HAMILTON, Circuit Judge.
This appeal presents two distinct claims. The first arises from plaintiff Joan Mulva-nia’s arrest and detention at the Rock Island County Jail in November 2010. Mul-vania claims the jail has a widespread practice of conducting strip searches with excessive force and without accommodating people who are experiencing mental distress. The second claim arises from ten other plaintiffs who joined the suit to challenge the Rock Island Sheriffs policy that requires female detainees to wear either white underwear or no underwear at all. They argue the policy is not rationally related to a legitimate governmental objective and that it impairs their dignity without sufficient justification. They also seek certification to pursue that claim as a class.
We affirm the district court’s grant of summary judgment against Mulvania on both of her claims. We reverse the district court’s grant of summary judgment against the other plaintiffs on the underwear policy, but we affirm denial of class certification on that claim. We recount the facts as told in the parties’ undisputed statement of facts. Where a dispute exists, we note the dispute and resolve it in favor of plaintiffs for purposes of summary judgment, giving them the benefit of reasonable inferences. E.g., Zerante v. DeLuca, 555 F.3d 582, 584 (7th Cir. 2009).
I. Mulvania’s Claims
A. Undisputed Facts of Mulvania’s Arrest and Detention
On November 7, 2010, two police officers arrested Joan Mulvania for domestic battery. They brought her to the Rock Island County Jail, but upon arrival, Mulvania refused to exit the vehicle. Several corrections officers moved her from the car to a holding cell in the jail. Mulvania’s speech was slurred, and she screamed obscenities, refused to cooperate with the officers, and was physically combative. The officers testified that Mulvania appeared intoxicated and was acting erratically. Mulvania claims she was experiencing a “posh-traumatic stress disorder flashback.” She disputes that the officers smelled alcohol on her breath. Defendants acknowledge that they did not smell alcohol, but they rely on hospital laboratory results from that day in which Mulvania tested positive for cocaine and cannabinoids.
Once in the holding cell, Mulvania refused to change from her clothes into a jail uniform, which is part of the jail’s booking process for all detainees. The defendants claim that misdemeanor detainees are permitted to change in a private room when they are cooperative; however, the plaintiffs dispute this. When detainees are not cooperative, the Sheriff permits officers to use reasonable force to ensure compliance with the policy.
After Mulvania refused to change into the jail uniform, two female corrections officers and three or four male officers restrained her and removed her clothing. They placed Mulvania on her stomach, held her arms straight over her head, and then lifted her shirt off. During this process, Mulvania banged her head against the floor and yelled, “They’re going to rape me.” After they removed her clothing, the officers draped a jail uniform over her naked body and left the holding cell. Several minutes later, Mulvania had a seizure and was brought to the hospital. After she returned from the hospital, she was released from the jail without any charges.
[853]*853B. Procedural History
In November 2010 Mulvania filed this suit under 42 U.S.C. § 1983 against Rock Island County and the Sheriff of Rock Island County. She alleged that the officers unlawfully arrested her, detained her without probable cause, conducted an unconstitutional strip search, used unreasonable force by shackling her, continued to detain her after she was informed that she would not be prosecuted, and sexually assaulted her because of her sexual orientation. Mulvania amended her complaint numerous times over the next several years, dropping most of her original claims and adding new ones, including the underwear claim.
On April 15, 2015, Mulvania sought to file a fourth amended complaint in which she intended to “delete all of the allegations pertaining to the individual defendants and to clarify plaintiffs official capacity claims against the Sheriff.” She also sought to add a new claim under the Americans with Disabilities Act. The district court denied her motion as it pertained to the Americans with Disabilities Act. The court said the new claim did not relate back to the third amended complaint and that it was not in the interest of justice to amend the complaint once again to add that new claim after so many years of litigation. The court permitted plaintiffs to file a fourth amended complaint “that includes only the allegations related to the underwear claim.”
