ORDER
Rafael Polanco and Margarita Gonzalez set fire to an apartment building because they were angry with one of its tenants, Janelle Fermaintt, whom they knew to be inside. The fire caused Fermaintt and her two children to be grievously and permanently injured. Polanco pleaded guilty to arson and Gonzalez pleaded guilty to arson and obstruction of justice. On appeal, they argue only that the district court miscalculated their advisory sentence and then imposed an unreasonable sentence. In reality, the court’s only arguable miscalculation actually benefitted the defendants. Moreover, the court thoroughly addressed the defendants’ nonfrivolous sentencing arguments and provided good reasons for imposing the sentences it chose. We therefore affirm the judgments.
I
Polanco and Gonzalez were living together as a couple, but Gonzalez hoped to reconcile with her former boyfriend, Erick Brito, who was also the father of one of her children. Brito had begun dating Janelle Fermaintt; this did not, however, stop him from accompanying Gonzalez on a multi-week trip to Mexico. Left behind in Chicago, Polanco and Fermaintt retaliated against their unfaithful lovers by having sex with each other. At some point while Gonzalez and Brito were still in Mexico, Gonzalez and Fermaintt exchanged taunts over the phone.
When Gonzalez returned from Mexico, she resumed her relationship with Polanco. Her competition with Fermaintt over Brito intensified, however, and soon threats of violence were being made on both sides. According to Gonzalez, Fermaintt threatened to torch Gonzalez’s car. The car, which actually belonged to Polanco, was indeed burned by someone.
*641One evening about six weeks after Gonzalez’s return from Mexico, she and Polan-co drove to a gas station and filled an empty laundry detergent bottle with gasoline. They then picked up a friend, Jennifer Trinidad, and drove to Fermaintt’s apartment building. Upon arrival they located Fermaintt’s car, and Gonzalez set it on fire (using Heet-brand antifreeze as an accelerant rather than the gasoline they had brought with them). They waited and watched as firefighters arrived and extinguished the flames, which had already spread to another car.
After the fire truck was gone and all the lights in Fermaintt’s fully occupied 12-unit building had gone out, Gonzalez announced that she was “not done yet.” She and Trinidad then entered Fermaintt’s building and Gonzalez doused the hallway and Fer-maintt’s apartment door with gasoline. Trinidad cautioned that Fermaintt’s children might be in the apartment, to which Gonzalez reportedly replied, “I don’t care,” and ignited the gasoline. The two women then joined Polanco outside and left the scene.
Inside her third-floor apartment, Fer-maintt awoke to the screams of her three-year-old daughter. The apartment was intolerably hot and filled with smoke. Fermaintt, with difficulty, reached both of her daughters (the elder was six) and began to look for a way out. There was no escaping through a door — Fermaintt lost a great deal of skin on her hand and arm trying — and so a window was their only hope.
Fermaintt opened a window and heard neighbors below cry out that help was on the way. But she and her daughters were burning and could not wait, so the neighbors quickly retrieved a plastic swimming pool to use as a makeshift net. Fermaintt then made the decision to drop her six-year-old daughter out of the window. The neighbors were able to break the girl’s three-story fall with the pool. At that point firefighters arrived and rescued Fer-maintt and her younger daughter using a ladder. All three suffered serious burns. The three-year-old’s lung collapsed and she was not expected to survive. The two girls remained hospitalized for weeks, and despite lengthy inpatient rehabilitation, both children have lost function in a limb, cannot be exposed to sunlight, must wear special compression garments 23 hours a day, and are permanently, severely scarred on their faces, hands, and bodies. Other residents of the apartment building suffered only minor injuries, but they lost property and their sense of security.
As police officers were investigating the arson, Gonzalez and Polanco attempted to manufacture an alibi. Gonzalez begged the father of one of her children, Dominick Correa, to tell police that she had been with him celebrating their child’s birthday at the time of the fire, and she convinced her sister to tell the same false story. Soon, however, the cover-up began to fall apart. Correa allowed law enforcement secretly to record a conversation with Gonzalez in which she acknowledged fabricating her alibi. Trinidad, whom Gonzalez had also instructed to lie, instead told investigators what had happened at Fer-maintt’s apartment. (Trinidad minimized her own involvement by explaining that she had been too afraid of Gonzalez to stop her or to leave.) Polanco and Gonzalez, suspecting that Correa had begun to cooperate with authorities, drove around until they encountered Correa’s pregnant girlfriend, whom Gonzalez threatened with a beating.
