KEARSE, Circuit Judge:

Plaintiff John Kogut, convicted of rape and murder in 1986 but retried and acquitted of those charges in 2005, appeals from a final judgment entered in the United States District Court for the Eastern District of New York following a jury trial before Joanna Seybert, Judge, dismissing his claims brought pursuant to 42 U.S.C. § 1983 and state law against defendants County of Nassau (the "County") and individual employees or former employees of the Nassau County Police Department ("NCPD") for, inter alia, due process violations and malicious prosecution. Kogut's claims were tried jointly with the similar claims asserted in an action brought by John Restivo and Dennis Halstead, who also had been convicted in 1986 of rape and murder of the same victim and whose convictions had also eventually been vacated. At the joint trial here, the jury found in favor of the defendants. On appeal, Kogut contends principally that the district court erred (1) in denying his motion for a separate trial of his claims, at which certain evidence that was admitted at the joint trial would, he argues, have been inadmissible, and (2) in denying his motion for a new trial after unadmitted and inadmissible evidence was given to the jury at the joint trial. For the reasons that follow, we affirm.

I. BACKGROUND

On November 10, 1984, sixteen-year-old Theresa Fusco failed to return home after leaving work in Lynbrook, New York. Her body was found on December 5, 1984. An autopsy revealed that her death was caused by ligature strangulation; a vaginal swab produced seminal fluids.

A. The Criminal Prosecutions

During the investigation by Detective Joseph Volpe and other NCPD detectives, Kogut, Halstead, and Restivo allegedly made various incriminating statements. On March 5, 1985, NCPD brought Restivo to NCPD headquarters for questioning. On March 6, 1985, Restivo signed a two-page statement (the "Restivo Statement"), written out for him by Volpe, which stated in part as follows:

(Restivo Statement at 1.)

Two weeks later, Kogut was brought in for questioning. After being questioned, and denying knowledge about the crimes against Fusco, Kogut agreed to return on a later date to take a polygraph examination. Kogut took the polygraph exam on March 25; he was then interrogated by Volpe and defendant Detective Robert Dempsey throughout the night. On March 26, Kogut signed a detailed seven-page confession, written out for him by Volpe, in which he implicated himself as well as Halstead and Restivo in the crimes against Fusco (the "Kogut Confession" or "Confession"). Acknowledging at the outset that he had been informed of his rights to remain silent and to have an attorney present (see Kogut Confession at 1), Kogut stated, inter alia, that on a night in November 1984, he, Restivo, and Halstead had been driving along in Restivo's van; they saw "a girl," "about 15 or 16 years old," walking along the road by the cemetery and offered her a ride home, which she accepted (id. at 2, 3). After the girl declined an invitation to have sex, Restivo drove the van into the cemetery; Halstead raped the girl while Kogut held her down; then Restivo raped her. (See id. at 3-4.) Restivo and Halstead carried the then-unconscious girl out of the van; when she began to revive and started saying she would "tell," the men decided that she must die, and Kogut strangled her to death with a nylon rope. (Id. at 4-6.) Kogut took the girl's body back to the van and the men then drove from the cemetery to a wooded area, where they left the body in deep brush, covered with leaves and wooden pallets. (See id. at 6-7.)

A videotape was made, in which an Assistant District Attorney ("ADA") advised Kogut of his constitutional rights; Kogut acknowledged that he understood them; and he repeated the above story. Kogut was promptly arrested. He was indicted on three counts: first-degree rape, second-degree murder in the course of rape; and intentional second-degree murder. Following additional investigation, Restivo and Halstead were also arrested and were indicted on the same charges.

At Kogut's trial in 1986, the written and videotaped iterations of his Confession were admitted in evidence. The prosecution also introduced hairs of Fusco that were allegedly found in Restivo's van. Kogut denied any involvement in the crime; he testified that the Confession was the creation of Volpe and Dempsey and was coerced. Kogut was found guilty on all counts. He was sentenced to serve 37½ years to life in prison.

