Marshall, C.J.
On January 30, 1993, the body of a seventeen year old woman was discovered in a wooded area in Rockland. A Superior Court jury convicted the defendant, William C. Jewett, Jr., the last known person to have seen the victim alive, of her rape and murder in the first degree by deliberate premeditation. On appeal, the defendant claims that the prosecutor acted improperly by not disclosing material evidence to the jury, that his trial counsel rendered ineffective assistance, and that the prosecutor offered false and deceptive evidence to the grand jury. The defendant also argues that the motion judge (who was not the trial judge) abused her discretion by denying his motion for a new trial without holding an evidentiary hearing. Finally, the defendant asserts that three errors — improper expert opinion on sexual assault, lack of an accident instruction, and admission of prejudicial bad acts evidence — none of which was objected to at trial or raised in the motion for a new trial, created a substantial likelihood of a miscarriage of justice mandating exercise of our authority under G. L. c. 278, § 33E, to order a new trial. We affirm the convictions of murder in the first degree and rape, and decline to exercise our power under G. L. c. 278, § 33E.
1. Facts. We summarize the facts in their light most favorable to the Commonwealth, reserving certain details for discussion in connection with the issues raised. The defendant and the victim had known each other socially for a number of years, but had never been romantically involved. On the evening of January 29, 1993, they both attended a party at a mutual friend’s apartment in Weymouth. Sometime before 1 a.m. on January 30, 1993, as the last guests were leaving the party, the defendant said he would drive the victim home. The defendant’s automobile, which was seventeen years old and unregistered, would not start, so a friend in a truck used jumper cables to start it. The automobile was running very noisily and backfir[358]*358ing, so the friend followed it for a short distance in his truck. The two vehicles parted ways in a parking lot after the defendant said the automobile was fine.
The victim had a 12:30 a.m. curfew. When she failed to arrive home by 1 a.m., her mother telephoned the apartment where the party had been held. By morning, both of the victim’s parents and some of her friends began looking for her in the neighborhood. After learning that the victim had left the party with the defendant, the victim’s father telephoned him. The defendant told him that he had dropped the victim off at the end of her street at about 12:30 a.m., because she wanted to finish her beer before going home.
Later that afternoon, while investigating what looked like a blue rag on his property, a resident of Turner Road in Rockland discovered the victim’s body lying partially covered by pine needles, twigs, and leaves in a wooded area. He telephoned the police. Dr. James Weiner, a State medical examiner, declared the victim dead at the scene and conducted a preliminary examination of the body. His examination revealed that the victim’s lipstick was not smeared, but her blouse was pulled off her left shoulder, and two buttons in the middle of the blouse had been tom off. Her pants were buttoned, but the zipper was open and broken. One leg of her pantyhose had been torn completely off, and one of her boots was missing. Her underwear and pantyhose were rolled up, and she appeared to have been redressed.
The victim’s body was transported to the medical examiner’s office for further investigation and autopsy. Dr. Weiner determined that the victim had died around 1:30 a.m., and had probably been moved to the Turner Road location after her death. He prepared a rape kit, collecting semen from the victim’s underwear and vagina, and sent the kit to the State laboratory for analysis. The following morning, Dr. William Zane, another State medical examiner, performed an autopsy. He observed scrapes, abrasions, and bruising to the victim’s face and neck, as well as hemorrhages on the surface of her face and around her heart and upper airway. From this evidence he determined that the victim had died as a result of asphyxia from strangulation, caused by either a soft ligature, fingers, or a forearm.
[359]*359The DNA analysis of the semen recovered from the victim’s underwear revealed a high probability that it had come from the defendant. Analysis of the semen recovered from the victim’s vagina was inconclusive, but the defendant could not be excluded as the source of the semen. A green thread found in the defendant’s automobile matched the victim’s blouse. The victim’s missing boot was found in the middle of a street in Weymouth, about three-tenths of one mile from the defendant’s house.
At trial, three residents of Turner Road, where the victim’s body was discovered, testified to seeing an automobile identical to the defendant’s, with a single male occupant, traveling very slowly down Turner Road between 2 a.m. and 3 a.m. Two other neighbors heard the sound of an automobile backfiring around the same time. Police later discovered that one of the defendant’s close childhood Mends lived on Turner Road.
