This is the second appeal from the dismissal of a federal civil rights suit. 42 U.S.C. § 1983. The district court initially dismissed it under Rule 25(a)(1) of the Federal Rules of Civil Procedure, on the ground that the motion to substitute the plaintiffs widow for the (original) plaintiff, who died while the suit was pending, was untimely. We reversed, 547 F.3d 869 (7th Cir.2008), instructing the district judge to allow the substitution. That kept the case alive, but the judge has again dismissed it, this time on the merits — he ruled that the complaint failed to state a claim. Hence this second appeal.
In October 2003 Chicago police stopped a car in which William O. Atkins, the plaintiffs decedent, was a passenger, and arrested him on the strength of a parole-violation warrant bearing the name ‘William Atkins.” He was held at the police station overnight and then transferred to the custody of the Illinois Department of Corrections, which placed him in Stateville prison. From the moment of his arrest he steadfastly denied that he was the William Atkins named in the warrant, but alternatively and inconsistently claimed that he was indeed the same Atkins but that his parole had expired, so that he could not have violated it — which seems in fact to be the case.
Released from the Department’s custody after 37 days, when the parole board acknowledged that he was being detained in error, Atkins sued the arresting officers, who are employees of the City of Chicago, plus the City itself, prison guards at State-ville, and other employees of the Department of Corrections. The state defendants are accused of having unjustifiably protracted a mistaken detention and imposed impermissible hardships during it, all in violation of rights conferred by the due process clause of the Fourteenth Amendment. The charge against the City defendants is that the arrest was unconstitutional because it was not based on probable cause; and we’ll start there.
When arrested, Atkins denied that he was the William Atkins named in the warrant and noted discrepancies between his identifying characteristics and the description in the warrant. Although both Atkinses were of the same race and sex and had the same first and last names, our William Atkins was slightly taller and somewhat heavier than the person described in the warrant and had a middle initial, which the name on the warrant lacked. But oddly — if they were different people — -the month and day of their birth (though not the year) were the same and the first three digits of their social security numbers were also the same.
The police did not have probable cause to stop the vehicle in which our William Atkins was riding, but clearly if he was the William Atkins named in the warrant the illegality of the stop did not invalidate the arrest. United States v. Johnson, 383 F.3d 538, 544-45 (7th Cir.2004); United States v. Green, 111 F.3d 515, 521 (7th Cir.1997); contra, United States v. Lopez, 443 F.3d 1280, 1285-86 (10th Cir.2006). In Green we said the question was whether “the causal chain has been sufficiently attenuated to dissipate the taint of the illegal conduct,” 111 F.3d at 521, and in like vein in Johnson we considered whether “a lawful arrest based on any outstanding warrant for a passenger in the vehicle constituted an intervening circumstance that dissipated any taint caused by an initial traffic stop that had lacked reasonable suspicion,” 383 F.3d at 544, and concluded that it did. But a simpler way to justify the result in those cases (and this one), without talking about “taints” and “dissipation” and “intervening circumstances” (and what do those terms mean, *827really?), is to note simply that the arrest was based on a valid warrant rather than on anything turned up in the illegal search. If police stopped cars randomly, looking for persons against whom there were outstanding warrants, the drivers and passengers not named in warrants would have good Fourth Amendment claims. But a person named in a valid warrant has no right to be at large, and so suffers no infringement of his rights when he is apprehended unless some other right of his is infringed, as would be the case had the police roughed up Atkins gratuitously in the course of trying to determine whether he was the person named in the warrant. Graham v. Connor, 490 U.S. 386, 396-97, 109 S.Ct. 1865, 104 L.Ed.2d 443 (1989); Catlin v. City of Wheaton, 574 F.3d 361, 366 (7th Cir.2009); Cortez v. McCauley, 478 F.3d 1108, 1127 (10th Cir.2007) (en banc). But that is not the plaintiffs complaint.
Yet in the course of making an arrest on the basis of an outstanding warrant the police may learn something that shows that the warrant does not actually create probable cause to arrest the person they’re arresting — suppose the warrant in this case had identified the person to be arrested as a woman, named Wanda Atkinson. The police would know at a glance that the William Atkins they were about to arrest was not the person named in the warrant and if they arrested him anyway it would be an illegal arrest because the mistake would not be “understandable” or “the arrest a reasonable response to the situation facing them at the time.” Hill v. California, 401 U.S. 797, 804, 91 S.Ct. 1106, 28 L.Ed.2d 484 (1971). As nearly as we can determine, the police who made the arrest made no mistake, as distinct from whoever failed to notice that Atkins’s parole had expired before his alleged violation of it. And if the police did make a mistake, it was a reasonable one.