Thereafter, Halstead and Restivo were tried together. Neither the Kogut Confession nor the Restivo Statement to the police was admitted at their trial. The prosecution introduced the hair evidence and evidence as to statements allegedly made by Restivo or Halstead to third parties. The latter evidence included a statement by Halstead that Halstead, Restivo, and Kogut had raped Fusco; and statements by Restivo that Restivo, Halstead, and Kogut had raped Fusco, that Restivo knew who had killed Fusco, and — prior to the discovery of her body — that the police would find that Fusco had been strangled. Restivo and Halstead were convicted on all counts; each was sentenced to serve 33-1/3 years to life in prison.

B. Vacatur of the Convictions

Beginning in 1993, samples of semen that had been recovered from Fusco's body at autopsy were subjected to DNA testing, along with DNA samples taken, by consent, from Kogut, Restivo, and Halstead. Tests conducted in 1994 and 1995 excluded all three men as the source of male DNA found in the samples recovered from Fusco's body. Based on these results, Kogut, Restivo, and Halstead promptly moved to vacate their convictions, but their motions were denied. In 2001-2003, new DNA testing was done by three laboratories. These tests identified the same single, intact DNA profile of a male who was "unknown" — i.e., was not Kogut, Restivo, or Halstead, or anyone in law enforcement's Combined DNA Index System database — as the source of the semen recovered from Fusco's body. In the spring of 2003, the County agreed to have the convictions of all three men vacated. Halstead and Restivo were not retried, and the charges against them were ultimately dismissed. Kogut, "based on his written and video confession" (Kogut brief on appeal at 3), was retried. Following a bench trial in 2005, he was acquitted.

C. The Present Action

Kogut commenced the present action in December 2006 pursuant to 42 U.S.C. § 1983 against numerous defendants, including the detectives involved in the investigation, alleging, inter alia, malicious prosecution with respect to his prosecution in 1985-1986 and his retrial in 2005. Two days later, Restivo and Halstead (or "Restivo/Halstead") commenced a similar action pursuant to § 1983 against many of the same defendants, alleging, inter alia, malicious prosecution with respect to the events in 1985-1986.

Kogut's complaint asserted, in addition to malicious prosecution, numerous claims, including denial of due process, false arrest, and false imprisonment. It alleged that the Confession attributed to him was entirely fictitious; that he was coerced into signing the Confession after some 15 continuous hours of questioning, during which he was repeatedly abused, verbally and physically; and that he was coerced into repeating the fictitious account on videotape. (See, e.g., Kogut Complaint ¶¶ 56, 58, 63.) Kogut alleged, inter alia, that he in fact was not informed of his constitutional rights (see id. ¶ 51), although he repeatedly asserted those rights (see id. ¶ 58); that he persistently denied any involvement in or knowledge of the events involving Fusco (see id. ¶¶ 48, 53); that the facts set out in the Confession had been learned by Volpe and Dempsey during the course of their investigation, were not provided by Kogut, and were put in the Confession "to create the illusion that KOGUT had specific personal knowledge about the victim, her manner of death, and the location of the body, amongst other things" (id. ¶ 60); and that defendants had conspired and agreed to lie about the interrogation events, both before the grand jury and at Kogut's criminal trials (see id. ¶ 65).

The amended complaint filed by Restivo and Halstead ("Restivo/Halstead Complaint") similarly asserted claims alleging that they were deprived of their rights to due process and a fair trial and that defendants maliciously prosecuted them. It alleged, inter alia, that Restivo, when questioned in March 1985 by Volpe, Dempsey, and other members of NCPD, had truthfully and repeatedly denied knowing anything about the Fusco crimes. (See, e.g., Restivo/Halstead Complaint ¶¶ 52, 57.) It alleged that, some seven hours after bringing Restivo to NCPD headquarters against his will, and after subjecting him to questioning and a polygraph test (see, e.g., id. ¶¶ 51-58), defendants began to abuse Restivo, "choking and punching him" in order "to coerce" him "into making a false accusation against Mr. Halstead" (id. ¶ 59). Only then did Restivo "sign a written statement created by defendants falsely indicating that Mr. Halstead had told him that he raped a girl in, near, or across from a cemetery and then strangled and killed her." (Id. ¶ 60.) The Restivo/Halstead complaint alleged that "Restivo had no involvement in the Fusco rape and murder nor did he know anyone who did...." (Id. ¶ 61.)