When the plaintiffs filed their fourth amended complaint, however, they included not only the underwear claim but also Mulvania’s earlier excessive force claim. The Sheriff moved to strike those allegations because they exceeded the court’s order granting leave to amend the complaint. On March 31, 2016, the district court granted the motion to strike, but also proceeded to address the merits of the claim to avoid deciding the case on a “procedural technicality.”
C. Summary Judgment on Excessive Force Claim
Mulvania claims the Rock Island County Jail has a widespread custom or practice of using excessive force to require detainees to change into jail-issued uniforms. She acknowledges that the jail’s official policy authorizes a use-of-force continuum to ensure compliance with the uniform policy. She claims that in practice, however, excessive force is the norm. The district court Concluded that Mulvania put forward insufficient evidence of such a custom or practice of using excessive force. We agree.
We review de novo the district court’s decision granting the Sheriffs motion for summary judgment. Chaib v. Geo Group, Inc., 819 F.3d 337, 340 (7th Cir. 2016). We construe all facts in the light most favorable to Mulvania, who is the non-moving party. Id. Summary judgment is appropriate if there is no genuine dispute of material fact and the Sheriff is entitled to judgment as a matter of law. Fed. R. Civ. P. 56(a).
Mulvania relies on two statements by corrections officers to support her claim of a widespread practice of using excessive force to ensure compliance with the jail’s uniform policy. Officer Bailey testified in his deposition, “When someone refuses to remove their clothes, we have to take their clothes away from them and give them a jumpsuit.” Officer Nesseler testified that if a detainee refuses to remove her clothing, ‘We just take ’em off.” Neither of these statements is evidence of the use of excessive force, let alone a widespread practice of it. The first statement is consistent with the Sheriffs stated use-of-force continuum policy. The second statement is quot[854]*854ed misleadingly by plaintiffs. Officer Nes-seler’s “We just take ’em off’ statement responded to the question: “how would you go about taking a detainee’s clothes off?” Her response is not evidence of any use of excessive force.
Mulvania argues, however, that the defendants did not challenge the sufficiency of the evidence in their motion for summary judgment. She claims that the district court raised this argument on its own and failed to give her notice and a reasonable time to respond on the issue as required by Rule 56(f). This is not correct. The defendants did argue that there was insufficient evidence of a widespread practice of excessive force in their motion. They claimed that Mulvania “cannot show that the policy of the Sheriff requires excessive force given the circumstances” nor can she “show a widespread practice or custom based on only her arrest and detention.” That was sufficient to require her to come forward with evidence of a widespread practice. It was not an error for the district court to decide the motion on these grounds.
D. Americans with Disabilities Act Claim
Mulvania argues next that the district court abused its discretion when it denied her motion for leave to amend her complaint to include a claim under the Americans with Disabilities Act (ADA), 42 U.S.C. § 12101 et seq. The ADA claim sought to challenge the jail’s intake procedures, alleging that the jail’s' practice of enforcing the uniform policy before providing mental health screening was unlawful. Mulvania alleged that she had PTSD and was experiencing a flashback during her intake, and that the jail policy failed to accommodate her disability.
The district court denied Mulvania’s motion for two reasons. First, the court said her motion did not relate back to the original pleading under Rule 15(c)(1) and was thus timebarred. The court noted that none of Mulvania’s earlier complaints included any reference to PTSD or mental health screening. Second, the court said that amending the complaint to allow the ADA claim would not further the interests of justice. See Fed R. Civ. P. 15(a). The court noted that Mulvania was attempting to recast her claims after years of litigation and that the lengthy delay in bringing the ADA claim seemed strategic.
