OPINION

SUTTON, Circuit Judge.

Shannon Graves and eight other "exotic dancers" were arrested in Ohio at various times and on various charges, ranging from prostitution to drug distribution to assault to witness intimidation. R. 122 at 1 n.1; see Graves v. Mahoning County, 534 Fed.Appx. 399, 401-03 (6th Cir.2013). Claiming that the police used invalid warrants to arrest them, they filed this § 1983 action against the county and townships that employed the arresting officers. But because they never alleged that the officers arrested them without probable cause — the key allegation needed to show an unconstitutional arrest under the Fourth Amendment — the district court dismissed their lawsuit. We agree and affirm.

I.

This case implicates the often-tricky interaction between the Fourth Amendment's two operative clauses. The first clause, the Reasonableness Clause, limits the government's power to search and seize. "The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures," it says, "shall not be violated." U.S. Const. amend. IV. The second clause, the Warrant Clause, describes the process officials must undertake before issuing a warrant. They must have "probable cause," it says, "supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized." Id.

II.

The plaintiffs allege that court clerks in Mahoning County issued arrest warrants that violate the Warrant Clause. To satisfy this clause's requirements, a neutral and detached magistrate must independently determine that probable cause exists after weighing the evidence supplied by the police. See Whiteley v. Warden, 401 U.S. 560, 564, 91 S.Ct. 1031, 28 L.Ed.2d 306 (1971); Giordenello v. United States, 357 U.S. 480, 487, 78 S.Ct. 1245, 2 L.Ed.2d 1503 (1958). The sole "evidence" that the clerks received in their cases, say the plaintiffs, came from police officers' "conclusory complaints," which "consist[ed] only of the officer[s'] [bare] conclusion[s] that the accused committed the offense[s]." R. 139 at 5. To make matters worse, the plaintiffs add, these clerks lack the constitutional power to issue warrants. Yet the clerks continue to issue these kinds of warrants, "rubber stamp[ing]" the police's conclusions and violating the Fourth Amendment along the way — a way allegedly littered with 6,747 defective arrest warrants per year in the county. Id. at 16.

The plaintiffs have a point. Although they are wrong about the power of county court clerks, who may issue arrest warrants, see Shadwick v. City of Tampa, 407 U.S. 345, 350-51, 92 S.Ct. 2119, 32 L.Ed.2d 783 (1972), they are right about the arrest warrants in the record, which appear to have been issued without any independent probable cause determination. Take the complaint used to obtain the warrant for one of the lead plaintiffs' arrests. "Shannon E. Graves," it says, "did knowingly aid or abet another in the sale of ... cocaine base ... in violation of Section 2925.03" of the Ohio Revised Code. R. 139-5 at 1. Based on that statement, and allegedly that statement alone, the clerk found that probable cause existed and issued an arrest warrant. The clerk heard none of the "operative fact[s]" in the case, Whiteley, 401 U.S. at 565, 91 S.Ct. 1031, and had no "foundation for [her probable cause] judgment," Jaben v. United States, 381 U.S. 214, 224, 85 S.Ct. 1365, 14 L.Ed.2d 345 (1965), yet issued a warrant all the same. That complaint is not unique. Many of the complaints in the record state only that "[the defendant] did [the elements of the crime]" "in violation of" some state law. E.g., R. 139-1 at 1. Such foundation-less conclusions do not provide "sufficient information to support an independent" probable cause judgment under the Warrant Clause, as the Supreme Court has held. Whiteley, 401 U.S. at 563-65, 91 S.Ct. 1031 (invalidating warrants based on materially identical complaints); e.g., Giordenello, 357 U.S. at 481, 78 S.Ct. 1245 (same); see Illinois v. Gates, 462 U.S. 213, 239, 103 S.Ct. 2317, 76 L.Ed.2d 527 (1983).

III.