1. Consolidation and the Motions for Separate Trials

In 2007, the district court granted a joint request by all parties to consolidate the Kogut and Restivo/Halstead cases for purposes of discovery. In March 2009, finding that the claims of Kogut and Restivo/Halstead involved common questions of law and fact, the court sua sponte consolidated the actions for all purposes.

In a Memorandum and Order dated August 3, 2009 ("Kogut I"), the district court dismissed some of plaintiffs' claims, including their claims for false arrest and false imprisonment. See Kogut I, at 27. The court also dismissed Restivo/Halstead's malicious prosecution claims and Kogut's 1985-1986 malicious prosecution claim, see id. at 17-18; but those claims were reinstated upon reconsideration, in a Memorandum and Order dated December 11, 2009 ("Kogut II"), at 14-16.

In the summer of 2012, Kogut and Restivo/Halstead filed motions requesting that their cases be tried separately. The motions argued that, pursuant to this Court's decision in Boyd v. City of New York, 336 F.3d 72 (2d Cir.2003) (or "Boyd"), the core question for the plaintiffs' respective claims of malicious prosecution was, as to each individual plaintiff, whether the defendants had probable cause to believe the prosecution of that individual could succeed based on the admissible evidence. Restivo/Halstead argued that the Kogut Confession could not be considered in the assessment of whether defendants had probable cause to prosecute Restivo or Halstead because it was inadmissible against them in their criminal proceedings, and that since the Confession would be admissible against Kogut, a joint trial would be highly prejudicial to Restivo and Halstead. Kogut, adopting the Restivo/Halstead legal arguments, argued that "[a]s is the case with the Kogut confession vis a vie [sic] Restivo/Halstead," various alleged statements that "will undoubtedly be used against Restivo/Halstead ... are likewise inadmissible against Kogut," and at a joint trial they would "potential[ly]... prejudice" Kogut. (Kogut's motion dated August 14, 2012, for a severance of his claims for trial, at 2.)

Kogut listed 10 statements attributed to Restivo or Halstead that Kogut viewed as excludable at a trial of his claims if not consolidated with trial of the claims of Restivo/Halstead. Of those statements, the following mentioned Kogut:

(Id. at 3 (emphases ours).)

At a status conference on August 16, 2012, the district court denied both Restivo/Halstead's and Kogut's motions for separate trials, ruling that the challenged statements would be admissible against each plaintiff for a limited purpose. (See Hearing Transcript, August 16, 2012 ("Kogut III"), at 7-10.) The court noted that

(Id. at 7.) It stated that although under Boyd the statements that were inadmissible at plaintiffs' underlying criminal proceedings were not admissible in this civil trial to show that defendants had probable cause to prosecute, they could nonetheless be admissible to negate another disputed element of the malicious prosecution claims, i.e., that defendants had prosecuted the plaintiffs with malice. (See id. at 5-7, 10-12.)

2. The Joint Trial

At the joint trial, the plaintiffs presented expert testimony to indicate that the hairs introduced at their criminal trials had not been found in Restivo's van but instead were taken from Fusco's body at autopsy (see Trial Transcript ("Tr.") 2093-106, 2209-28); and Kogut and Restivo testified, consistent with their respective complaints, that the incriminating statements they supposedly made to the police were false, were created by Volpe and Dempsey, and were the product of abuse and coercion (see id. at 1355-95, 1400-16, 3622-36). The Restivo Statement was introduced and was the subject of testimony from various witnesses. Other statements focusing on statements attributed to Restivo and Halstead were also introduced.

