DUFFLY, J.

The defendant was indicted for the armed robbery and murder of Paula Doherty. The victim was last seen alive on Saturday, September 30, 2006, at her Medford residence, where she, a friend, the defendant, and the defendant's nephew had been using cocaine. When the friend left at 5:30 P.M. that afternoon, the defendant had passed out in a chair in the victim's room and the victim was preparing to go to sleep. On Monday, October 2, after the victim failed to return telephone calls, the friend went to the victim's house to check on her, and discovered the body of the victim, who had been beaten to death. A Superior Court jury found the defendant guilty of murder in the first degree on theories of extreme atrocity or cruelty and felony-murder, with armed robbery as the predicate felony.

On appeal, the defendant contends that the trial judge erred in denying his motions for a required finding of not guilty, because the circumstantial evidence of guilt was insufficient to establish that the defendant was at the scene of the crime during the period when the victim was robbed and killed. The defendant argues also that the judge erred in allowing the admission of expert testimony concerning the potential absence of blood on the victim's killer. We conclude that there was no error requiring reversal and, after a careful review of the record, that there is no reason to exercise our authority under G. L. c. 278, § 33E, to order a new trial or to reduce the murder conviction to a lesser degree of guilt.

1. Facts. Based on evidence introduced at trial, the jury could have found the following.

a. Events of September 28 to 30, 2006. The victim sold cocaine from her residence, including to the defendant, who lived two or three houses away. On Thursday, September 28, 2006, at the victim's request, the defendant and his nephew, Sean Kanode, drove the victim to a bank where the defendant cashed a check in the amount of $1,100, and handed the cash to the victim.2

The following day, Friday, at about 6 P.M., the victim's childhood friend, Jean McCarthy, arrived at the victim's home in Medford, where they planned to use cocaine, consume alcohol, and play cards. The victim had been in the process of renovating the house, and although there was electricity, there was no running water, some windows were missing, and some walls were torn down. Tools were scattered throughout the interior, including saws, drills, hammers, and crowbars. The victim led McCarthy to a back room, which the victim had set up as her living space. The bed, consisting of two mattresses on the floor, piled on top of each other, was in a corner, with one side flush along a wall and a chair at its foot. When McCarthy arrived, the defendant and Kanode were present. The four spent the rest of that evening and the early morning hours of Saturday drinking, using cocaine, and playing cards; McCarthy gave the victim $50 for some cocaine, which the victim put into her pants pocket; the victim kept cocaine in another pocket. Kanode left at approximately 5 A.M. on Saturday morning, but the others stayed until late in the afternoon.

Over the course of that period, a number of people arrived at the house in order to purchase cocaine, after telephoning the victim to arrange the transaction. While some transactions took place elsewhere in the apartment, at least three people came into the back room to conduct the transaction. Each of the three paid in cash, which the victim placed in her pants pocket. The defendant was present for each transaction that took place in the back room. At no point during the period from Friday evening through the late afternoon on Saturday did McCarthy see the defendant with any money, although at some point on Saturday the defendant left and returned a short time later with an antique clock to trade for money or drugs. At approximately 5:30 P.M. on Saturday afternoon, as McCarthy was preparing to return to her home, the defendant appeared to be passed out in the chair at the foot of the victim's bed, and the victim was lying down and seemed sleepy. As she left, McCarthy told the victim to get up and lock the door behind her, and the victim did so.

Soon after McCarthy left, Barbara Welch, one of the victim's customers from the previous night, began to call the victim on her cellular telephone, but was unable to reach her. A call Welch placed to the victim's telephone around 6 P.M. was answered by a male; when Welch asked him if "Paula" was there, he responded that she was asleep. On Sunday, October 1, Welch tried to telephone the victim many times, but there was no answer, and, contrary to her usual practice, the victim did not return Welch's calls.

b. Discovery of victim's body. On the evening of Monday, October 2, after the victim had failed to return telephone calls placed the previous day, McCarthy went to the victim's house to check on her. McCarthy found the porch door standing open, the front door to the house unlocked, and the victim dead in the back room. Her body was partially on the bed. Everything else appeared to be almost exactly as it had been when McCarthy left the previous Saturday at 5:30 P.M. Responding police officers observed that the victim was lying diagonally across the mattress, face down, with her head towards the corner of the room and her left shoulder resting on the floor. After an initial sweep to secure the house, police contacted emergency medical services.

c. Police investigation. At approximately 5 A.M. on Tuesday morning, police began a canvass of the neighborhood. Later that morning, State police Trooper Michael Banks observed the defendant and Kanode sitting on the front steps of their house a few doors away. Banks and other officers asked the two whether they had seen anything unusual at the victim's home, and they replied in the negative. The following day, after police interviewed McCarthy, Banks returned to the defendant's house and asked him if he would speak with police. The defendant and Kanode drove to the police station and were interviewed.