But that does not mean the plaintiffs prevail. To establish a cognizable Fourth Amendment claim, the plaintiffs must show a violation not of the Warrant Clause but of the Reasonableness Clause. "[F]or § 1983 liability" in Fourth Amendment cases, "the seizure must be `unreasonable.'" Brower v. County of Inyo, 489 U.S. 593, 599, 109 S.Ct. 1378, 103 L.Ed.2d 628 (1989); see, e.g., Robertson v. Lucas, 753 F.3d 606, 618 (6th Cir.2014). And violating the Warrant Clause does "not invariably violate the Reasonableness Clause." Baranski v. Fifteen Unknown Agents of Bureau of Alcohol, Tobacco & Firearms, 452 F.3d 433, 438 (6th Cir.2006) (en banc); see, e.g., Whiteley, 401 U.S. at 565-66, 91 S.Ct. 1031; cf. Virginia v. Moore, 553 U.S. 164, 169, 128 S.Ct. 1598, 170 L.Ed.2d 559 (2008). The plaintiffs may not prevail merely by showing that they were arrested with a defective warrant; they must show that they were unreasonably seized.

The Fourth Amendment prohibits "unreasonable searches and seizures," not warrantless ones. See Brigham City v. Stuart, 547 U.S. 398, 403, 126 S.Ct. 1943, 164 L.Ed.2d 650 (2006); Gramenos v. Jewel Cos., 797 F.2d 432, 440-42 (7th Cir. 1986). What is "unreasonable" varies from case to case, from type of seizure to type of seizure. "[N]either a warrant nor probable cause, nor, indeed, any measure of individualized suspicion, is an indispensable component of reasonableness in every circumstance." Nat'l Treasury Emps. Union v. Von Raab, 489 U.S. 656, 665, 109 S.Ct. 1384, 103 L.Ed.2d 685 (1989). No one thinks, for example, that the border patrol needs a warrant (or even individualized suspicion) to seize a person at the airport to check his eligibility to enter the country. Cf. United States v. Martinez-Fuerte, 428 U.S. 543, 566-67, 96 S.Ct. 3074, 49 L.Ed.2d 1116 (1976). It is only when the seizure at issue "requires a warrant" that "the failure to satisfy the Warrant Clause" creates a problem. Baranski, 452 F.3d at 445.

The seizure at issue in today's case — an arrest — does not require a warrant. Warrantless arrests were "taken for granted at the founding," Moore, 553 U.S. at 170, 128 S.Ct. 1598 (quotation omitted), and the passage of time has only deepened that understanding, see, e.g., id. at 171, 128 S.Ct. 1598. In case after case, courts ask not whether the police had a valid arrest warrant but whether the seizure was "reasonable." See, e.g., United States v. Watson, 423 U.S. 411, 414-24, 96 S.Ct. 820, 46 L.Ed.2d 598 (1976); Carroll v. United States, 267 U.S. 132, 155-56, 45 S.Ct. 280, 69 L.Ed. 543 (1925); Boykin v. Van Buren Township, 479 F.3d 444, 449-50 (6th Cir. 2007); Thacker v. City of Columbus, 328 F.3d 244, 251, 255-57 (6th Cir.2003).

That means arrests are "reasonable" when the officer had "probable cause to believe that a criminal offense has been or is being committed." Devenpeck v. Alford, 543 U.S. 146, 152, 125 S.Ct. 588, 160 L.Ed.2d 537 (2004); see Wayne R. LaFave, 3 Search & Seizure: A Treatise on the Fourth Amendment § 5.1(b) (5th ed. 2015). Yes, there are exceptions — say for arrests in a home. Payton v. New York, 445 U.S. 573, 589-601, 100 S.Ct. 1371, 63 L.Ed.2d 639 (1980). But no such exception applies here, leaving us with the general rule: "[E]ven [when] the arrest warrant is invalid," probable cause is "sufficient to justify arrest." United States v. Fachini, 466 F.2d 53, 57 (6th Cir.1972) (collecting cases); see, e.g., Whiteley, 401 U.S. at 565-66, 91 S.Ct. 1031; U.S. ex rel. Gockley v. Myers, 450 F.2d 232, 241 (3d Cir.1971).