Several of the defendant’s friends testified regarding his statements and demeanor on the morning of January 30, 1993. Two friends testified that the defendant told them that the victim’s father had telephoned him to say that the victim was missing. The defendant also told one of these Mends that he did not want to get into trouble because his automobile was unregistered and uninsured, and told two friends that he hoped nothing had happened because he did not have an alibi. Friends who saw the defendant that day and the following testified that he was “[njervous,” “pacing,” and “agitated.” The defendant denied to his friends and the police that he had ever had sexual intercourse with the victim, even after the DNA match was later revealed in the newspapers.
Four years later, after the defendant had been indicted for the victim’s rape and murder and incarcerated pending trial, he confessed to another inmate, Mark Obershaw, that he and the victim had kissed in his automobile and were planning to have intercourse, but that she refused at the last minute. He told Obershaw that he had sexual intercourse with her anyway, and that when he finished, the victim started yelling that he had raped her and that she was going to tell her father. The defendant first told Obershaw that he had accidentally strangled the victim, but later told him that he “had to” strangle her so that he would [360]*360not be charged with rape. He then “got emotional” and put the body in the trunk and drove to a street where “one of his best friends lived” because “[h]e knew a spot where he could put the body.” He told Obershaw that he drove slowly down the street because his automobile had a loud muffler, backed up to a spot near the woods, and covered the body with pine needles and brush.
The defendant did not testify at trial. His attorney argued that the victim’s death was accidental, caused by “positional asphyxiation”1 during consensual intercourse with the defendant. He also argued that, after the victim died, the defendant tried to dispose of the body in a panic.
2. Prosecutorial misconduct. The bulk of the defendant’s appeal centers on testimony regarding the age of the sperm analyzed by the Commonwealth’s experts. Contrary to the theory presented by his attorney at trial, the defendant now maintains that he and the victim had had consensual sexual intercourse one or two days prior to her death. He argues, for the first time on appeal, that hearsay statements in a police report and two handwritten police notes prove that the sperm found in the victim’s underwear and in her vagina was twenty-four to thirty-six hours old at the time of her death, and that the prosecutor improperly deprived the jury of the “material” evidence of the age of the sperm. We examine this new claim only to determine whether there was a substantial likelihood of a miscarriage of justice at trial. See Commonwealth v. Wallis, 440 Mass. 589, 593 (2003).
We begin by reviewing in some detail the evidence regarding the age of the sperm. As noted above, around 11 p.m. on January 30, 1993, Dr. Weiner recovered semen samples from the victim’s underwear and from inside her vagina and sent the samples to the State laboratory for analysis. There they were examined by Mary McGilvrey, a chemist employed by the Commonwealth, who testified that none of the sperm cells in the two samples she examined “had tails.” She explained that an intact sperm cell consists of a head, neck, and tail, and that the tails are quite fragile, the first part of the sperm cell to degrade after it is [361]*361deposited in the vagina. She testified further that the presence of intact tails indicates that the sperm was deposited “more recently as opposed to a longer period of time,” but that if no tails are present, she is unable to draw any conclusion about the age of the sperm.2 McGilvrey testified that, in addition to degradation over time, sperm tails can be shed by certain extraction techniques, such as the process used to recover the sperm cells from the victim’s underwear.