Anyway the plaintiff’s real complaint is not about the initial error but about the time it took to correct it — the state defendants are thus the main target. Atkins was transferred from the Cook County jail to Stateville within a day of his arrest, but it was another 36 days before the prison released him, having finally satisfied itself that he was not a parole violator. The complaint alleges that he protested continuously against his detention.
Due process requires government to follow reasonable procedures for minimizing mistaken deprivations of liberty. In determining what is reasonable “the court must consider the weight of the interest at stake, the risk of error, and the costs of additional process.” Hernandez v. Sheahan, 455 F.3d 772, 777 (7th Cir.2006); see Mathews v. Eldridge, 424 U.S. 319, 334-35, 96 S.Ct. 893, 47 L.Ed.2d 18 (1976); cf. Sutton v. City of Milwaukee, 672 F.2d 644, 645-47 (7th Cir.1982). The interest in liberty increases in weight the longer a person is detained, and the accuracy of the procedures for avoiding mistaken detentions that is constitutionally required increases concomitantly. In the case of persons arrested for violating parole, a preliminary hearing to determine probable cause must be conducted “as promptly as convenient after arrest while information is fresh and sources are available,” and a plenary hearing must be held within a “reasonable time after the parolee is taken into custody” — normally two months. Morrissey v. Brewer, 408 U.S. 471, 484-88, 92 S.Ct. 2593, 33 L.Ed.2d 484 (1972). Parole proceedings are traditionally administrative rather than judicial, so the hearing need not be held before a judicial officer. Id. at 486, 92 S.Ct. 2593. Illinois’s procedures, codified at 20 111. Admin. Code § 1610.140, comply with the standard set forth in the Morrissey case. *828Faheem-El v. Klincar, 841 F.2d 712, 722-23 (7th Cir.1988) (en banc).
Atkins had a preliminary hearing on the seventh day after his arrest but failed to persuade the hearing officer that it was a case of misidentification. He muddied the waters by arguing that he should be released because his parole had expired. Probably it had expired, but to offer contradictory grounds was bound to arouse the hearing officer’s suspicion. Alternative pleading is permissible but a person who says both that I am not the X named in the parole-violation warrant and I am that X but my parole expired is calling himself a liar. The hearing officer’s failure to find misidentification thus was reasonable.
The full hearing took place 29 days later, and Atkins was released on that day. The delay was well within the two-month deadline set by the Brewer case. The plaintiff contends that guards and miscellaneous prison staff have a continuing constitutional duty, even when there are constitutionally adequate formal administrative remedies against unjustified imprisonment, to conduct an exhaustive investigation of a prisoner’s claim of misidentification. Prisons would be unmanageable if the contention were accepted. “Given the requirements that arrest be made only on probable cause and that one detained be accorded a speedy trial, we do not think a sheriff executing an arrest warrant is required by the Constitution to investigate independently every claim of innocence, whether the claim is based on mistaken identity or a defense such as lack of requisite intent. Nor is the official charged with maintaining custody of the accused named in the warrant required by the Constitution to perform an error-free investigation of such a claim. The ultimate determination of such claims of innocence is placed in the hands of the judge and the jury.” Baker v. McCollan, 443 U.S. 137, 145-46, 99 S.Ct. 2689, 61 L.Ed.2d 433 (1979). We have rejected a rule “under which every deputy [sheriff] must be open to persuasion for as long as a person is in custody.” Hernandez v. Sheahan, supra, 455 F.3d at 777. Such a rule “would create a substantial possibility that by presenting his contention over and over even a guilty suspect would eventually find a deputy who did not understand the weight of the evidence and let him go. That would frustrate the public interest in carrying out the criminal law.” Id.; see also Askew v. City of Chicago, 440 F.3d 894, 895 (7th Cir.2006); Pasiewicz v. Lake County Forest Preserve District, 270 F.3d 520, 524 (7th Cir.2001).
