POSNER, Circuit Judge.

A jury in a state court in Wisconsin convicted Audrey Edmunds of first-degree reckless homicide in the death of a seven-month-old baby, Natalie Beard, for whom Edmunds was providing day care. Edmunds was sentenced to 18 years in prison. After exhausting her state remedies, see State v. Edmunds, 228 Wis.2d 175, 602 N.W.2d 760 (1999); State v. Edmunds, 229 Wis.2d 67, 598 N.W.2d 290 (1999), she sought federal habeas corpus, lost, and now appeals. She argues that the exclusion of evidence of the parents' demeanor on the day of their baby's death deprived her of her constitutional right to present a defense. Chambers v. Mississippi, 410 U.S. 284, 302, 93 S.Ct. 1038, 35 L.Ed.2d 297 (1973).

An hour after Natalie was dropped off at Edmunds' house early one morning, Edmunds dialed 911 to report that Natalie felt limp, appeared to be unconscious, and was not breathing. Natalie was rushed by paramedics to the hospital, where she remained in a semicomatose state until she died that night. There was medical testimony that death was due to a cerebral hemorrhage probably caused by violent shaking or hitting within the preceding 24 hours — a period during which the only access to Natalie except by Edmunds was by Natalie's parents. Edmunds' defense was that one or both of the parents, probably the father, had done the violent shaking or hitting, and she presented evidence that the father suffered migraine headaches, that Natalie's frequent crying and illnesses had caused him stress, and that he had been alone with her for 45 minutes the night before her death. The parents testified that they had never shaken or hit Natalie, and evidence was presented by other witnesses that they were caring and loving parents. And against Edmunds' theory was the fact that Edmunds herself testified that Natalie had appeared to be completely normal when she was dropped off at Edmunds' house the morning of her death. The medical evidence was that it was unlikely that if she had been shaken so violently the night before as to induce a cerebral hemorrhage she would have appeared normal the next morning. There was also evidence that Edmunds had once hit another child on the head with a book. Natalie's frequent crying, which Edmunds speculates had provoked the father to shake her, may have provoked Edmunds instead.

The excluded evidence was evidence that would have been given by three witnesses: (1) the helicopter pilot who brought Natalie to the hospital, who saw the parents a few minutes after he arrived walking normally in the parking lot of the hospital, appearing neither distraught nor emotional, and later speaking with an "odd" lack of panic in their voices; (2) a police officer who talked to the parents toward evening, and observed that the father seemed "nervous" and "fidgety"; and (3) a chaplain who met with the parents twice during the afternoon, and who thought they displayed "a guarded demeanor, showing very limited expression of grief," which was not what he would have expected in the circumstances; he also thought that the father had seemed afraid to enter Natalie's hospital room, and he observed that in the hospital room the father stood a few feet behind his wife with his hands in his pockets and then left the room while his wife remained. The trial judge excluded all this evidence on the ground that "absent someone who has the expertise to interpret reactions, I don't think the observations have any probative value." No expert testified, and no scholarly literature was tendered to the judge, concerning the proper interpretation of the parents' behavior.

Edmunds raised the constitutional issue throughout the state court proceedings, but the state courts did not address it, treating it instead as a matter purely of state evidence law. The Antiterrorism and Effective Death Penalty Act requires us to uphold a state court's application of a rule of constitutional law laid down by the Supreme Court (such as the rule of Chambers v. Mississippi) as long as it is reasonable, 28 U.S.C. § 2254(d)(1); Williams v. Taylor, 529 U.S. 362, 404-05, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000), but if there is no application, there is no ruling to defer to. But this is in general, not in every case. Although the state overstates the case to say that if a state court finds that the exclusion of some piece of evidence did not violate the rules of evidence then a fortiori it could not violate the Constitution — the state court might as in Chambers itself have applied an evidentiary rule more restrictive than the Supreme Court interprets the Constitution as permitting, see 410 U.S. at 295-303, 93 S.Ct. 1038; Rock v. Arkansas, 483 U.S. 44, 62, 107 S.Ct. 2704, 97 L.Ed.2d 37 (1987); Washington v. Texas, 388 U.S. 14, 15-23, 87 S.Ct. 1920, 18 L.Ed.2d 1019 (1967) — that reservation has no application here. The trial judge excluded the evidence because he thought its probative value was negligible without a foundation that had not been laid. The rule thus applied was Wisconsin's counterpart of Fed.R.Evid. 403, which no one supposes unconstitutional. If his ruling was reasonable, there is no basis for deeming it unconstitutional.

It may have been incorrect. The judge allowed testimony of Edmunds' allegedly hysterical demeanor on the fatal day — so, she asks, why not evidence concerning the parents' demeanor? — though it is hard to see how her being hysterical would, in the circumstances, have indicated guilt, and the prosecutor did not mention her hysteria in the closing argument. Evidence concerning witnesses' demeanor, whether on or off the stand, is routinely admitted to establish that a witness is lying, had guilty knowledge, etc. E.g., United States v. Zafiro, 945 F.2d 881, 888 (7th Cir. 1991); Rothgeb v. United States, 789 F.2d 647, 651 (8th Cir. 1986); Dyer v. MacDougall, 201 F.2d 265, 268-69 (2d Cir. 1952) (L. Hand). In United States v. Frappier, 807 F.2d 257, 262 (1st Cir. 1986), "testimony that appellant's behavior at the wake of her deceased husband was emotionless and self centered" was admitted as bearing on her guilt — and that is the type of evidence that Edmunds wanted to present here. Even closer is the evidence admitted in Commonwealth v. Counterman, 553 Pa. 370, 719 A.2d 284, 301 (1998): "a medical social worker" testified "that when she met Counterman [the defendant] at the hospital he did not appear to be grieving over the deaths of his children, that he expressed concerns about insurance, and that when she met Mrs. Counterman, she appeared frightened of her husband." See also Bagwell v. State, 270 Ga. 175, 508 S.E.2d 385, 388-89 (1998); State v. Jobe, 486 N.W.2d 407, 417 (Minn. 1992); People v. Snow, 44 Cal.3d 216, 242 Cal.Rptr. 477, 746 P.2d 452, 458 (1988).