The plaintiffs' complaint fails to account for this imperative. They never allege that they were arrested without probable cause. Without facts going to this "crucial question," Draper v. United States, 358 U.S. 307, 310, 79 S.Ct. 329, 3 L.Ed.2d 327 (1959), the plaintiffs cannot state a Fourth Amendment § 1983 claim against anyone, see Brower, 489 U.S. at 599-600, 109 S.Ct. 1378, the county and townships included, see Monell v. Dep't of Soc. Servs., 436 U.S. 658, 691, 694-95, 98 S.Ct. 2018, 56 L.Ed.2d 611 (1978), because they have not alleged a violation of their rights. The district court thus correctly dismissed this case at the Rule 12(b)(6) stage.

IV.

The plaintiffs respond that "Whiteley is clearly controlling on this point." Appellants' Br. 15 (quotation omitted). They are right — but for the wrong reason. Whiteley held, in the plaintiffs' favor, that an officer's conclusory complaint rendered the arrest warrant defective under the Fourth Amendment. 401 U.S. at 562-65, 91 S.Ct. 1031. But the Court did not stop there. It went on to determine that the arresting officer lacked "probable cause for arrest without a warrant." Id. at 566, 91 S.Ct. 1031. Only that ruling made the arrest unreasonable; a defective warrant alone was not enough. It is not enough here either.

The plaintiffs add that the district court should have allowed them leave to amend their complaint. But the district court did let them amend — four times. And each time, the plaintiffs wasted the opportunity. They repeatedly exceeded the "court's leave" to amend, Fed.R.Civ.P. 15(a)(2), by, for example, adding new claims, new plaintiffs, and scores of new defendants when the court's orders allowed only for clarification of the existing complaint. Each time the court struck the amended complaint. It did not abuse its discretion in doing so. See Foman v. Davis, 371 U.S. 178, 182, 83 S.Ct. 227, 9 L.Ed.2d 222 (1962); Evans v. Pearson Enters., Inc., 434 F.3d 839, 853 (6th Cir.2006). Most critically, through pages and pages of proffered additions, the plaintiffs "never alleged ... that they were arrested without probable cause." Graves v. Mahoning County, No. 4:10CV2821, 2015 WL 403156, at *6 n. 10 (N.D.Ohio Jan. 28, 2015). The Civil Rules do not displace the reasoned discretion — the judgment — of district courts to say enough is enough.

In the category of too little too late, the plaintiffs contend, in one paragraph in their appellate brief, that they "were arrested by police officers who lacked any probable cause to arrest [them] independent of the facially invalid arrest warrant." Appellants' Br. 19. But they conceded at oral argument that they did not make that allegation in the complaint, where it needs to be to get past a Rule 12(b)(6) motion. In the absence of allegations of "particular (and material) facts" establishing a claim, Omnicare, Inc. v. Laborers Dist. Council Constr. Indus. Pension Fund, ___ U.S. ___, 135 S.Ct. 1318, 1332, 191 L.Ed.2d 253 (2015), the plaintiffs have not stated a cognizable § 1983 claim.

All of this, we appreciate, may fail to come to grips with a lurking concern: If the police may arrest individuals without a valid warrant, why go through the trouble of obtaining one? A partial answer exists in the search context. A reviewing court is more likely to find a warrantless search unreasonable than a search with a warrant. See United States v. Ventresca, 380 U.S. 102, 106, 85 S.Ct. 741, 13 L.Ed.2d 684 (1965). And if it does, it may exclude the evidence found in that search — evidence often pivotal to securing a conviction. "[Z]ealous officers" looking to "ferret[] out crime," Johnson v. United States, 333 U.S. 10, 13-14, 68 S.Ct. 367, 92 L.Ed. 436 (1948), thus have an incentive to obtain a warrant: they want to use the evidence against the suspect. See Davis v. United States, 564 U.S. 229, 131 S.Ct. 2419, 2426-27, 180 L.Ed.2d 285 (2011).