Of the 10 statements listed in Kogut's motion for a separate trial as likely to prejudice him unless his claims were tried separately, only the three described in Part I.C.1. above mentioned Kogut. Of those three, neither of the statements attributed to Restivo was introduced at the joint trial. The statement attributed to Halstead (i.e., his alleged statement to O'Hanlon that Halstead, Restivo, and Kogut raped Fusco (the "O'Hanlon-Halstead statement")) was the subject of testimony from three witnesses here: Restivo's criminal defense attorney who testified that O'Hanlon had testified to that statement at the Restivo/Halstead criminal trial, a former ADA who testified that O'Hanlon testified at that trial that Halstead said Kogut killed Fusco, and Halstead who testified at the joint trial here that he had made no such statement to O'Hanlon.

The jury was asked to decide the claims of Kogut, Restivo, and Halstead, individually, against each of six or seven specified individual defendants (a) for deprivations of plaintiffs' respective rights to due process and a fair trial "either by fabricating evidence or by withholding material exculpatory or impeachment evidence" (Verdict Sheet, November 29, 2012, Questions 1-3), and (b) for malicious prosecution (see id. Questions 4-7). It found in favor of each defendant in response to each of those questions. In addition, as to defendant Sean Spillane, who was head of NCPD's homicide bureau in 1985, the jury found that "while supervising Volpe, Dempsey and the other defendant police officers," Spillane "created a policy or custom under which unconstitutional practices occurred," but that a reasonable officer in Spillane's position as the Commanding Officer of the Homicide Bureau in 1985 would not have understood his conduct to be unconstitutional. (Id. Questions 8(b), (c).) And with regard to a state-law claim for negligent supervision, asserted by Kogut, the jury found that although the County was "responsible for the acts of defendant Spillane in failing to supervise," the failure to supervise did not "cause[] an injury to Plaintiff Kogut." (Id. Questions 9, 10.)

3. Plaintiffs' Motions for a New Trial

Both Kogut and Restivo/Halstead moved pursuant to Fed.R.Civ.P. 59(a) for a new trial. Kogut argued principally that there were procedural and evidentiary errors (see Part II.B. below), that the verdict was against the clear weight of the evidence, and that the denial of his pretrial motion for separate trials caused him prejudice because of the admission of evidence that would not have been admissible if his claims had been tried separately. In particular, he claimed to have been prejudiced by the introduction of character evidence as to Halstead's dating a teenage girl and contributing to the delinquency of teenage girls, and by testimony concerning statements about Fusco's murder allegedly made to third parties by Restivo. None of the alleged Restivo statements about Fusco mentioned or described Kogut, although one of the defendant detectives testified that Restivo, when questioned about the Fusco murder, said he was "fearful of those two guys," which the detective interpreted as "meaning Kogut and Halstead" (Tr. 5541).

The district court denied Kogut's motion for a new trial, see Kogut v. County of Nassau, Nos. 06-CV-6695, 06-CV-6720, 2013 WL 3820826, at *18 (E.D.N.Y. July 22, 2013) ("Kogut IV"), stating, inter alia, that it was not persuaded that any of the evidence Kogut cited was prejudicial to him or affected his substantial rights, see id. at *11.

The district court granted Restivo/Halstead's new-trial motion in part, finding, inter alia, that the jury charge on the probable cause element of Restivo and Halstead's malicious prosecution claims "may have misled the jury" as to the correct legal standard, i.e., may have led the jury to believe that it could consider the Kogut Confession in determining whether defendants had probable cause to prosecute Restivo or Halstead. Id. at *5. The court ordered that Kogut's case and Restivo/Halstead's case be unconsolidated, and it ordered that final judgment be entered terminating Kogut's case.

II. DISCUSSION

On appeal, Kogut contends principally that the evidence relating to statements attributed to Restivo or Halstead was not admissible against him at his criminal trials, and that the district court therefore erred (a) in denying his pretrial motion for separate trials and (b) in denying his posttrial Rule 59 motion for a new trial. (See Kogut brief on appeal at 31-43.) He also argues that he was entitled to a new trial because, inter alia, certain unadmitted evidence was inadvertently sent into the jury room, and he challenges certain of the court's instructions and evidentiary rulings. For the reasons that follow, the circumstances of which Kogut complains do not, either singly or in combination, warrant the conclusion that the district court erred or otherwise abused its discretion.