One could argue for drawing a distinction between a person arrested for a parole violation who denies he violated his parole and a person arrested for a parole violation who denies that he is the person named in the arrest warrant. The fact that parole violations are adjudicated administratively is one of the terms of parole, and by accepting parole a prisoner accepts the procedures, held constitutional by the Supreme Court, for adjudicating parole violations. “Revocation deprives an individual, not of the absolute liberty to which every citizen is entitled, but only of the conditional liberty properly dependent on observance of special parole restrictions.” Morrissey v. Brewer, supra, 408 U.S. at 480, 92 S.Ct. 2593. But a person arrested for a parole violation who had not actually been named in the arrest warrant — who might never have been convicted of a crime, and therefore never have been paroled, in his life — is not someone who accepted administrative adjudication as the price of parole. He could therefore argue for the same right as a person arrested on other grounds — the right to a judicial (not administrative) determination of probable *829cause to hold him, conducted within two days (not seven days) of the arrest, as required by County of Riverside v. McLaughlin, 500 U.S. 44, 56-57, 111 S.Ct. 1661, 114 L.Ed.2d 49 (1991), and Gerstein v. Pugh, 420 U.S. 103, 125, 95 S.Ct. 854, 43 L.Ed.2d 54 (1975); cf. Hernandez v. Sheahan, supra, 455 F.3d at 777; Patton v. Przybylski, 822 F.2d 697, 700-01 (7th Cir.1987); Brown v. Patterson, 823 F.2d 167, 169 (7th Cir.1987); Fed.R.Crim.P. 32.1(a)(1). The argument could be bolstered by noting that Illinois law allows parole-violation warrants to be issued by parole officials, without any involvement of a judicial officer. 730 ILCS 5/3 — 14—2(c), - 2(c-l); People ex rel. Johnson v. Pate, 47 Ill.2d 172, 265 N.E.2d 144, 146 (1970); People ex rel. Jefferson v. Brantley, 44 Ill.2d 31, 253 N.E.2d 378, 379 (1969).
Against this it can be argued that to entitle a person who is arrested for violating parole and claims mistaken identity to a judicial hearing would give every such arrestee a right to two hearings: a judicial hearing to verify his identity (for he could always deny that he was the person named in the warrant, though he would risk punishment for perjury if were lying) and, if his claim of mistaken identity was rejected, an administrative hearing to determine whether he had in fact violated his parole.
But before a new constitutional right is declared, it would be prudent to inquire into the relative merits of judicial and administrative determinations of identities of alleged parole violators. We shouldn’t disparage factfinding by nonjudicial hearing officers; much factfinding is delegated to them, on the theory that specialization in adjudicating a particular type of legal dispute may offset any disadvantages flowing from the lesser independence of such officers. And it is not always lesser: Illinois judges, unlike the parole board’s hearing officers, are elected. Nor are issues of mistaken identity fraught with legal subtleties that only judges can plumb. It is far from clear, therefore, that there would be a gain in accuracy from requiring a judicial hearing on top of the administrative hearing that is already required, let alone a gain great enough to outweigh the administrative burden that such a requirement would place on the state — a state that happens to be on the brink of bankruptcy, if not over the brink.
In any event, there is no need to decide in this case whether there might be a constitutional entitlement to a judicial hearing in eases of alleged mistaken identity of parole violators. For even if the question were answered in the plaintiffs favor, it would not warrant any relief. The question is novel, and the defendants therefore protected from liability for damages for possibly answering it incorrectly by the doctrine of qualified immunity. Narducci v. Moore, 572 F.3d 313, 318 (7th Cir.2009); see Pearson v. Callahan, 555 U.S. 223, 129 S.Ct. 808, 818-22, 172 L.Ed.2d 565 (2009).
We are left with the claim that Atkins was so badly mistreated at State-ville that he was deprived of liberty without due process of law.
The complaint alleges that when he arrived at Stateville he was wearing a diamond stud in one of his ears. He swallowed it “to prevent the defendants from stealing his property.” He was then “placed in a cell naked without a mattress, sheets, blankets, or water until [he] defecated his earring.” We haven’t been told why the prison wanted the earring, but probably prisoners are forbidden to wear jewelry, as it would invite theft and brawls, and jewelry often has sharp edges or a sharp pin and so can be used as a weapon. Rowland v. Jones, 452 F.2d 1005, 1006 (8th Cir.1971) (per curiam). The complaint does not question the propriety of the *830defendants’ insistence on recovering the earring, only the indignities allegedly inflicted on Atkins in the four days that he spent in a “dry cell” before the earring emerged.
The most serious indignities alleged— the only ones that might support a claim of constitutional magnitude — are that he was “denied drinking water and/or food for several days.” Depriving a person of food for four days would impose a constitutionally significant hardship, Reed v. McBride, 178 F.3d 849, 853-54 (7th Cir.1999); Foster v. Runnels, 554 F.3d 807, 814-15 and n. 5 (9th Cir.2009); Simmons v. Cook, 154 F.3d 805, 808 (8th Cir.1998); depriving him of all liquids for four days would be far worse. “A human can be expected to survive for weeks without food, but a thirsty person deprived of water would last [only] a matter of days.” Jessica Hamzelou, “Nil By Mouth,” New Scientist, Apr. 16, 2010, p. 37; see also Survival Topics, “How Long Can You Survive Without Water?” www.survivaltopics.com/survival/howlong-can-you-survive-without-water/ (visited Jan. 19, 2011).