But there is no equivalent to exclusion in the seizure context. You can't "exclude" an arrest, and courts don't release people just "because the officers failed to secure a warrant." Gerstein v. Pugh, 420 U.S. 103, 113, 95 S.Ct. 854, 43 L.Ed.2d 54 (1975). How, then, does a rule allowing arrests without a "seizure warrant" incentivize getting a warrant? We can think of at least four possibilities.

One is that police officers still have a law-enforcement explanation for obtaining a seizure warrant. As with searches, courts more often will deem seizures reasonable when they're associated with a warrant. Officers want their seizures to be reasonable not because they're worried about excluding the arrest, but because they're worried about excluding evidence discovered in a search incident to the arrest. These searches often turn up the most critical evidence in the case. See, e.g., Herring v. United States, 555 U.S. 135, 137, 145, 129 S.Ct. 695, 172 L.Ed.2d 496 (2009). But when courts hold that an arrest is invalid, that tree spoils its fruit; the invalid arrest often ruins the opportunity to use evidence discovered in a search incident to the arrest in a later prosecution. See Wong Sun v. United States, 371 U.S. 471, 484-88, 83 S.Ct. 407, 9 L.Ed.2d 441 (1963).

Another reason is that officers have a personal explanation for getting a warrant. Seizing individuals without probable cause (more likely to happen without a warrant than with one) may expose officers to personal risk. Section 1983 actions — like this one — not only expose them to money damages liability but also interfere with their work. Most police officers entered law enforcement with the goal of sending others, not themselves, to court.

Still another reason is that other laws may require officers to obtain a warrant. The Fourth Amendment, like other Bill of Rights provisions, sets a national floor. Federal, state, and local statutes, and state constitutions, may (and frequently do) establish protections beyond that floor. Ohio, to use one example, appears to impose a warrant requirement for misdemeanor arrests when the crime is not "committed in the officer's presence." State v. Henderson, 51 Ohio St.3d 54, 554 N.E.2d 104, 106 (1990); see Ohio Rev.Code § 2935.03; cf. Moore, 553 U.S. at 168-73, 128 S.Ct. 1598.

One more reason is that the Fourth Amendment requires a prompt judicial determination of probable cause (generally within 48 hours) after warrantless arrest. County of Riverside v. McLaughlin, 500 U.S. 44, 53-58, 111 S.Ct. 1661, 114 L.Ed.2d 49 (1991). An officer's choice, therefore, is not now or never; it is now or later. See Drogosch v. Metcalf, 557 F.3d 372, 378-79 (6th Cir.2009).

That is not a complete answer, to be sure. Even if obtaining arrest warrants frequently will be the best practice, that does not mean it will be the practice that happens. "[B]ut the Constitution does not require police to follow the best recommended practices," which leaves a gap "between the wise and the compulsory." Gramenos, 797 F.2d at 442. What matters for now is that the compulsory does not require a warrant for an arrest, however unwise the defendants' alleged practices may be.

That leaves one other point — also not made by the claimants — but worth mentioning. Many of the plaintiffs' arrests were for misdemeanors, most commonly for prostitution. See Ohio Rev.Code § 2907.25(A), (C)(1). These alleged misdemeanors, according to the complaint, were committed outside the presence of the arresting officers. And it's an open question at the Supreme Court, it turns out, "whether the Fourth Amendment" requires officers to get a warrant "for purposes of misdemeanor arrests" committed "[outside] the[ir] presence." Atwater v. City of Lago Vista, 532 U.S. 318, 340 n. 11, 121 S.Ct. 1536, 149 L.Ed.2d 549 (2001) (quotation omitted).