A. The Denial of Separate Trials

Both a decision by the district court to consolidate cases and a denial by the court of a motion for separate trials are reviewed under an abuse-of-discretion standard. See, e.g., Johnson v. Celotex Corp., 899 F.2d 1281, 1284-85 (2d Cir.) (consolidation), cert. denied, 498 U.S. 920, 111 S.Ct. 297, 112 L.Ed.2d 250 (1990); Alaniz v. Zamora-Quezada, 591 F.3d 761, 773 (5th Cir.2009) (separate trials); see generally Garber v. Randell, 477 F.2d 711, 714 (2d Cir.1973) (severance); 9A C. Wright & A. Miller, Federal Practice and Procedure § 2392, at 182-83 (3d ed.2008) (an order granting or denying separate trials is reviewed "under the well-established abuse of discretion standard"). "A district court has abused its discretion if it has (1) based its ruling on an erroneous view of the law, (2) made a clearly erroneous assessment of the evidence, or (3) rendered a decision that cannot be located within the range of permissible decisions." Manganiello v. City of New York, 612 F.3d 149, 165 (2d Cir.2010) (internal quotation marks omitted).

Kogut contends, in part, that the court's decision is entitled to no deference because "in denying his motion to sever, the court gave absolutely no consideration to his interests, whatsoever." (Kogut brief on appeal at 35; see id. at 34-36.) This contention borders on the frivolous.

The rulings denying Kogut's and Restivo/Halstead's motions for separate trials were announced at a status conference that began with the court noting the Restivo/Halstead motion, noting the motion by Kogut, and noting that there were aspects of the Restivo/Halstead motion with which Kogut disagreed. (See Kogut III, at 5.) Although in explaining its denial of the separate trial motions, the court expressly discussed only the extent to which the Kogut Confession would be admissible against Restivo and Halstead, the court's fundamental rationale — that a statement inadmissible at a criminal trial could nonetheless be admissible in an ensuing civil action asserting claims of malicious prosecution because of its relevance to the malice element of such a claim (see id. at 7-10) — was obviously applicable to Kogut's challenge to the admissibility against him of the statements of Restivo or Halstead listed in Kogut's motion. And its applicability was evidently understood by the attorneys representing Kogut at that conference; there was ample opportunity for them to speak up if they believed the court had not sufficiently considered Kogut's position. They made no such suggestion.

As a substantive matter, the district court's explanation no doubt focused more explicitly on the admissibility against Restivo and Halstead of the Kogut Confession because it posed a clearer danger of unfair prejudice to them than any of the statements described in Kogut's motion posed to Kogut. The Kogut Confession was the sole focus of the Restivo/Halstead separate-trial motion and was a written and videotaped confession to the authorities, recounting the rape and murder of Fusco by Kogut, Restivo, and Halstead in devastating detail. In addition, Restivo/Halstead had made a motion in limine to preclude introduction of the Kogut Confession as a defense to their malicious prosecution claims. Kogut's separate-trial motion, in contrast, did not involve any direct evidence such as a videotaped confession. Rather, Kogut's motion listed 10 statements that he anticipated would be offered against Restivo and Halstead; nine of them were statements attributed to Restivo or Halstead by persons other than the authorities, and the tenth — attributed to Restivo by the authorities — did not mention Kogut. Indeed, seven of the 10 statements anticipatorily challenged by Kogut did not mention him, either explicitly or implicitly; and Kogut had not made any in limine motion to preclude admission of any of the Restivo or Halstead statements against him. Kogut has not proffered any persuasive basis for a conclusion that in substance the denial of his separate-trial motion was an abuse of discretion.