We review for abuse of discretion the district court’s denial of Mulvania’s motion to amend her complaint. Hall v. Norfolk Southern Railway Co., 469 F.3d 590, 594 (7th Cir. 2006). As a general rule, district courts should liberally grant leave to amend pleadings. Fed. R. Civ. P. 15(a); Roman v. Davis, 371 U.S. 178, 182, 83 S.Ct. 227, 9 L.Ed.2d 222 (1962) (reversing denial of leave to amend by citing Rule 15(a)(2)’s mandate to freely grant leave to amend and stating “this mandate is to be heeded”); Barry Aviation Inc. v. Land O’Lakes Municipal Airport Comm’n, 377 F.3d 682, 687 & n.3 (7th Cir. 2004) (collecting cases). This liberal approach to amendments is particularly important where the law is uncertain, such as with pleading standards. Runnion v. Girl Scouts of Greater Chicago & Northwest Indiana, 786 F.3d 510, 520 (7th Cir. 2015) (“In the wake of Twombly and Iqbal, there remain considerable uncertainty and variation among the lower courts as to just how demanding pleading standards have become .... In the face of that uncertainty, applying the liberal standard for amending pleadings, especially in the early stages of a lawsuit, is the best way to ensure that cases will be decided justly and on their merits.”) (citations omitted).
Despite this generally liberal approach to pleading amendments, the dis[855]*855trict court did not abuse its discretion in this case. The court quite reasonably found that Mulvania’s amendment would not have furthered the interests of justice. Fed. R. Civ. P. 15(a). We have noted that “district courts have broad discretion to deny leave to amend where there is undue delay, bad faith, dilatory motive, repeated failure to cure deficiencies, undue prejudice to defendants, or where the amendment would be futile.” Arreola v. Godinez, 546 F.3d 788, 796 (7th Cir. 2008); accord, e.g., Runnion, 786 F.3d at 520 (noting undue delay is sound basis for denying leave to amend pleadings).
Here, the district court found that the plaintiffs had unreasonably delayed introducing the ADA claim, and the court suggested that the delay was strategic. Mulva-nia could have alleged the ADA claim at the beginning of the suit. The lengthy delay could not be justified by newly discovered information. Moreover, allowing the new claim after several years of litigation would have burdened the defendants by requiring them to engage in-substantial additional discovéry. The court also found that the claim would be futile because it would be barred by the two-year statute of limitations for ADA claims. The district court set forth sufficient reasons to deny the proposed amendment. It did not abuse its discretion.
II. White Underwear Policy Claim
Mulvania filed her third amended complaint on April 24, 2012. It added ten plaintiffs who sued the Sheriff because of his policy that requires female detainees to wear white underwear or no underwear at all. The policy allows a detainee to purchase underwear from the jail’s commissary if she has sufficient funds. It is unclear how much the underwear costs or when the underwear would be delivered to the detainee. In addition, a detainee may contact family or friends outside of the jail and ask them to bring her white underwear.
Mulvania added these ten plaintiffs in response to the defendants’ argument that she was not representative of the class because she was not wearing underwear when she arrived at the jail. The other plaintiffs are women who were required to remove their underwear due to the policy. Some plaintiffs allege that corrections officers watched as they removed their underwear and changed into jail uniforms. They describe the experience as “very uncomfortable,” “embarrassing,” “humiliating,” and “upsetting.” They argue that the policy is not rationally related to a legitimate governmental objective and that it imposes an unjustified dignitary harm in violation of their rights under the Fourth, Eighth, and Fourteenth Amendments.
The Sheriffs sole stated rationale for the underwear policy was to prevent detainees from extracting ink from colored underwear. The theory was that detainees could use that ink to make tattoos. The Sheriff did not identify any instances of this occurring, but testified that he was “told ... when [he] wrote the policy” that such a security concern exists. The district court denied certification to the proposed class on August 15, 2012, in part because plaintiffs failed to satisfy the numerosity and predominance requirements of Rule 23(a) and (b)(3).
A. Summary Judgment on Merits
Plaintiffs' appeal the district court’s grant of summary judgment against their challenge to the white underwear policy. The court found that while the Sheriffs security interest in the underwear policy was “weak,” the dignity intrusion to plaintiffs was “minimal.” The court made this finding based in part on its conclusion that the policy was close to the “correctional [856]*856mainstream” and because detainees would be forced to go without underwear for at most one day. The court noted that plaintiffs’ declarations discussed only the “actual process of removing their underwear” and did not show that they suffered dignitary harm when forced to go without underwear throughout the rest of their detention. Noting that “Federal courts defer to the judgment of jail administrators,” the court ruled that the Sheriff was entitled to summary judgement.