With this technical background in mind, we turn to the defendant’s specific assignments of error. The defendant claims that three pieces of evidence, all of which were provided to defense counsel prior to trial, establish the presence of “old” sperm on the victim. He maintains that this evidence lends support to his contention that he and the victim had consensual sexual intercourse one day or more prior to her death. The first is a typewritten police report, prepared by Rockland Detective Sergeant Richard Craig, who did not testify at trial. His report contains the following entry: “Last night, Trp. Berna had advised me that he’d learned from the State Police Laboratory that while the post mortem did not reveal that [the victim had] been raped, it did reveal that [she] had sex approximately 36 hours or so before death, because there were small amounts of sperm deep inside her vagina. The lab also confirmed small deposits of ‘old’ sperm on her panties, which indicated she had changed her panties some time after her sexual encounter. The lack of sperm, etc., on her body would be consistent with her having showered, as had been reported to us earlier.” The other evidence, two handwritten notes of unknown authorship, are reproduced in the margin.3
[362]*362Assuming arguendo that this evidence was admissible,4 and considering it in the context of the trial as a whole, a rational juror could not have considered it new, material, or helpful in any way, much less potentially “dispositive,” as the defendant claims. The three hearsay statements are inconsistent and ambiguous. They differ as to the estimate of the age of the sperm, and it is impossible to determine whether any of the notations concerning the time of sexual intercourse was attributable to McGilvrey or rather was the mere speculation of the author. The defendant’s claim that the documents represented evidence impeaching McGilvrey’s testimony is further weakened by the fact that, even assuming McGilvrey had told a police officer that the sperm was twenty-four to thirty-six hours old, her estimate was consistent with the theory that the defendant and the victim had had sexual intercourse on the night of the murder.5 In addition, no other evidence produced by either party indicated that the defendant and the victim had had sexual intercourse one or two days prior to her death, nor did defense counsel suggest this at trial. The defendant’s friends in fact testified that the defendant and the victim were socially acquainted but not romantically involved prior to the night of the victim’s death. Considered carefully and in light of the evidence as a whole, the allegedly exculpatory documents cannot be said to be material to his defense, presented for the first time on the appeal, that he and the victim had sexual intercourse prior to the night of the victim’s death.
Nor do we credit the defendant’s charge that the prosecutor presented false evidence to the jury by creating the “impression that the sperm evidence corroborated his theory of the case.” “A prosecutor is certainly under an obligation to refrain from [363]*363presenting testimony at trial which he or she knows or should know is false.” Commonwealth v. Sullivan, 410 Mass. 521, 532 (1991). The defendant, however, does not claim that McGilvrey’s testimony was false, but only that the prosecutor created a false “impression” by not disclosing to the jury the allegedly inconsistent hearsay statements in the police report and notes. The prosecutor had produced the police report and the two notes to the defense counsel during discovery prior to trial. It was not the prosecutor’s duty to try the defendant’s case for him by attempting to impeach the testimony of the Commonwealth’s own witnesses with cryptic and inconclusive documents in the defense counsel’s possession.6
3. Ineffective assistance of counsel. The defendant claims that his trial counsel was ineffective because he did not cross-examine McGilvrey or the testifying police officers about the statements in the police report and the notes, or otherwise “investigate” this “potentially dispositive” evidence. Yet, as we have already seen, the police report and the two anonymous notes were anything but dispositive. Trial counsel does not necessarily provide ineffective assistance by “not prob[ing] every inconsistency,” Commonwealth v. Sylvester, 35 Mass. App. Ct. 906, 907 (1993), particularly where the alleged inconsistency does not pertain to defense counsel’s theory of the case, positional asphyxiation during consensual intercourse. Given the implausibility of the defendant’s new theory of the evidence on appeal, this is not an instance where “better work might have accomplished something material for the defense.” Commonwealth v. Satterfield, 373 Mass. 109, 115 (1977). See Commonwealth v. Saferian, 366 Mass. 89, 96 (1974). The claim of ineffective assistance of counsel is unpersuasive.
4. Impairment of the grand jury. The defendant’s final claim regarding the police report and notes is that the integrity of the grand jury process was impaired because the prosecutor offered deceptive evidence that probably influenced the grand jury’s [364]*364decision to indict. Because the defendant did not challenge the indictments prior to trial, he has waived his right to challenge them on appeal, and we consider only whether his assertion raises a substantial risk of a miscarriage of justice. Cf. Commonwealth v. Fernandes, 430 Mass. 517, 521 n.13 (1999). It does not.
The defendant argues that he was prejudiced by the statement that, when asked by a grand juror about the age of the sperm recovered from the victim’s body, Detective Richard Nagle told the grand juror that his question would be better answered by the laboratory personnel who conducted the DNA analysis. The defendant claims that Detective Nagle should have responded by disclosing the hearsay statements made in the police report and the handwritten notes, and that in failing to do so, Detective Nagle intentionally misled the jury, leading to the indictments.
