of his supervised release by battering her and by missing required appointments with his probation officer.

At sentencing, the government argued for three years' imprisonment, while Lee argued for no more than a year and a day. He made several arguments in favor of the shorter sentence, but only one is at issue in this appeal: that using the federal revocation proceedings to punish him for the battery would be "the tail wagging the dog." Lee pointed out that the battery was "a state court misdemeanor in Scott County," and a misdemeanor "under Iowa law can't get more than a year." If the matter were "handled in the state court system," Lee argued, the court "probably would have made both parties go to counseling, get treatment to try to repair the family unit." Instead, the government had gone "full-bore litigation for a Grade C violation, a misdemeanor," and was seeking three years' imprisonment even though the Guidelines range was eight to fourteen months.

The district court sentenced Roland to 30 months' imprisonment and six years of supervised release. It justified that sentence by recounting Lee's numerous violations of supervised release leading up to his attack on Roland, by crediting Roland's account of Lee's battery, and by acknowledging the need to deter further criminal conduct and protect the public. Lee appeals that sentence.

II.

Under our decision in United States v. Cunningham , a district court imposing a sentence must address a criminal defendant's "principal" arguments in mitigation unless they are "so weak as not to merit discussion." 429 F.3d 673, 679 (7th Cir. 2005) ; see also United States v. Davis , 764 F.3d 690, 694 (7th Cir. 2014) ; Rita v. United States , 551 U.S. 338, 357-58, 127 S.Ct. 2456, 168 L.Ed.2d 203 (2007) ("The sentencing judge should set forth enough to satisfy the appellate court that he has considered the parties' arguments and has a reasoned basis for exercising his own legal decisionmaking authority."); cf. Chavez-Meza v. United States , --- U.S. ----, 138 S.Ct. 1959, 1965, --- L.Ed.2d ---- (2018) (acknowledging that the sentencing judge should "make[ ] clear that he or she has considered the parties' arguments"). To trigger that requirement, the defendant's argument must be "fully developed" and "supported by a compelling factual basis." United States v. Jackson , 547 F.3d 786, 795 (7th Cir. 2008). And it must be one of the defendant's "principal" arguments;

*873a district court need not offer a reason for rejecting every one of the defendant's contentions. United States v. Martinez , 650 F.3d 667, 672 (7th Cir. 2011).

Lee claims that the district court violated Cunningham by ignoring one of his principal arguments in mitigation. When it imposes a sentence, the district court must consider a set of statutory factors, including "the need to avoid unwarranted sentencing disparities among defendants with similar records who have been found guilty of similar conduct." See 18 U.S.C. § 3553(a)(6) (initial sentence) & 18 U.S.C. § 3583(e) (revocation of supervised release). Lee characterizes his discussion of the penalties for battery under Iowa law as an argument about this sentencing factor, and he complains that the district court did not respond to it in articulating the basis for Lee's sentence. Invoking Cunningham , he insists that we must remand his sentence with instructions that the court put its reasons for rejecting Lee's "unwarranted disparities" argument on the record.

The problem is that Lee did not make an "unwarranted disparities" argument, so he did not trigger the district court's duty under Cunningham . At sentencing, Lee contended that he would face only a one-year sentence if he were being prosecuted in state court for domestic battery; he also asserted (apparently without evidence) that such a prosecution would "probably" just result in his being sent to counseling. This is certainly an argument that the worst of his offenses was not serious enough to justify a higher sentence. But it is not an argument that an above-Guidelines sentence would create a disparity "among defendants with similar records who have been found guilty of similar conduct ," and that such a disparity would be unwarranted. United States v. Durham , 645 F.3d 883, 897 (7th Cir. 2011). Lee did not identify any defendant with a similar record (for example, one with a conviction for drug trafficking) found guilty of similar conduct (for example, violating multiple conditions of supervised release, including by committing a domestic battery), much less explain why a comparatively higher sentence was unwarranted in his case. See United States v. Anaya-Aguirre , 704 F.3d 514, 518 (7th Cir. 2013) (holding that a sentencing court need not address an unwarranted-disparities argument unless the defendant provides a "sufficient evidentiary showing" that his situation is comparable to defendants who received a lower sentence). Because Lee did not make any of these points, he did not come close to presenting a developed, meritorious argument that the proposed sentence would create unwarranted disparities between him and similarly situated defendants. And the district court had no obligation to address an argument that Lee did not make.