On appeal plaintiffs claim, among other things, that the district court erred by viewing the facts in the light most favorable to the defendants. We review de novo the district court’s grant of summary judgment for the Sheriff. Chaib, 819 F.3d at 340.
Because plaintiffs were pretrial detainees, not convicted prisoners, we assess their claim under the Fourteenth Amendment instead of the Eighth Amendment. In Bell v. Wolfish, the Supreme Court held that the Fourteenth Amendment’s Due Process Clause prohibits holding pretrial detainees in conditions that “amount to punishment.” 441 U.S. 520, 535, 99 S.Ct. 1861, 60 L.Ed.2d 447 (1979). A pretrial condition can amount to punishment in two ways: first, if it is “imposed for the purpose of punishment,” or second, if the condition “is not reasonably related to a legitimate goal — if it is arbitrary or purposeless — a court permissibly may infer that the purpose of the government action is punishment.” Id. at 538-39, 99 S.Ct. 1861. The Supreme Court recently explained that “a pretrial detainee can prevail by providing only objective evidence that the challenged governmental action is not rationally related to a legitimate governmental objective or that it is excessive in relation to that purpose.” Kingsley v. Hendrickson, 576 U.S. -, -, 135 S.Ct. 2466, 2473-74, 192 L.Ed.2d 416 (2015).
Defendants offer meagre justification for the white underwear policy. The only evidence in the record that supports the policy is the Sheriffs deposition testimony that he was “told ... when [he] wrote the policy” that such a security concern about tattoo ink exists. There is no evidence that detainees at the Rock Island County Jail have ever extracted ink from colored underwear to make tattoos. Nor, for that matter, have defendants identified an instance of this occurring anywhere else. The district court asserted that the policy might be close to the “correctional mainstream,” but we find no support for that conclusion in the record.
In its summary judgment order, the district court noted: “While the underwear policy may strike the reader as odd, and the Sheriffs explanation as implausible, the Court notes that many other jails have the same or similar policies.” Mulvania v. City of Rock Island, No. 4:10-cv-04080-SLD-JEH, slip op. at 15 n.11 (C.D. Ill. Mar. 31, 2016). The court then cited four cases to demonstrate this point, noting that “the Jail’s interest is perhaps close to the correctional mainstream and therefore makes the Court’s view of the> Sheriffs rationale stronger.” Id., citing Gaston v. McCoy, No. 15cv1054, 2015 WL 3484237 (C.D. Ill. June 1, 2015); Gallup v. Schmaeling, No. 12-cv-1264, 2013 WL 4855181 (E.D. Wis. Sept. 10, 2013); Batchelor v. Fenwick, 710 F.Supp.2d 811, 816 (S.D. Ind. 2010); Marriott v. County of Montgomery, 426 F.Supp.2d 1, 9 (N.D.N.Y. 2006).
We agree that the white underwear policy seems odd and that the Sheriffs explanation seems at least questionable. We disagree that the four cases cited by the district court show that “many other jails” have the same policy or that the policy may be within the “correctional main[857]*857stream.” Most of these cases are distinguishable from the Rock Island County Jail’s white underwear policy. Even if they were not, four cases are insufficient to establish the norms of correctional institutions. We address the four cases in turn.
Gaston involved a pro se complaint that merely alleged that a jail would not provide the plaintiff with underwear. 2015 WL 3484237, at *1. It did not claim that detainees were forced to remove their nonwhite underwear as a jail policy. Failing to give a new detainee underwear is considerably different from taking away her underwear. The second case, Gallup, was another pro se complaint. It did allege that the jail had a white underwear policy. 2013 WL 4855181, at *2. In any event, though, these unsupported allegations in unrelated complaints do not prove any fact sufficient for the court to make a finding at summary judgment.