Although “several days” could as a semantic matter be more than four, the allegation that Atkins was “placed in a cell naked without a mattress, sheets, blankets, or water until [he] defecated his earring” (emphasis added) implies that these deprivations would end when the earring finally emerged, and that, the complaint alleges, was on the fourth day. The complaint also alleges that Atkins “agreed to drink milk to cause the defecation, though he was lactose intolerant,” so he was not denied liquids for four days; his complaint contains an internal contradiction. If he defecated on the fourth day, he must have drunk milk earlier that day, or on a previous day.
The allegation that he was deprived of food and water for several days is not inconceivable, which is the traditional standard for rejecting factual allegations in a complaint out of hand and dismissing the suit, as illustrated by Best v. Kelly, 39 F.3d 328, 330 n. 3 (D.C.Cir.1994), which approved the dismissal of a claim that a “Branch of the Government, took my Face off of my Head, went into my Scull & Put a Computer Chip of some kind & a Camera System which makes me Project Images or Pitchers, many Feet in Front of me.” And in Lee v. Clinton, 209 F.3d 1025, 1025 (7th Cir.2000), we upheld the dismissal of “two insane complaints charging the United States and China with a conspiracy to ‘bio-chemieally and biotechnologically infect and invade’ various people including Lee with a mind reading and mental torture device that Lee calls ‘Mind Accessing and Torturing via Remote Energy Transferring (MATRET).’ To elude MATRET, Lee claims to have developed a variety of space technologies, oddly including an email system and nanny services, that will enable the victims of MATRET to relocate to MATRET-free planets.” The claims described in Best and Lee fall into the category of the “essentially fictitious,” a category of claims that does not engage the jurisdiction of the federal courts. Bailey v. Patterson, 369 U.S. 31, 33, 82 S.Ct. 549, 7 L.Ed.2d 512 (1962); see Hagans v. Lavine, 415 U.S. 528, 536-37, 94 S.Ct. 1372, 39 L.Ed.2d 577 (1974). It would be strange to think that such eases could not be dismissed without putting the parties to the burden of further pleading, of discovery, and perhaps even of trial (though such trials would be fun).
The allegation about Atkins’s being deprived of food and water for four days is not in that class. It is not impossible; it is merely implausible. But it is highly implausible. Remember that the indignities to which the prison guards allegedly subjected Atkins are said to have been inci*831dental to their desire to recover his earring. Deprivation of food and liquids would retard rather than accelerate the fulfillment of that desire. And we know that he was not denied all liquids, which is the pertinent category (not water), because the complaint alleges that he drank milk. In addition there is no allegation that he incurred any physical injury from the alleged deprivations.
All three amended complaints imply, fantastically, that Atkins was forced to remain naked for the entire 37 days of his incarceration, for they state that the defendants violated his civil rights by “forcing him to remain naked in a cell” (emphasis added). But even if all that is meant is that he was intermittently forced to remain naked, this is hard to believe. Nor is the nakedness alleged merely incidental to the conducting of frequent strip searches, for that is a separate allegation, and the allegation that he was forced to remain naked is bracketed with an allegation that the defendants “den[ied] him clothes.”
There is also a curious evolution of allegations in successive iterations of the complaint. The initial complaint, though it alleged that Atkins had been denied drinking water until he defecated his earring, did not mention any deprivation of food but instead alleged that “for the first couple of days at Statesville [sic ], [he] did not eat because the defendants wrongfully desired to obtain [his] earring.” This suggests that any deprivation of food was short-lived and self-inflicted.
The four successive complaints are riddled with contradictions. And they are not pro se complaints. They were drafted by the plaintiffs lawyer. We have noted that the original complaint didn’t mention deprivation of food by the prison as distinct from Atkins’s refusing to eat for two days. The first amended complaint dropped all reference to deprivation of food or drink, while the second amended complaint restored the claim that Atkins had been “denied drinking water” but said nothing about food. Not until the third amended complaint do we read that Atkins was denied “food and/or water,” which still leaves unclear whether it was one or both. And the response to the defendants’ motion to dismiss that complaint muddied the waters further by stating that the defendants had “deprived him of water and/or food for several days and [made] him drink milk.” Milk is not water, but it is a substitute for water. The plaintiffs final submission to the district court listed all the ways in which the “defendants forced [Atkins] to endure unconstitutional mistreatment” but did not include in the list deprivation of food or water.