Polanco and Gonzalez were questioned by federal agents and both denied involvement with the fire. Polanco later admitted to a grand jury that Gonzalez had set the fire, but he insisted that he was unaware of her plan in advance. Unbeknownst to *642Polanco, investigators already knew from his debit-card records that he was the one who had purchased the gasoline that night.
The grand jury indicted Gonzalez and Polanco. Both were charged with arson affecting interstate commerce, see 18 U.S.C. § 844(i), and Gonzalez was also charged with obstruction of justice, see 18 U.S.C. § 1503(a). After their arrests, the pair continued to disavow their roles in setting Fermaintt’s apartment on fire by blaming each other and Trinidad. But eventually, faced with the evidence, Polan-co admitted that he purchased the gasoline with the knowledge that Gonzalez would use it to burn Fermaintt’s apartment, and Gonzalez admitted that she started the fire to hurt Fermaintt, knowing full well that her rival’s children might be present. Both defendants steadfastly denied that their intention was to kill. Instead of going to trial, Gonzalez and Polanco pleaded guilty without a plea agreement to all charges.
Following the defendants’ change of plea hearings, a probation officer compiled presentence investigation reports. The officer calculated Polanco’s guidelines imprisonment range at 78 to 97 months, reflecting a criminal history category of I and a total offense level of 28 (base offense level 24, see U.S.S.G. § 2K1.4(a)(1), plus two levels because there were vulnerable victims, see id. § SAl.l(b)(l), and two levels for obstructing justice by perjuring himself, see id. § 3C1.1). Gonzalez’s range was calculated at 97 to 121 months. Like Polanco, her criminal history category was I, but her offense level was higher than his because, in addition to receiving the adjustments that Polanco received, her level was increased by two because she had a leadership role in the offense, see id. § 3Bl.l(c).
The arson guidelines instruct that the attempted-murder guidelines be applied when the arsonist’s objective was to kill someone, see id. §§ 2K1.4(c), 2A2.1(a)(l), but the probation officer did not use the attempted murder guidelines to calculate the defendants’ sentences. The officer explained that, although Gonzalez had said that she wanted to “fuck up” Fermaintt, neither Gonzalez nor Polanco ever stated that they intended to kill anyone. Still, the probation officer did not feel that a guidelines sentence was appropriate for either defendant in light of the damage they caused; she recommended an above-guidelines sentence based on numerous “departure” criteria recognized in the guidelines.
Before the sentencing hearing, the government and the defendants submitted objections to the presentence report. Both defendants argued that they should be given credit for acceptance of responsibility (because they had pleaded guilty and expressed remorse) and that they should not receive the “vulnerable victims” adjustment (because they did not target Fer-maintt’s children). Gonzalez stated in addition that she was a mere participant in the offense, not an organizer or leader. The government countered that when a defendant has obstructed justice, credit for acceptance of responsibility is bestowed only in extraordinary cases, see U.S.S.G. § 3E1.1 cmt. n. 4; United States v. Black, 636 F.3d 893, 900 (7th Cir.2011), and the level of acceptance in this case was not extraordinary. The government also argued that the cross reference to the attempted-murder guidelines should apply because the defendants’ intent to kill could be inferred from their actions: they used gasoline, a powerful accelerant, to set fire to a building they knew to be occupied, and they certainly knew that fire is very destructive, having just destroyed a car in the same way. According to the government’s sentencing memoranda, Gonzalez’s advisory sentence under the guidelines *643was life imprisonment and Polanco’s was 324 to 405 months.
At the sentencing hearing the district judge first heard from witnesses, medical experts, and victims about the terrible consequences of the apartment fire. The judge next heard argument from both sides on the proper guidelines calculations. Those arguments largely followed the written submissions. The judge first ruled that the guidelines calculations from the presentence report were correct. She explained that the attempted-murder cross reference should not apply because she found no evidence of an intent to Ml. Gonzalez, the judge decided, should receive an offense-level adjustment for having a leadership role because she hatched the arson plan and gave orders to Polanco and Trinidad. Neither defendant was entitled to credit for acceptance of responsibility in part because they continued to obstruct justice even after learning of the children’s injuries. Gonzalez’s offense level, the judge concluded, was 30 and Polan-co’s was 28.