Nor is there merit in Kogut's contention that the district court erred in denying his motion for a new trial on the ground that it should have granted separate trials. In making his motion for a new trial on this ground, Kogut principally incorporated by reference his pretrial motion for separate trials; he made no effort to focus his posttrial motion on the statements that were actually admitted at the joint trial. As it turned out, from the 10-item list set out in his pretrial motion, the only two Restivo statements that mentioned Kogut (allegedly made to Thomas McBride and Steven Dorfman, see Part I.C.1. above) — as well as several of the statements that did not mention Kogut — were not introduced. Only one of the statements that mentioned Kogut — the O'Hanlon-Halstead statement — was introduced at trial. But Kogut's motion for a new trial contained no discussion of the O'Hanlon-Halstead statement. He did argue that he was prejudiced by the introduction of various statements attributed to Restivo, only one of which had been listed in his pretrial severance motion (and none of which mentioned Kogut), and these arguments were addressed by the district court. Although Kogut's new-trial motion also stated that it incorporated the arguments he had made in his severance motion — in which the O'Hanlon-Halstead statement was one of the 10 listed — that pretrial motion had argued the "potential" for prejudice. Kogut's motion for a new trial made no argument that the evidence admitted with regard to the O'Hanlon-Halstead statement caused him actual prejudice.

As Kogut did not argue to the district court that he was entitled to a new trial because he was prejudiced by the admission of the evidence as to the O'Hanlon-Halstead statement, his present reliance on that evidence (see Kogut brief on appeal at 40-41) is reviewable only for plain error. A plain error is (1) an error (2) that is plain, (3) that prejudicially affected the defendant's "substantial rights" and (4) that "seriously affect[ed] the fairness, integrity or public reputation of judicial proceedings." United States v. Olano, 507 U.S. 725, 732, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993) (internal quotation marks omitted). Kogut cannot meet this standard.

Kogut's complaint about the evidence as to the O'Hanlon-Halstead statement does not satisfy even the first element of this test, for we cannot conclude that its admission was error. With regard to that statement — as with regard to evidence against Restivo or Halstead that did not mention Kogut — Kogut argues simply that the evidence "was admissible only as to Restivo and Halstead" and its admission prejudiced Kogut. (Kogut brief on appeal at 38; see, e.g., id. at 42-43.) But the basis for his premise that it was inadmissible against him in the present case is his argument, relying principally on Boyd v. City of New York, 336 F.3d 72 (see, e.g., Kogut brief on appeal at 47; reply brief on appeal at 14-15), that those statements were not admitted, and were inadmissible, at his criminal trial. He also argues that many of these alleged statements were irrelevant because they were made after Kogut was arrested. (See, e.g., Kogut brief on appeal at 5; id. at 47 (characterizing Boyd as "holding that a criminal defendant's statement, made after his arrest, cannot contribute to the probable cause determination" (emphasis in brief)); reply brief at 14.) Kogut's arguments misconstrue Boyd and ignore the basis for the district court's ruling on admissibility here.

Boyd was an appeal from the dismissal of a claim for malicious prosecution on a motion for summary judgment. See 336 F.3d at 75. Boyd had been prosecuted for possession of a stolen vehicle with knowledge that it was stolen; the police had probable cause to believe that Boyd knew it was stolen based only on a statement he made in response to their questioning. See id. at 74, 77. Although there was no dispute that the statement was made before Boyd was given Miranda warnings, Boyd claimed it was made after he was arrested, and the officers claimed it was made before he was arrested. See id. at 74. If made after his arrest, it was an un-Mirandized custodial statement that was inadmissible at his criminal trial. The statement was eventually suppressed on the ground that it was an un-Mirandized custodial statement; and as it was the only evidence the officers had as to Boyd's knowledge that the vehicle was stolen, the criminal charges against him were dismissed. See id. at 75, 77.