The validity of the inferences drawn from demeanor evidence in these settings has been questioned. As Olin Guy Well-born III, "Demeanor," 76 Cornell L.Rev. 1075 (1991), bluntly puts it, summarizing empirical studies: "According to the empirical evidence, ordinary people cannot make effective use of demeanor in deciding whether to believe a witness." Yet it would be an unreasonable curtailment of a criminal defendant's constitutional right to put on a defense for a judge to forbid the defendant's lawyer to draw attention to aspects of demeanor that the lawyer thought undermined an adverse witness's testimony. We cannot find a case on the point, but perhaps only because the suggestion is too outré to have been litigated. The demeanor evidence at issue in this case, however, is of a different character. It presupposes a benchmark consisting of "normal" behavior in the face of a shocking incident. Is it true that a "normal" (and innocent) father in the situation of Natalie's father would have strode unhesitatingly into Natalie's hospital room? Would not have kept his hands in his pocket? Would have walked at an abnormal pace in the parking lot? Would have had panic in his voice yet would have been neither nervous nor fidgety? Maybe so; but these propositions, and the others necessary to show that one or both parents manifested lack of grief and consciousness of guilt, are not so obvious that a judge who like Olin Well-born thought them devoid of probative value could be thought unreasonable, though again we cannot find a case on the point, let alone a U.S. Supreme Court case — which cannot however help Edmunds.

The trial judge's assessment of Edmunds' demeanor under cross-examination had a somewhat solider basis in common experience: "[T]he cross-examination of the defendant [Edmunds] was devastating to the defense. The transition from a confident, comfortable, organized witness on direct examination to a halting, uncomfortable, insecure witness on cross-examination was remarkable. The tone of voice, the body language (i.e., looking pleadingly toward her counsel before answering questions), the pace of the answers changed dramatically from the presumably well-prepared direct to the not totally predictable cross by a very skilled prosecutor." Indeed the cross-examination brought out significant contradictions between Edmunds' trial testimony and the statement she had given the police a few days after Natalie's death. For example, she had told the police (according to one of the officers who had interviewed her) that on the fatal morning, until shortly before Natalie's collapse, Natalie had been "tracking" Edmunds — that is, had been making eye contact with her, as babies instinctively do. This would have been unlikely behavior for a severely neurologically damaged baby, and at trial Edmunds denied that Natalie had been tracking. Her testimony was further undermined by such implausible statements as that she had loved Natalie as much as she loved her own children, even though Natalie was a fussy and difficult baby who had been in Edmunds' care for only 17 days before the child's death.

At the oral argument Edmunds' able counsel acknowledged to us that if his position were correct, had Natalie's father rather than Edmunds been prosecuted for the death of Natalie the demeanor evidence that Edmunds' counsel wanted to present on her behalf would have been admissible on behalf of the prosecution. What is sauce for the goose is sauce for the gander. We are dealing with a type of evidence that, so far as anyone connected with the present proceedings seems to know, is of unknown probative value, yet likely to be damaging, as much to a defendant as to a prosecution witness. In these circumstances the judge did not exceed the bounds of reason when he said that " absent someone who has the expertise to interpret reactions, I don't think the observations have any probative value."

Edmunds might have tried to introduce expert evidence that the parents' demeanor indeed fit a pattern that reputable research has shown to be indicative of lack of grief and consciousness of guilt, cf. Krist v. Eli Lilly Co., 897 F.2d 293 (7th Cir. 1990), or she might have presented such evidence to the judge in an effort to persuade him that the lay testimony that Edmunds wanted to present would indeed have significant probative value. Cf. United States v. Hall, 165 F.3d 1095, 1120 (7th Cir. 1999) (concurring opinion). In the absence of such evidence, the demeanor evidence was — or so the trial judge could find without taking leave of his senses — too speculative to be admissible.

Conceivably the chaplain might have been qualified as an expert witness to offer an opinion on this matter, cf. State v. Robinson, 146 Wis.2d 315, 431 N.W.2d 165, 167-68 (1988); a chaplain assigned to a hospital is probably as much an expert on the characteristic demeanor of persons in the extremity of grief as a worker at a rape crisis center is an expert on the characteristic demeanor of victims of sexual assault, as held in the Robinson case. See also United States v. Parish, 308 F.3d 1025, 1030 (9th Cir. 2002); United States v. Bighead, 128 F.3d 1329, 1330 (9th Cir. 1997). But that wasn't done either. Edmunds' trial lawyer did try to offer expert opinion testimony, similar to the testimony offered by the chaplain, by an emergency room nurse who observed Natalie's parents. We do not know whether the trial judge even ruled on the matter. The nurse did not testify, and Edmunds does not mention the matter in her appeal.

In the circumstances, we conclude that the exclusion of the evidence concerning the parents' demeanor did not violate Edmunds' constitutional rights.

AFFIRMED.