In Batchelor, an opinion from 2010, the district court noted that a jail used to have a white underwear policy “whereby inmates wearing colored underwear were asked to exchange it for white underwear.” Batchelor, 710 F.Supp.2d at 816. In addition to the fact that the policy had been revoked, the Batchelor policy is readily distinguishable from the Rock Island policy. The policy may have been voluntary (detainees were “asked” to exchange their underwear), and detainees appeár to have been given underwear to replace their nonwhite underwear (“in exchange for”). Finally, in Marriott, it is unclear that a white underwear policy existed. There the court said that the defendants’ assertion about a white underwear policy “contravenes all of the prior testimony given by defendants and their officials — no CO, Jail administrator, or other official ever testified about arrestees and their white underwear.” 426 F.Supp.2d at 9.
Even if we assume the Rock Island County Jail is not the only jail ever to have had a white underwear policy, this record does not show the policy is within any correctional mainstream. Even if all four of these cases involved similar white underwear policies, that would still seem to imply that the Rock Island County Jail’s policy is an outlier. See Holt v. Hobbs, 574 U.S. -, -, 135 S.Ct. 853, 866, 190 L.Ed.2d 747 (2015) (“While not necessarily controlling, the policies followed at other well-run institutions would be relevant to a determination of the need for a particular type of restriction.”), citing Procunier v. Martinez, 416 U.S. 396, 414 n.14, 94 S.Ct. 1800, 40 L.Ed.2d 224 (1974). We make no judgment now about whether the policy is within a correctional mainstream, but this record does not show that it is.
Any security justification for the underwear policy is further undermined by defendants’ own claim that they often did not enforce the policy. Defendants state that the prohibition “was not consistently applied” and that “detainees often were permitted to wear colored underwear.” This admission supports an inference that the asserted security concern about tattoo ink from underwear is not genuine. See King v. McCarty, 781 F.3d 889, 898 (7th Cir. 2015) (prisoner challenged jail’s use of a transparent jumpsuit to transport prisoner: “Detainees arriving at the intake facility from other jails were not wearing similar garments, which at least tends to suggest that such clothing is not necessary for safe and secure penal transfers”). The irregular enforcement of the underwear policy also creates the potential for abuse, for instance by providing a way to harass bothersome detainees.
Giving plaintiffs the benefit of favorable inferences from this record, a reasonable trier of fact could find that the white underwear policy is not rationally related to a [858]*858legitimate governmental objective, or is at least excessive in relation to such a purpose. This conclusion, without more, supports an inference that the policy punishes pretrial detainees in violation of the Fourteenth Amendment. Kingsley, 576 U.S. at -, 135 S.Ct. at 2473-74; Bell, 441 U.S. at 539, 99 S.Ct. 1861. We therefore reverse the district court’s grant of summary judgment against the plaintiffs on their challenge to the white underwear policy.
Even if the jail’s policy might ultimately be found to be rationally related to a legitimate governmental objective, the deprivation it imposes must not be excessive in relation to that purpose. Kingsley, 576 U.S. at -, 135 S.Ct. at 2473-74. This assessment calls for considering not just the government’s interest but also the dignity interests of the plaintiffs. See Brown v. Plata, 563 U.S. 493, 510, 131 S.Ct. 1910, 179 L.Ed.2d 969 (2011) (although prisoners are deprived of many rights while in custody, “the law and the Constitution demand recognition of certain other rights. Prisoners retain the essence of human dignity inherent in all persons.”).
Dignity serves an important balancing function alongside the legitimate safety and management concerns of jails and prisons. See King, 781 F.3d at 897 (“Claims such as [plaintiffs] require that we consider the larger tension between the privacy and dignity of prisoners and the pressing institutional needs for security and safety. Courts give wardens substantial deference in pursuing the latter ends, but that deference is not complete.”); see also Canedy v. Boardman, 16 F.3d 183, 186 (7th Cir. 1994) (“The judicial inquiry, then is to ‘balanc[e] the significant and legitimate security interests of the institution against the privacy interests of the inmates.’ ”), quoting Bell, 441 U.S. at 560, 99 S.Ct. 1861. Without the counterweight of dignity, a jail could presumably set forth security reasons to require detainees to remain naked throughout their detention or other such unseemly measures. The Constitution forbids such tactics. It requires consideration of individual dignity interests when assessing the permissibility of restrictive custodial policies.