i. Defendant's first statement. The defendant told police that he knew the victim because she lived down the street, and that he had purchased cocaine from her in the past. He recently had relapsed and had gone to her house on Saturday, where he had stayed from approximately 8:30 A.M. until about 2 or 3 P.M. He brought an antique clock to the victim's house, for which he received $30 that he used to purchase an "8-ball" of cocaine, and left when he had run out of money to purchase additional cocaine. The defendant then walked to a nearby park to consume his remaining cocaine, returned home, and went to bed.

ii. Events at the James Street house. After comparing the defendant's statement with that of his nephew, police subpoenaed the telephone records for the defendant's landline in order to look for an incoming call that Kanode said the defendant made on Sunday night, October 1. Police determined that he had made the call from Peter Milonopoulos's landline telephone at his house on Pearl Street in Somerville. Milonopoulos testified that he had seen the defendant arrive at the house of his friend, Michael Wolfe, who lived around the corner on James Street, at 9 P.M. or 10 P.M. on Saturday, September 30.

The James Street house was the home of Gary Young, Wolfe's uncle and a longtime friend of the defendant, and Young's girl friend, Madeline Osborne, and also was a "crack house" where people gathered to purchase and use drugs, including "crack" cocaine. Wolfe, who had been released from jail at 7:05 P.M. that evening and arrived home approximately forty minutes later, testified that the defendant had arrived at the James Street house after 8:30 P.M.3 Young and Osborne said that the defendant was at their house twice on Saturday, once earlier in the day, while it was still light out, and then later that night.4 Osborne said that the defendant returned sometime between 11 P.M. and midnight; he appeared a little shaky and nervous, and told everyone in the house that if anyone came looking for him, he was not there.

The defendant told Young that he had been working that day and that he cut his finger while cleaning gutters. Young thought the defendant's pants appeared dirty and "painted," and that the defendant might have wiped the blood from the cut onto his pants.5 At some point during the night, the defendant asked Young if he could borrow some clothes because his were dirty. Although the defendant was not seen with more than $40 while he was at the victim's house from Friday evening through Saturday at 5:30 P.M., he had cocaine and a considerable amount of cash when he arrived at the James Street house. In total, witnesses at the house observed the defendant spend hundreds of dollars, making at least two purchases of cocaine during the evening of Saturday, September 30, and into the early morning hours of Sunday, October 1.6

At some point, the defendant asked Osborne to wash the clothes he had been wearing when he arrived and some other laundry he had with him.7 During the day on Sunday, Osborne took the clothes the defendant had been wearing, as well as two of his shirts and a pair of pants, some clothes belonging to Young, and some of her own clothes, to a nearby laundry. She saw a maroon stain on one pair of pants. In the ten to fifteen years that they had known each other, the defendant had not previously asked her to do his laundry.

iii. Defendant's second statement. On the evening of October 6, 2006, police again requested that the defendant come to the police station; the defendant agreed to be interviewed, was given Miranda warnings, and agreed to having the interview tape recorded.8 The defendant told police that after leaving the victim's house on Saturday afternoon sometime between 2 and 3 P.M., he went to Young and Osborne's James Street house.9 He shared "a little pot" with others at the house, and "mooched drugs from" others. At some point in the early morning hours of Sunday, October 1, he fell asleep at the James Street house, after using some heroin provided by Young. Late Sunday night, the defendant called his son to come pick him up. Lacking a vehicle to use, the defendant's son and Kanode came to meet him, and the three of them walked back to their home.

d. Trial proceedings. i. Forensic evidence. The Commonwealth's forensic pathologist, Dr. Phillip Robert Croft, who conducted the autopsy, determined that the cause of the victim's death "was blunt force injuries of the head with skull fractures and brain contusions." The victim suffered fourteen abraded lacerations to the back and top of her head; the injuries were caused by blows that could have numbered up to fourteen, depending on the object with which the victim was struck. The victim had wounds to the back of her hands that were consistent with a person "trying to protect themselves or ward off blows." In Croft's opinion, it was equally possible that the victim was killed on Saturday or Sunday, but it was not likely that the death occurred later than very early Monday morning.

A State police criminalist who assisted in processing the crime scene observed and made a chart of nine damaged or dented areas ("impact areas") located on the wall above the victim. The impacts were located in an circular area of approximately one square foot. Red-brown stains were observed in seven of the impacts. In the criminalist's opinion, the damage was caused by an object hitting the wall. No bloodstains were observed either leading out of the bedroom or in the hallways and areas exiting the dwelling. The blood and blood spatter was focused in the corner of the room where the victim's body was found. There was what appeared to be brain matter on the victim's pillow.