We reversed the grant of summary judgment dismissing Boyd's malicious prosecution claim, because the divergent versions of the sequence of events created a genuine issue of material fact for trial. We noted that the statement in question would have provided the officers with "the minimum requisite probable cause to believe that the prosecution could succeed. However, ... if the statement was made after Boyd's arrest, it would clearly not be admissible and then there would be no probable cause to believe the prosecution could succeed," because that statement was "the only evidence the police had that could reasonably indicate" that Boyd knew the vehicle was stolen. Id. at 77 (emphases added). Accordingly, the timing of Boyd's statement in relationship to the time of his arrest was crucial. There is no similarity between that case and this. Kogut's reliance on Boyd for the proposition that statements by Restivo or Halstead could not be considered because they were made after Kogut's arrest is misplaced.

We also do not interpret Boyd to mean that only evidence that was in fact admitted at the criminal trial may be considered in a subsequent civil trial on the issue of probable cause to prosecute. Prosecutors are not required to offer into evidence every shred of evidence they have as to guilt; and if they have sufficient admissible evidence, Boyd does not preclude the admission of additional evidence in the later civil suit.

In sum, the circumstances in Boyd — which concerned an un-Mirandized statement that was the only evidence the police had to support one of the elements of the offense with which Boyd was charged and which necessitated a focus on the relative timing of the statement and Boyd's arrest — bear no resemblance to the circumstances here. The challenged statements of Restivo and Halstead — although not admissible at Kogut's criminal trial — were obviously not the only evidence the defendants in this case had to prove Kogut's guilt. Kogut's Confession, both as written and as videotaped, was preceded by his acknowledgement that he had received Miranda warnings; Kogut does not contend that it was inadmissible at his criminal trial; and the jury was entitled to find that the Confession in and of itself gave the detectives ample probable cause to believe that the prosecution against him would succeed.

The district court denied Kogut's motion for a separate trial on the ground that the statements attributed to Restivo and Halstead were admissible not on the issue of whether the detectives had probable cause to prosecute Kogut but rather on the lack-of-malice element of Kogut's malicious prosecution claim. We do not see any indication in the record that Kogut argued to the district court that its ruling as to relevance was erroneous; nor would such an argument have been meritorious. "Evidence is relevant if ... it has any tendency to make a fact" that is "of consequence in determining the action" "more or less probable than it would be without the evidence." Fed.R.Evid. 401. In this Court, Kogut repeatedly argues that the statements attributed to Restivo or Halstead should have been excluded because, by mentioning "details" that were described in the Kogut Confession, those statements "corroborated" his Confession. (Kogut brief on appeal at 21; see, e.g., id. at 31, 42, 48, 58-59.) That argument proves too much: The detectives' receipt of corroboration for Kogut's Confession would increase the likelihood that their prosecution of Kogut was not motivated by a "`wrong or improper motive,'" i.e., "`something other than a desire to see the ends of justice served,'" Lowth v. Town of Cheektowaga, 82 F.3d 563, 573 (2d Cir.1996) (quoting Nardelli v. Stamberg, 44 N.Y.2d 500, 502-03, 406 N.Y.S.2d 443, 445, 377 N.E.2d 975 (1978)). Accordingly, the district court's ruling that corroborating statements were relevant to the malice element of Kogut's malicious prosecution claims was not error.

To the extent that Kogut contends that the statements should have been excluded in spite of their relevance because they were unduly prejudicial to him (see Kogut reply brief on appeal at 15), see generally Fed.R.Evid. 403, we are unpersuaded. Kogut's own Confession, detailed, written, and videotaped, made the general statements by other persons — only one of which even mentioned him — pale by comparison. We see no abuse of discretion in the district court's conclusion that the introduction of statements that were relevant on the issue of malice, and most of which did not explicitly or implicitly mention Kogut, did not unfairly prejudice him.