Here, the plaintiff-detainees allege a credible dignitary' harm. They describe their experiences being deprived of their underwear as “very uncomfortable,” “embarrassing,” “humiliating,” and “upsetting.” In addition, the policy resulted in detainees attending their own court hearings without underwear. At least one plaintiff was deprived of her underwear during her menstrual cycle.
This indignity lasted for indeterminate periods of time. The district court found that detainees would be deprived of underwear for at most one day, but we have not found support for that finding. Defendants appear to concede this point in their brief. Thus, even if the white underwear policy turns out to be rationally related to a legitimate interest, the dignitary harm imposed by the policy might still be excessive in relation to that interest.
B. Denial of Class Certification
Plaintiffs also appeal the district court’s denial of class certification for the underwear claim. They argue the district court erred when it concluded that they failed to meet the predominance and numerosity requirements of Rule 23.. We agree that the district court incorrectly applied the predominance requirement, but we find no error in its numerosity ruling. We affirm the denial of class certification.
Federal Rule of Civil Procedure 23 governs class certification. A court may certify a plaintiff class when the named plaintiff demonstrates that the proposed class meets the four requirements of Rule [859]*85923(a) — numerosity, commonality, typicality, and adequacy of representation — and at least one of the branches of Rule 23(b). Oshana v. Coca-Cola Co., 472 F.3d 506, 513 (7th Cir. 2006). Plaintiffs have the burden of demonstrating that the requirements of Rule 23 are met. Wal-Mart Stores, Inc. v. Dukes, 564 U.S. 338, 350, 131 S.Ct. 2541, 180 L.Ed.2d 374 (2011).
District courts have “broad discretion to determine whether certification of a class-action lawsuit is appropri-áte.” Chavez v. Illinois State Police, 251 F.3d 612, 629 (7th Cir. 2001), quoting Mira v. Nuclear Measurements Corp., 107 F.3d 466, 474 (7th Cir. 1997). We review for abuse of discretion the district court’s denial of class certification. Chicago Teachers Union, Local No. 1 v. Board of Education of City of Chicago, 797 F.3d 426, 433 (7th Cir. 2015).
Plaintiffs sought class certification pursuant to Rule 23(b)(3), which requires that “questions of law or fact common to class members predominate over any questions affecting only individual members.” The district court concluded that common issues did not predominate in the underwear claim because the damages would vary for individual class members based on factors such as how long a detainee was deprived of her underwear, whether she was on her menstrual cycle or pregnant, and other considerations. In short, the court concluded that “there would be no simple or formulaic method to calculate these damages across all of the individuals of the proposed class.” Mulvania v. Sheriff of Rock Island County, No. 4:10-cv-4080-SLD-JAG, 2012 WL 3486133, at *9 (C.D. Ill. Aug. 15, 2012).
This reasoning was a mistake. “It has long been recognized that the need for individual damages determinations at [a] later stage of the litigation does not itself justify the denial of certification.” Mullins v. Direct Digital, LLC, 795 F.3d 654, 671 (7th Cir. 2015); see also, e.g., Schleicher v. Wendt, 618 F.3d 679, 685 (7th Cir. 2010) (“The possibility that individual hearings will be required for some plaintiffs to establish damages does not preclude certification.”); William B. Rubenstein, Newberg on Class Actions, § 4:54 (5th ed. Dec. 2016 Update) (“[C]ourts in every circuit have uniformly held that the 23(b)(3) predominance requirement is satisfied despite the need to make individualized damage determinations and a recent dissenting decision of four Supreme Court Justices characterized the point as “well nigh universal.’”), citing Comcast Corp. v. Behrend, 569 U.S. -, -, 133 S.Ct. 1426, 1437, 185 L.Ed.2d 515 (2013) (Ginsburg and Breyer, JJ., joined by Sotomayor and Kagan, JJ., dissenting).