After discussing the applicable guidelines, the judge asked the lawyers to present their arguments on the “appropriate sentence” for the defendants. The government went first, arguing for an above-guidelines sentence of 50 years for Gonzalez and 37 for Polanco based on the heinousness of their offense, the horrible-but-foreseeable consequences to the victims, and the uncharged criminal conduct of which the defendants were also guilty (the car fire). Gonzalez’s lawyer conceded that there was nothing mitigating in his client’s offense conduct, but he reminded the judge that Gonzalez grew up with an unaf-fectionate mother, was raped at age 11 by her uncle, and has five children. The lawyer also argued that Fermaintt had provoked Gonzalez (a relevant factor under U.S.S.G. § 5K2.10) by threatening her and (possibly) burning her car, and he stressed that Gonzalez is in need of rehabilitation. Polanco’s lawyer then attempted to put his client’s actions in context by explaining that Polanco was hopelessly in love with Gonzalez, is unloved by his family, and is “one of the most confused, dumbest criminals.”
After hearing these arguments as well as statements from the defendants expressing remorse, the judge (again agreeing with the presentence report) explained that an above-guidelines sentence was appropriate. She rejected the defendants’ argument that purported threats from Fermaintt were somehow mitigating — the proper response would have been to call the police, she explained — and she opined that the defendants’ status as parents was more aggravating than mitigating, as it made their crime against children harder to understand. The judge emphasized the senselessness of the defendants’ acts and the fact that they understood “what a raging and uncontrollable weapon a fire really is.”
The judge then discussed the numerous circumstances of the case that fit the guidelines’ criteria for upward “departures”: serious physical injury, see U.S.S.G. § 5K2.3; extreme psychological injury (the girls live in fear and face questions and stares as a result of their disfigurement), see id. § 5K2.3; extreme conduct (the defendants waited for the building’s occupants to turn out their lights for bed, and they used a powerful accelerant), see id. § 5K2.8; uncharged conduct (the car fire), see id. § 5K2.21. She was willing to accept that the defendants were remorseful, but she concluded that, all things considered, Gonzalez’s actions actually merited an offense level of 39 (imprisonment range of 262 to 327 months) and Polanco’s merited an offense level of 37 (210 to 262 months). She then sentenced Gonzalez to 300 months and *644Polanco to 210 months, and she acceded to the defendants’ requests to be treated for drug addiction. (Gonzalez received 120 months on her obstruction count, to be served concurrently with her arson sentence.)
After the sentences were announced, the government requested that the judge discuss 18 U.S.C. § 3553(a) explicitly in case there was any doubt that she had applied it. The judge then explained that the § 3553(a) factor that weighed most heavily in her decision was. the need to promote respect for the law.
II
On appeal Polanco and Gonzalez first argue that the district judge made a procedural error in sentencing them when she determined that, based on the departure criteria in the guidelines, the defendants merited a higher offense level than the applicable guidelines produced. The defendants point out that “departures” were rendered obsolete by United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005), and that the judge can sentence above the guidelines range (or within the guidelines for that matter) only through § 3553(a). Although the defendants recognize that departure criteria may still be considered by way of analogy to § 3553(a), see United States v. Lucas, 670 F.3d 784, 791 (7th Cir.2012), they deny that this is what the judge did in this case. Instead, they contend, she miscalculated the guidelines range, imposed what she believed was a within-guidelines sentence, and treated that sentence as presumptively reasonable. The defendants’ evidence of this is that the judge failed to cite § 3553(a) specifically when discussing departures and that she filled out a “statement of reasons” form for each defendant in which she listed Gonzalez’s offense level at 39 and Polanco’s at 37, rather than at their actual guidelines ranges.