But it's not an open question at our court. The "requirement that a misdemeanor must have occurred in the officer's presence to justify a warrantless arrest," we have explained, "is not mandated by the Fourth Amendment." United States v. Smith, 73 F.3d 1414, 1416 (6th Cir.1996). In applying this rule, we have rejected § 1983 claims under the Fourth Amendment for these kinds of warrantless arrests (though without explanation). See, e.g., Pyles v. Raisor, 60 F.3d 1211, 1215 (6th Cir.1995); see also, e.g., Boykin, 479 F.3d at 449-50; Thacker, 328 F.3d at 256-57; Collins v. Nagle, 892 F.2d 489, 494-95 (6th Cir.1989). This may be why the plaintiffs don't mention the issue in their appellate brief or for that matter distinguish the rules for misdemeanor and felony arrests.

Other circuits agree with our approach. See, e.g., Budnick v. Barnstable Cty. Bar Advocates, Inc., 989 F.2d 484, at *3 n. 7 (1st Cir.1993) (per curiam) (unpublished); Street v. Surdyka, 492 F.2d 368, 372 (4th Cir.1974); Fields v. City of South Houston, 922 F.2d 1183, 1189 (5th Cir.1991); Woods v. City of Chicago, 234 F.3d 979, 992-95 (7th Cir.2000); Barry v. Fowler, 902 F.2d 770, 772 (9th Cir.1990); see also, e.g., Vargas-Badillo v. Diaz-Torres, 114 F.3d 3, 5-6 (1st Cir.1997); Veatch v. Bartels Lutheran Home, 627 F.3d 1254, 1258-59 (8th Cir.2010); Knight v. Jacobson, 300 F.3d 1272, 1276 n. 3 (11th Cir.2002). Some state courts also agree. See, e.g., State v. Harker, 240 P.3d 780, 786-87 (Utah 2010). The government has agreed in at least one case. See, e.g., United States Br. 12, United States v. Horne, 339 Fed.Appx. 343 (4th Cir.2009) (No. 08-4844), 2008 WL 5069739. So have commentators. See, e.g., LaFave, supra, § 5.1(c); cf. Thomas Y. Davies, Recovering the Original Fourth Amendment, 98 Mich. L. Rev. 547, 551 (1999). And so have several past Justices. Welsh v. Wisconsin, 466 U.S. 740, 756, 104 S.Ct. 2091, 80 L.Ed.2d 732 (1984) (White, J., dissenting, joined by Rehnquist, J.); cf. Watson, 423 U.S. at 429, 96 S.Ct. 820 (Powell, J., concurring).

All the while, though, no court has devoted much more than a line or two to this issue.

There are, to be sure, some sound reasons for our court's position, as all of this company suggests. The Supreme Court has rejected a similar rule — that constables could constitutionally arrest without a warrant only for breaches of the peace. Atwater, 532 U.S. at 344-45, 121 S.Ct. 1536. In rejecting this rule, the Court noted that common law sources "reached divergent conclusions with respect to officers' warrantless misdemeanor arrest power." Id. at 328, 121 S.Ct. 1536. At least some of those sources spoke of "[t]he constable[`s]... great original and inherent authority with regard to arrests," 4 William Blackstone, Commentaries *289, which allowed them to arrest without a warrant for "some misdemeanors" committed outside their presence, including for some sexual crimes, see 2 Matthew Hale, Pleas of the Crown 88-89 (1736); accord 2 William Hawkins & John Curwood, Treatise of Pleas of the Crown 120-22, 132 (8th ed.1824). Some antebellum colonial and state laws allowed warrantless arrests for these kinds of misdemeanors. See, e.g., Digest of the Laws of New Jersey 1709-1838, at 585-86 (Lucius Q.C. Elmer ed. 1838) (1799 Act) ("It shall be the duty of every constable, and lawful for any other person, to apprehend, without warrant or process, any [`common prostitute[]']."); Colonial Laws of Massachusetts 139 (1889) (1646 Act) (similar); see also Atwater, 532 U.S. at 336-38, 121 S.Ct. 1536 (collecting materials). Modern laws more and more do the same thing. See id. at 355-60, 121 S.Ct. 1536 (collecting statutes); William A. Schroeder, Warrantless Misdemeanor Arrests and the Fourth Amendment, 58 Mo. L. Rev. 771, 776-86 & nn. 7-22 (1993) (same). And the common law felony/misdemeanor distinction has been called "arbitrary" and "highly technical." Tennessee v. Garner, 471 U.S. 1, 14, 20, 105 S.Ct. 1694, 85 L.Ed.2d 1 (1985).