In cases like this, where damages must be assessed individually, district courts may “bifurcate the case into a liability phase and a damages phase.” Mullins, 795 F.3d at 671. The district court thus, erred when it ruled that class certification was precluded based on the need for damages to be assessed individually. This error was harmless, however, because the court did not abuse its discretion when it ruled that plaintiffs failed to meet the numerosity requirement.
To satisfy Rule 23’s numerosity requirement, the proposed class must be “so numerous that joinder of all members is impracticable.” Fed. R. Civ. P. 23(a)(1). While there is no magic number that applies to every case, a forty-member class is often regarded as sufficient to meet the numer-osity requirement. See Swanson v. American Consumer Industries, Inc., 415 F.2d 1326, 1333 & n.9 (7th Cir. 1969) (even forty class members “is a sufficiently large group to satisfy Rule 23(a)”); see also Rubenstein, Newberg on Class Actions, [860]*860§ 3:12 (“[A] class of 40 or more members raises a presumption of impracticability of joinder based on numbers alone.”).
The plaintiffs estimated that their class would have forty-one members. The district court identified several problems with plaintiffs’ calculation and overall nu-merosity argument,, yet plaintiffs fail to address most of these problems on appeal. First, as the district court noted, plaintiffs did not address the impracticability of join-der in their amended motion in support of class certification. Nor do they on appeal. See Pruitt v. City of Chicago, 472 F.3d 925, 926-27 (7th Cir. 2006) (affirming denial of class certification; no showing that joinder of forty possible class members was impracticable). Second, plaintiffs did not explain critical ambiguities in how they calculated the potential class size. Nor do they on appeal. Third, the district court disagreed with plaintiffs’ class start date of November 15, 2008, which is two years before Mulvania’s first complaint. Plaintiffs address only this third issue on appeal. The district court’s first two reasons alone would be sufficient for us to affirm its ruling. The court’s approach to the third issue — the class start date — likewise was not an abuse of discretion.
The district court calculated a class of 29 members based on a class start date of April 24, 2010, two years before Mulvania filed the third amended complaint, which first introduced the underwear class allegations. Plaintiffs argue that this class start date is incorrect because, under Rule 15(c), the third amended complaint “related back” to the initial complaint Mulvania filed on November 15, 2010. Plaintiffs cited no authority to support this calculation method in their briefs, but at oral argument they cited Arreola v. Godinez, 546 F.3d 788, 796 (7th Cir. 2008).
Arreola does not stand for the proposition that plaintiffs claim. Although Arreola did address relation back under Rule 15(c) and numerosity under Rule 23(a), it addressed them separately. Id. at 796 (district court did not abuse discretion by granting leave to amend complaint to add class allegations to claim that related back to initial complaint); id. at 798 (plaintiff provided sufficient information in the record to establish numerosity).
One of the examples in Arreola might seem to assume that Rule 15(c) may push back the class start date to an earlier complaint (before any class allegations were made) for the purpose of satisfying Rule 23(a)’s numerosity requirement. See id. However, Arreola made no holding to that effect. The court merely hypothesized, for illustrative purposes, the ways in which the plaintiff in that case could easily meet the numerosity requirement. The court’s example showed how the record could have supported a finding that the putative class would exceed 350 members. It would have made no difference in the court’s example if it had used either complaint to calculate the class start date.
Plaintiffs cite no authority that directly supports their argument, and we need not make their arguments for them. See Vaughn v. King, 167 F.3d 347, 354 (7th Cir. 1999) (“It is not the responsibility of this court to make arguments for the parties.”). The district court did not err by basing its start date for the numerosity calculation on the third amended complaint, which is when the white underwear class allegations were first introduced.
We AFFIRM the district court’s grant of summary judgment for defendants on Mulvania’s excessive force claim, its partial denial of Mulvania’s motion to amend her complaint, and its denial of class certification in the underwear matter. We REVERSE the district court’s grant of summary judgment to defendants in the [861]*861underwear matter, and we REMAND for further proceedings consistent with this opinion.