Finally, we note that in its jury charge, the district court did not pursue the nuanced treatment of the Restivo or Halstead statements that was reflected in its pretrial rulings, in that it did not state, with respect to Kogut's malicious prosecution claims, that the jury could consider the Restivo or Halstead statements only on the issue of malice rather than on the issue of probable cause to prosecute. However, "[a]t every stage of the proceeding, the court must disregard all errors and defects that do not affect any party's substantial rights," Fed.R.Civ.P. 61; a substantial right is implicated if there is a "likelihood that the error affected the outcome of the case," Tesser v. Board of Education, 370 F.3d 314, 319 (2d Cir.2004) (internal quotation marks omitted). Here, given that, on the probable cause issue, the jury had before it the detailed self-incriminating Kogut Confession in writing and on videotape, we cannot conclude that the general Restivo or Halstead statements swayed the jury on that issue in any material way. The instructions, if erroneous in failing to parse the issues to which the Restivo/Halstead statements were relevant, did not affect Kogut's substantial rights.

B. Other Contentions

Kogut's additional contentions do not require extended discussion. He complains, inter alia, that the trial court erred in admitting certain evidence against him and in excluding expert evidence he proffered. We apply abuse-of-discretion review to a trial court's evidentiary rulings, see, e.g., Old Chief v. United States, 519 U.S. 172, 174 n. 1, 117 S.Ct. 644, 136 L.Ed.2d 574 (1997); United States v. Abel, 469 U.S. 45, 54-55, 105 S.Ct. 465, 83 L.Ed.2d 450 (1984), including those as to the admissibility of expert testimony, see, e.g., General Electric Co. v. Joiner, 522 U.S. 136, 138-39, 141-43, 118 S.Ct. 512, 139 L.Ed.2d 508 (1997); Salem v. United States Lines Co., 370 U.S. 31, 35, 82 S.Ct. 1119, 8 L.Ed.2d 313 (1962) ("[T]he trial judge has broad discretion in the matter of the admission or exclusion of expert evidence, and his action is to be sustained unless manifestly erroneous."); Chin v. Port Authority of New York & New Jersey, 685 F.3d 135, 160-61 (2d Cir.2012), cert. denied, ___ U.S. ___, 133 S.Ct. 1724, 185 L.Ed.2d 785 (2013). We see no abuse of discretion in any of the district court's evidentiary rulings.

Kogut's complaint that the jury was exposed to unadmitted and inadmissible documents that were inadvertently delivered to the jury room has greater substance, but we conclude that that event did not warrant a new trial. The incident occurred near the end of deliberations, when the jury asked to see the documentary evidence as to Kogut's polygraph examination. Kogut's polygraph documentation had been admitted in evidence in redacted form, but counsel for defendants and Restivo/Halstead inadvertently sent into the jury room the unredacted documents — including one form containing the polygraph examiner's determination that Kogut had been lying during his examination and one background form that contained information on Kogut's prior criminal history. "Counsel noticed the error within minutes, and Court personnel retrieved the documents. Upon retrieval, however, one juror stated `I think you want this back,' referring to the polygraph exhibits. (Trial Tr. 6196.)." Kogut IV, 2013 WL 3820826, at *9.

After the swift retrieval of the documents, the court immediately took action as requested by the parties:

Id. at *10 (quoting Tr. 6199). And the court reminded the jury of the court's prior instructions that polygraph results were not admissible and should not be used by the jury for any purpose. See Kogut IV, 2013 WL 3820826, at *10.

In addition, at the request of counsel for Kogut, the court "questioned each individual juror as to whether they could follow the Court's directive." Id. Each juror responded in the affirmative (see Tr. 6199-200), and it is "normal[to] presume that a jury will follow an instruction to disregard inadmissible evidence inadvertently presented to it, unless there is an overwhelming probability that the jury will be unable to follow the court's instructions," Greer v. Miller, 483 U.S. 756, 766 n. 8, 107 S.Ct. 3102, 97 L.Ed.2d 618 (1987) (internal quotation marks omitted). We see no such probability here. The record does not indicate that Kogut made any other request for curative action, and "at no time during discussion of the matter did Plaintiffs' counsel request a mistrial," Kogut IV, 2013 WL 3820826, at *10.

On this record, we cannot conclude that the district court abused its discretion in denying the posttrial motion for a new trial on the basis of the inadvertently delivered documents.

CONCLUSION

We have considered all of Kogut's arguments on this appeal and have found in them no basis for reversal. The judgment of the district court is affirmed.