“[I]t is not enough for dismissal of an indictment that false or deceptive evidence was presented to the grand jury. Two further elements normally must be shown. First, our cases have required a showing that false or deceptive evidence was given to the grand jury knowingly and for the purpose of obtaining an indictment. . . . Second, the defendant must show that the presentation of the false or deceptive evidence probably influenced the grand jury’s determination to hand up an indictment. This requires a showing not only that the evidence was material to the question of probable cause but that, on the entire grand jury record, the false or deceptive testimony probably made a difference.”
Commonwealth v. Mayfield, 398 Mass. 615, 621-622 (1986).
Here, the defendant has provided no evidence, nor do we discern any, that Detective Nagle wrote any of the three documents in question, or even knew about them. Further, while it was the State chemist and not the DNA testing laboratory who evaluated the age of the sperm, the defendant has produced no evidence that Detective Nagle’s answer was intended to mislead or deceive the grand jury. Finally, even if Detective Nagle did intentionally deceive the grand jury for the purpose of obtaining the indictments — and we do not suggest that this is the case — the hearsay statements would not have swayed the grand [365]*365jury, for the reasons stated above. See id. The defendant’s charge is unsupported, and the indictments stand.
5. Motion for a new trial. In asserting that the judge erred in denying his motion for a new trial, the defendant first avers that he was denied effective assistance of counsel with regard to the sperm evidence. For the reasons stated above, we disagree.
The defendant also argues that he is entitled to a new trial because the prosecution failed to disclose certain promises and inducements it made to the defendant’s former fellow inmate, Mark Obershaw, in exchange for his testimony against the defendant. At the time of the defendant’s trial, Obershaw was awaiting trial on a charge of murder in the first degree. On direct examination in the defendant’s trial, Obershaw testified that he had entered into a cooperation agreement with the Commonwealth under which he was promised that he would serve his time out of State if convicted, in return for his testimony regarding the defendant’s confession. Obershaw also confirmed having been told that his testimony at the defendant’s trial would not affect the charges against him.
To support his allegations concerning a further, covert deal between Obershaw and the prosecution, the defendant submitted two documents. The first was an affidavit by his appellate counsel. The affidavit recounted a conversation with Obershaw in which Obershaw allegedly told the affiant that he had been led to believe that his testimony against the defendant would result in his not being convicted of murder in the first degree. The second supporting document was an excerpt from a hearing in Obershaw’s case. In that transcript, Obershaw’s trial counsel represented to the court that a meeting occurred among Obershaw, a police officer, and two assistant district attorneys during which Obershaw asked whether he could arrange for a plea bargain. According to Obershaw’s trial counsel, someone at the meeting responded, “No we can’t. But you got nothing to worry about, this is not a first degree case .... The best deal we can make for you is we’ll let you serve your time anywhere you want in the United States of America if you go to jail, in a facility comparable to ours.”
Nothing here raises a substantial issue. The defendant failed to obtain affidavits from Obershaw or Obershaw’s trial counsel. [366]*366His submissions, again, are replete with layered hearsay. See Commonwealth v. McDonough, 400 Mass. 639, 643 n.8 (1987). More importantly, at the time Obershaw gave evidence at the defendant’s trial, he was awaiting trial on a charge of murder in the first degree, a charge of which he was subsequently convicted. See Commonwealth v. Obershaw, 435 Mass. 794 (2002). This fact weighs heavily against the allegation that Obershaw was promised a reduction in charges for testifying against the defendant at the time of the defendant’s trial. Given the tenuousness of the evidence filed in support of the defendant’s motion, we cannot say that the motion judge abused her discretion in denying it. See Commonwealth v. Wallis, 440 Mass. 589, 596 (2003).
Finally, the defendant claims that the motion judge abused her discretion by not conducting an evidentiary hearing on the matter. However, he was not entitled to an evidentiary hearing in the circumstances. See id. (“A judge may, in his or her discretion, decide a motion for a new trial without an evidentiary hearing where no substantial issue is raised by the motion or affidavits”).