But there are valid competing arguments that deserve to be addressed at some point. The common law, most sources say, prohibited an officer from "mak[ing] a [warrantless] arrest for a misdemeanor [unless] the crime was committed in his presence." Gramenos, 797 F.2d at 441. The Supreme Court has called this the "usual" common law rule, Carroll, 267 U.S. at 156-57, 45 S.Ct. 280; see Kurtz v. Moffitt, 115 U.S. 487, 498-99, 6 S.Ct. 148, 29 L.Ed. 458 (1885), and other sources have said the same thing, see, e.g., American Law Institute, Code of Criminal Procedure, Commentary to § 21, at 231-38 (1930) (collecting sources).

What was reasonable at common law often tells us what is reasonable under the Fourth Amendment. It "sheds light on the obviously relevant, if not entirely dispositive," meaning of "reasonable." Payton, 445 U.S. at 591, 100 S.Ct. 1371 (footnote omitted); see, e.g., Moore, 553 U.S. at 168-69, 128 S.Ct. 1598; Wilson v. Arkansas, 514 U.S. 927, 931, 115 S.Ct. 1914, 131 L.Ed.2d 976 (1995); California v. Hodari D., 499 U.S. 621, 624, 111 S.Ct. 1547, 113 L.Ed.2d 690 (1991). The reason the Court attempts to "unearth[] the Amendment's original meaning" by examining the common law, Atwater, 532 U.S. at 326, 339, 121 S.Ct. 1536, may well be because, as Justice Story put it, the Fourth Amendment does "little more than... affirm[] [the] great constitutional doctrine of the common law," 3 Commentaries on the Constitution of the United States 748 (1833).

Some state courts, following this logic, have constitutionalized the common law rule. They have held that statutes that "authorize[] an arrest, without a warrant, for a misdemeanor not committed in the presence of the officer making the arrest" are unconstitutional, Polk v. State, 167 Miss. 506, 142 So. 480, 481 (1932) — either under the Fourth Amendment, its State's equivalent, or both, see, e.g., Ex parte Rhodes, 202 Ala. 68, 79 So. 462, 464-67 (1918); In re Kellam, 55 Kan. 700, 41 P. 960, 961 (1895); see also Gunderson v. Struebing, 125 Wis. 173, 104 N.W. 149, 151 (1905); Robison v. Miner, 68 Mich. 549, 37 N.W. 21, 25 (1888), overruled by Burroughs v. Eastman, 101 Mich. 419, 59 N.W. 817, 819 (1894). Some commentators have urged modern courts to do the same. See, e.g., Schroeder, supra, 58 Mo. L. Rev. at 777, 853.

With sound arguments on each side, it's no wonder that the Court has left the question open, even while deciding related questions about warrantless arrests. See, e.g., Moore, 553 U.S. at 168-73, 128 S.Ct. 1598; Atwater, 532 U.S. at 341 n. 11, 121 S.Ct. 1536; Watson, 423 U.S. at 414-24, 96 S.Ct. 820. And it's no wonder that some judges have flagged the issue. See, e.g., Veatch, 627 F.3d at 1258-59 (Colloton, J.); Gramenos, 797 F.2d at 441 (Easterbrook, J.). Today, however, is not the day to address it.

For these reasons, we affirm.