No step of the defendants’ argument is persuasive: the district judge did not miscalculate their offense levels, impose what she mistakenly believed were within-guidelines sentences, or presume those sentences to be reasonable. To begin with, the defendants’ assertion that the judge miscalculated their offense levels relies entirely on the judge’s incomplete discussion of how departure factors can increase or decrease a sentence; they have ignored what the judge actually did. As described above, at the sentencing hearing the judge explicitly found that Gonzalez’s offense level was 30 and Polanco’s 28 (calculations also found in the presentence report, to which the defendants make no objection) before she instructed counsel to present arguments on the “appropriate sentence.” Although the judge did not mention § 3553(a) at that point, or when she referred to the “departure” factors, the reasons that she gave for the sentences she imposed were consistent with § 3553(a), which is what matters. See United States v. Panaigua-Verdugo, 537 F.3d 722, 728 (7th Cir.2008). Additionally, the judge did not say or imply that she was imposing a within-guidelines sentence, nor did she ever state or imply that she was presuming any particular sentence to be reasonable.
The fact that the “statement of reasons” forms reflect the offense levels that the judge thought appropriate rather than the defendants’ actual offense levels is immaterial. The written form is trumped by the judge’s oral explanation of the sentence, in keeping with the rule that a judge’s statements at sentencing always take precedence over the written judgment. See United States v. Cephus, 684 F.3d 703, 709 (7th Cir.2012); United States v. McHugh, 528 F.3d 538, 539 (7th Cir.2008). Moreover, the judge also checked boxes on each form accurately indicating that she had adopted the presentence report without *645change and had imposed above-guidelines sentences.
Although the judge could have made clearer that the defendants’ offense levels had not actually changed and that, post-Booker, departures apply only through § 3553(a), it is apparent to us that she was cognizant of her discretion and obligations: she acknowledged the correct guidelines range at the outset, she thoroughly explained why she imposed the sentences she did, and she never suggested in any way that she was bound by the guidelines.
Polanco and Gonzalez also argue that the district judge erred proeedurally by not addressing some of their § 3553(a) arguments. A defendant’s principal arguments at sentencing must be addressed, though there is no need for the judge to state the obvious. See United States v. Gary, 613 F.3d 706, 709-10 (7th Cir.2010). Gonzalez says that the judge should have discussed her cooperation with law enforcement, her rape at the age of 11 by her uncle, and the fact that she committed her offense under the influence of marijuana. Polanco contends that the district judge should have addressed the facts that he was employed, paid child support, and had a learning disability.
The idea that the judge ignored Gonzalez’s cooperation argument can be dismissed out of hand because Gonzalez made no such argument; in fact her lawyer acknowledged at sentencing that she would get no credit for cooperation. The issues Gonzalez did raise but the judge did not discuss were not developed. A lawyer must do more than simply call the court’s attention to a sad fact about a defendant’s life; the lawyer must connect the fact to the defendant’s crime in some way. See United States v. Jackson, 547 F.3d 786, 795-96 (7th Cir.2008). Polanco’s challenge fares no better: though the issues he identifies as mitigating were mentioned in the presentence report, they were raised neither in his sentencing memorandum nor at sentencing.
Finally, Gonzalez and Polanco argue that their sentences are greater than necessary to achieve the sentencing goals found in § 3553(a) and are thus unreasonable. They again stress that the district judge gave insufficient reasons for the sentences she selected. Yet the judge explained their sentences thoroughly, and her only mistake was one that benefitted the defendants: not applying the attempted-murder cross reference. The judge said that there was no evidence of an intent to kill, but we agree with the government that the defendants’ intent to kill could be inferred from their actions, see United States v. Peugh, 675 F.3d 736, 741 (7th Cir.2012); United States v. Perez, 612 F.3d 879, 887 (7th Cir.2010), particularly considering that a preponderance of the evidence is normally sufficient at sentencing, see United States v. Mitchell, 635 F.3d 990, 992-93 (7th Cir.2011); United States v. Reuter, 463 F.3d 792, 793 (7th Cir.2006). Had the murder cross-reference been applied, Gonzalez’s offense level would have been 43, making her advisory sentence the statutory maximum of 40 years, and Polanco’s would have been 41, making his guidelines range 324 to 405 months. The sentences they received—300 months and 210 months respectively—cannot be called unreasonably high when their sentences could legitimately have been so much higher.
The judgment of the district court is Affirmed.