III.

Lee next asks that we perform a limited remand to require the district court to file a written statement of reasons. When a district court sentences a criminal defendant, it must announce "the reasons for its imposition of the particular sentence" in open court, including, if applicable, an explanation of why the district court chose a sentence outside of the range recommended by the Sentencing Guidelines. 18 U.S.C. § 3553(c). Except for the Cunningham challenge that we rejected above, Lee does not allege that the district court failed to orally explain its reasons for sentencing Lee to an above-Guidelines sentence. But the district court did not fill out a "statement of reasons" form that committed those reasons to writing. 18 U.S.C. § 3553(c)(2). Lee asks us to remand his case so that the district court can complete the form.

It is unclear whether the statute requires the form when a court revokes supervised *874release. The Eleventh Circuit has said that it does, United States v. Parks , 823 F.3d 990, 993-94 (11th Cir. 2016) ; the Eighth Circuit has reached the contrary conclusion, albeit under a prior version of the statute, United States v. Cotton , 399 F.3d 913, 915-16 (8th Cir. 2005). We do not need to decide that issue, however, because any error is harmless.

Lee has suffered no prejudice from the lack of a written statement of reasons, because the district court's oral explanation was sufficient. A district court must explain its sentence so that a reviewing court can evaluate the adequacy of its rationale. See Chavez-Meza , 138 S.Ct. at 1965 ("If the court of appeals considers an explanation inadequate in a particular case, it can send the case back to the district court for a more complete explanation."). But it is the explanation that matters, not the form in which it appears. United States v. Baker , 445 F.3d 987, 991 (7th Cir. 2006) ("[It] is irrelevant whether [the court's] rationale is contained in a written statement or, alternatively, was articulated orally at the sentencing hearing."). And Lee is complaining about the absence of the document, not the adequacy of the explanation. We agree with our sister circuits: when the oral statement of reasons is sufficient, we will not remand simply because the written statement is lacking. United States v. Jackson , 848 F.3d 460, 465 (D.C. Cir. 2017) (collecting cases); United States v. Vazquez-Martinez , 812 F.3d 18, 25-26 (1st Cir. 2016).

This approach makes sense, because the written statement of reasons is not a procedural safeguard for the defendant; rather, it serves a record-keeping function for the Sentencing Commission. Jackson , 848 F.3d at 463-64. Before a 2010 amendment, 18 U.S.C. § 3553(c)(2) required a sentencing court to state with specificity its reasons for giving a non-Guidelines sentence in "the written order of judgment and commitment." Congress eliminated that requirement in 2010, amending the statute to require that a court instead include its explanation in "a statement of reasons form issued under section 994(w)(1)(B) of title 28." Pub. L. No. 111-174, § 4, 124 Stat. 1216, 1216 (2010). That section, in turn, obliges the Chief Judge of each district to ensure that the courts of that district send information to the Commission relating to each sentencing. Courts send the Commission data about the sentence imposed, the offense, and the demographic information of the offender; they also relay documents relating to the conviction and sentence, including a "written statement of reasons" that "include[s] the reason for any departure from the otherwise applicable guideline range." 28 U.S.C. § 994(w)(1)(B). That statement must be provided on a form designed by the Commission. Id. The Commission ultimately analyzes the aggregated reports and makes recommendations to Congress based on its analysis. 28 U.S.C. § 994(w)(3). The statutory scheme does not contemplate that the reports to the Commission will play any role in the individual cases that generate them; instead, the reports are for the Commission to use in the course of its work. In short, the written statement of reasons appears to serve principally, if not exclusively, an administrative purpose unrelated to the rights of the defendant. See Jackson , 848 F.3d at 464 ; Vazquez-Martinez , 812 F.3d at 25-26 ; United States v. Shakbazyan , 841 F.3d 286, 292 (5th Cir. 2016).

Because the form is a means of collecting data for the Commission, a defendant ordinarily suffers no harm when a sufficiently explained sentence fails to generate a written statement of reasons.1

*875True, the requirements of § 994(w)(1)(B) are designed to benefit criminal defendants generally by helping the Commission improve sentencing practices. But a criminal defendant is not harmed by the omission of his sentence from the aggregate data the Commission uses to analyze the system. Absent identifiable prejudice to the defendant, a district court's failure to file the form is not itself grounds for vacating and remanding the sentence to the district court.

* * *

The district court's judgment is AFFIRMED.