Bell Atlantic Corp. v. Twombly, 550 U.S. 544, 127 S.Ct. 1955, 167 L.Ed.2d 929 (2007), and Ashcroft v. Iqbal, — U.S. -, 129 S.Ct. 1937, 173 L.Ed.2d 868 (2009), require that a complaint be dismissed if the allegations do not state a plausible claim. The Court explained in Iqbal that “the plausibility standard is not akin to a ‘probability requirement,’ but it asks for more than a sheer possibility that a defendant has acted unlawfully.” Id. at 1949. This is a little unclear because plausibility, probability, and possibility overlap. Probability runs the gamut from a zero likelihood to a certainty. What is impossible has a zero likelihood of occurring and what is plausible has a moderately high likelihood of occurring. But one sees more or less what the Court was driving at: the fact that the allegations undergirding a plaintiffs claim could be true is no longer enough to save it. Twombly and Iqbal do not reject the principle that when a complaint is dismissed for failure to state a claim the reviewing court is to assume that the factual allegations made in the complaint (unless fantastic, or contradicted in *832the complaint itself or in documents attached to it) are true. But the complaint taken as a whole must establish a nonnegligible probability that the claim is valid, though it need not be so great a probability as such terms as “preponderance of the evidence” connote. Iqbal like this was a case in which the defendants were public officers entitled to immunity from damages liability if they were acting in good faith. The earlier a case is dismissed, the more meaningful the immunity.
When the Court said in Iqbal “we do not reject these bald allegations on the ground that they are unrealistic or nonsensical,” id. at 1951, it didn’t mean that nonsensical allegations can survive a motion to dismiss; that wasn’t the rule even before Twombly and Iqbal. The point was rather that the allegations in Iqbal, though somewhat paranoid, were not nonsensical; nevertheless the Court ordered dismissal.
After Twombly and Iqbal a plaintiff to survive dismissal “must plead some facts that suggest a right to relief that is beyond the ‘speculative level.’ ” In re marchFIRST Inc., 589 F.3d 901, 905 (7th Cir.2009). And (another rule that antedates Twombly and Iqbal) he can plead himself out of court by pleading facts that show that he has no legal claim. Hecker v. Deere & Co., 556 F.3d 575, 588 (7th Cir.2009); Tamayo v. Blagojevich, 526 F.3d 1074, 1086 (7th Cir.2008); EEOC v. Concentra Health Services, Inc., 496 F.3d 773, 777 (7th Cir.2007); Orthmann v. Apple River Campground, 757 F.2d 909, 915 (7th Cir.1985); Trudeau v. FTC, 456 F.3d 178, 193 (D.C.Cir.2006). So suppose some of the plaintiffs factual allegations are unrealistic or nonsensical and others not, some contradict others, and some are “speculative” in the sense of implausible and ungrounded. The district court has to consider all these features of a complaint en route to deciding whether the complaint has enough substance to warrant putting the defendant to the expense of discovery, Bell Atlantic Corp. v. Twombly, supra, 550 U.S. at 558-59, 127 S.Ct. 1955; Francis v. Giacometti, 588 F.3d 186, 193 and n. 2 (4th Cir.2009), or, in a case such as this (like Iqbal itself), burdening a defense of immunity. Ashcroft v. Iqbal, supra, 129 S.Ct. at 1953-54; Smith v. Duffey, 576 F.3d 336, 339-40 (7th Cir.2009); Amore v. Novarro, 624 F.3d 522, 529-30 (2d Cir.2010); Fletcher v. Burkhalter, 605 F.3d 1091, 1095-96 (10th Cir.2010).
We are left in darkness as to whether the plaintiff is actually alleging that Atkins was denied food or water for four days, or for a lesser, but still constitutionally significant, length of time. The plaintiffs lawyer has had four bites at the apple. Enough is enough. United States ex rel. Garst v. Lockheed-Martin Corp., 328 F.3d 374, 378-79 (7th Cir.2003).
All this is apart from the futility of the suit. Atkins is the only witness for the plaintiff, and Atkins is dead. His widow would be happy to testify to what he told her had happened to him, but her testimony would be inadmissible hearsay. There is no other evidence to support the charge of unconstitutional conditions of confinement, and no suggestion that any defendants, or other members of the prison staff, are prepared to support the plaintiffs version of the facts — or, should we say, any of the plaintiffs versions.
The district court was correct to dismiss the suit.
Affirmed.