6. G. L. c. 278, § 33E, review. Under G. L. c. 278, § 33E, we “review the whole case to determine whether there has been any miscarriage of justice in convicting the defendant of murder in the first degree.” Commonwealth v. Marquetty, 416 Mass. 445, 452 (1993). The defendant argues that three errors, not raised below, warrant our particular consideration: improper expert opinion on sexual assault, lack of an accident instruction, and admission of prejudicial bad acts evidence. He contends that, even if the errors do not by themselves raise a substantial likelihood of a miscarriage of justice, in concert they prejudiced him sufficiently to warrant a new trial. See Commonwealth v. Carlino, 429 Mass. 692, 695-696 (1999). We disagree.
a. Expert opinion on sexual assault. At trial, both of the Commonwealth’s medical examiners, Dr. Weiner7 and [367]*367Dr. Zane,8 testified on direct examination that the victim had been sexually assaulted. This testimony was improper. Our courts have held many times that, “[u]nless there are particular facts which require a medical expert, a physician is not considered to have professional knowledge which would be of assistance to the jury in determining whether a rape has occurred.” Commonwealth v. McNickles, 22 Mass. App. Ct. 114, 120-121 (1986). See, e.g., Commonwealth v. Federico, 425 Mass. 844, 849 (1997) (expert may not opine on whether victim was subject to sexual abuse); Commonwealth v. Gardner, 350 Mass. 664, 667 (1966) (expert cannot testify whether victim was raped where jury are equally capable of making such determination); Commonwealth v. Syrafos, 38 Mass. App. Ct. 211, 216 (1995) (not within expert’s special experience to testify whether sexual intercourse was consensual or forced); Commonwealth v. Mendrala, 20 Mass. App. Ct. 398, 404 (1985) (unless there are special factual circumstances, witness may not be asked directly whether rape or sexual assault has occurred). [368]*368Therefore, in the absence of special circumstances, an expert may not be asked whether a rape or sexual assault has occurred. See Commonwealth v. McNickles, supra at 121. Here, no such special circumstances existed. Both physicians based their opinions on circumstantial evidence that die jury were equally competent to evaluate — the presence of the defendant’s semen on the victim’s underwear, tom buttons on the victim’s blouse, a tom stocking, and a broken zipper on the victim’s pants. See notes 7 and 8, supra. It was well within the ken of the average juror to evaluate such evidence. See Commonwealth v. Federico, supra at 849; Commonwealth v. Gardner, supra at 667; Commonwealth v. Syrafos, supra at 216; Commonwealth v. McNickles, supra at 120-121; Commonwealth v. Mendrala, supra at 404.
Commonwealth v. Miller, 435 Mass. 274 (2001), and Commonwealth v. Pikul, 400 Mass. 550 (1987), both cited by the Commonwealth, do not compel a contrary result, because neither is factually analogous. The victim in Commonwealth v. Miller, supra, suffered significant physical injuries to her groin and vaginal areas, which the medical expert determined were indicative of a single deadly physical attack on her body, a “sexually related death.” See id. at 276, 278. Unlike Dr. Weiner and Dr. Zane, the medical examiner in Miller did not opine whether the sexual intercourse between the defendant and the victim, which the defendant admitted, was consensual or forced. See id. at 278.
In Commonwealth v. Pikul, supra at 553, three medical experts testified that the cause of the victim’s death was “traumatic [sexual] asphyxia,” or, in other words, that the victim had suffocated during “forced oral sex.” In that case, again, the sexual contact was not merely an event that preceded death, but was the actual cause of death. Id. at 552-553. In addition, as the victim was a minor, consent was not an issue. See id. at 550. In the instant case, however, there was no evidence or allegation that sexual violence was the cause of death, or even that it contributed to the victim’s death. Expert testimony was not required to assist the jury in evaluating the ultimate issue whether the victim had been raped.
Our conclusion that the testimony was improperly admitted [369]*369does not end our inquiry. The defendant did not object to the admission of this testimony at trial. Therefore, in the case of the rape conviction, we must determine whether the error created a substantial risk of a miscarriage of justice. See Commonwealth v. Grandison, 433 Mass. 135, 141-142 (2001). Although the testimony should not have been admitted, there was more than sufficient evidence, apart from this testimony, on which a rational jury could have based their conviction. Both medical examiners testified that two buttons in the middle of the victim’s blouse had been tom off, her open pants’ zipper was broken, and her stockings tom. More significantly, Obershaw testified to statements made by the defendant that the victim refused to have sexual intercourse with him, that he had nevertheless proceeded to have intercourse with her, and that the victim accused the defendant of rape before he killed her. In addition, the only motive presented at trial for the victim’s murder, as opposed to her accidental death, was that the defendant wished to conceal that rape. The jury’s conviction of the defendant of murder in the first degree indicates that they rejected the defendant’s accident theory, and the purposeful nature of the killing itself corroborated the motive that the defendant had articulated in his admissions to Obershaw. In the circumstances of this case, the erroneously admitted testimony did not create a substantial risk of a miscarriage of justice.
The murder conviction also stands. That conviction could only be disturbed if the error created a substantial likelihood of a miscarriage of justice. See Commonwealth v. Wallis, 440 Mass. 589, 593 (2003). Here, the erroneously admitted testimony was not material to the murder charge. The defendant’s conviction of murder in the first degree was supported not by the expert testimony that the victim had been sexually assaulted, but by the fact that the defendant was the last known person to see the victim alive, the physical evidence of asphyxiation by strangulation, the defendant’s unusual behavior during the days following the murder, the eyewitness testimony placing the defendant’s automobile on the street where the victim’s body was later discovered, the fact that the defendant had recently had sexual intercourse with the victim, and the defendant’s jailhouse confession. There is little likelihood that, [370]*370without the opinions as to sexual assault, the jury would have rendered a different verdict.
b. Accident instruction. The defendant claims that because the theory of his defense was that the victim’s death was an accident, the jury should have received an instruction on accident. Where the evidence fairly raises the possibility of accident, the defendant is entitled, if he requests, to have the judge instruct the jury that the Commonwealth has the burden of proving beyond a reasonable doubt that the death was not accidental. Commonwealth v. Zezima, 387 Mass. 748, 756 (1982). We agree that the defendant fairly raised the possibility of an accident at trial. Defense counsel argued accident as the cause of death in his opening and closing remarks, he questioned both medical examiners about positional asphyxia on cross-examination, and Obershaw testified that the defendant first told him that the death was an accident. The defendant, however, did not request an accident instruction at trial or object to the jury instructions on this ground, so we review to determine whether the lack of a specific instruction on accident created a substantial likelihood of a miscarriage of justice. See Commonwealth v. Wallis, supra at 593.
Although the judge did not give a specific instruction on accident, she twice instructed the jury that the Commonwealth had to prove that the death was the result of an unlawful killing, and that an unlawful killing does not include a killing which is the result of an accident. She further instructed the jury that the Commonwealth was required to prove all the elements of murder in the first degree, including an unlawful killing, beyond a reasonable doubt. The instructions, viewed as a whole, did not impermissibly shift the burden of proof to the defendant. See Commonwealth v. Lowe, 391 Mass. 97, 110, cert. denied, 469 U.S. 840 (1984). Contrast Commonwealth v. Zezima, supra at 757.
c. Bad acts evidence. The defendant’s final claim is that the judge improperly permitted Obershaw to testify to derogatory statements that the defendant allegedly made about the victim. He asserts that the statements were irrelevant because they were made many years after the murder took place and were unfairly prejudicial. There was no error.
[371]*371“It is well settled that the prosecution may not introduce evidence of a defendant’s prior or subsequent bad acts for the purpose of demonstrating bad character or propensity to commit the crime charged. . . . However, such evidence may be admissible, if relevant, to show a common scheme or course of conduct, a pattern of operation, absence of accident or mistake, intent, or motive. . . . To be sufficiently probative the evidence must be connected with the facts of the case or not be too remote in time.” (Citations omitted.) Commonwealth v. Barrett, 418 Mass. 788, 793-794 (1994). Obershaw testified that when he and the defendant discussed the defendant’s case, the defendant referred to the victim as a “cunt,” said that “she was nobody to me,” and added that he “[did not] want to do time because of this bitch.” These statements were properly admitted for the purpose of showing hostility toward the victim, which is relevant to motive. See Commonwealth v. Barrett, supra at 794. Because the statements were made contemporaneously with the defendant’s discussion of the events of the murder, they were directly connected to the facts of the case, and their remoteness in time to the crime itself is not material. See id. The obvious vulgarity of the defendant’s statements may be somewhat prejudicial, but here the prejudice does not outweigh the probative value of evidence of his hostility toward the victim.
7. Conclusion. For the reasons outlined above, we affirm the convictions of murder in the first degree and rape, and the order denying the defendant’s motion for a new trial.
So ordered.