According to Detective Lieutenant Kenneth F. Martin, the Commonwealth's bloodstain pattern analyst, the bloody event took place in the corner near the mattress. Martin opined that, depending on the weapon used, the direction in which the weapon struck the point of impact, and the position of the victim, there would not necessarily be any resulting impact blood spatter or cast-off from the weapon on the perpetrator. The victim was found in what Martin called a "well" between the mattress and the wall, which would restrict outward radiation of the blood. Martin described bloodstains on the wall above the mattress indicating that the victim's body had been in that area and created a stain while sliding downward, ultimately resting as the body was found. The instrument used to inflict the wounds was narrow, approximately one inch or one and one-half inches in width.10

Although another cellular telephone was found at the scene, police were unable to locate the cellular telephone belonging to the victim that Welch and others had been calling that weekend. According to records from the victim's telephone service provider,11 the last activity posted for that cellular telephone was on Saturday, September 30, 2006, at 8:25 P.M.12

The clothing the victim had been wearing was examined by a technician in the office of the medical examiner. No currency was found in the pockets of the victim's jeans, or anywhere amongst her personal possessions. The Commonwealth's deoxyribonucleic acid (DNA) expert, Cailin Drugan, who conducted an analysis of DNA recovered from inside the pockets of the victim's jeans, testified that the major DNA profile in all four of the pockets matched the DNA profile of the defendant.13 She also testified that it was probable that the major profile was the result of a primary transfer, meaning that the contributor made direct contact with the inside of the victim's pockets.

The defendant's motions for a required finding of not guilty at the close of the Commonwealth's case and at the close of all the evidence were denied. After the jury convicted the defendant of armed robbery and murder in the first degree on theories of felony-murder and extreme atrocity or cruelty, the judge dismissed the armed robbery conviction as duplicative. Because the defendant was convicted of murder on both theories of murder advanced by the Commonwealth, the conviction of armed robbery should not have been dismissed. See Commonwealth v. Felder, 455 Mass. 359, 370-371 (2009), citing Commonwealth v. Brum, 441 Mass. 199, 200 n.1 (2004) ("Where, as here, the conviction of murder is based on a theory in addition to the theory of felony-murder, the conviction of the underlying felony stands").

2. Discussion. The defendant argues that the evidence was insufficient for the jury to convict him on either theory of murder advanced by the Commonwealth, and that his motions for a directed verdict should have been allowed. He argues also that the admission of certain testimony by the Commonwealth's blood spatter expert requires a new trial, because the testimony erroneously invaded the province of the jury. We conclude that the evidence was sufficient to support both of the Commonwealth's theories, and that there was no error in the admission of the expert's testimony. In addition, in our review pursuant to G. L. c. 278, § 33E, we note an error not raised by the defendant; we conclude that certain portions of the prosecutor's closing argument were impermissible because they were not based on evidence admitted at trial, but that the improper argument did not create a substantial likelihood of a miscarriage of justice.

a. Sufficiency of the evidence. The defendant contends that the evidence introduced was not sufficient to establish his presence at the victim's house at the time she was killed; that others who were present to purchase drugs on the evening of Friday, September 29, and the early morning hours of Saturday, October 1, had equal motive and opportunity to rob the victim; that the method of the killing was more consistent with a motive other than robbery; and that the victim's former boy friend, with whom she had a conflict, would appear to have had such a motive.

In considering whether the evidence was sufficient to support a conviction,

Commonwealth v. Woods, 466 Mass. 707, 712-713, cert. denied, 134 S.Ct. 2855 (2014).

Under the theories of murder advanced by the Commonwealth, it was required to prove that the defendant unlawfully killed the victim either with extreme atrocity or cruelty or in the course of committing a felony. Because the jury convicted the defendant on both theories, evidence supporting either theory would suffice to affirm the verdict. Commonwealth v. Whitaker, 460 Mass. 409, 416-417 (2011), citing Commonwealth v. Hensley, 454 Mass. 721, 734 n.9 (2009). The evidence presented was sufficient to support both theories.

i. Felony-murder. To prove that the defendant was guilty of felony murder, the Commonwealth was required to establish that the defendant committed a homicide during the commission of a felony, here, armed robbery. See Commonwealth v. Stewart, 460 Mass. 817, 821 (2011). "It would be enough that the homicide[] occurred as part of the defendant's effort to escape responsibility for the underlying felony." Id., quoting Commonwealth v. Ortiz, 408 Mass. 463, 466 (1990).

The evidence presented would have permitted a rational trier of fact to find, beyond a reasonable doubt, that the defendant killed the victim during an armed robbery. The jury could have found that the defendant was aware that the victim possessed a large amount of cash, which she kept in the pockets of her jeans, along with a supply of cocaine. On September 28, the defendant cashed a check for the victim in the amount of $1,100, and was present when three people, during the evening of September 29, gave the victim cash that she put into her pants pockets. After an initial purchase of cocaine, the defendant was not seen with any money during the approximately twenty-four hour period that he was at the victim's home ingesting cocaine provided by the victim and others. This evidence is sufficient to establish the defendant's motive to rob the victim. See Commonwealth v. Lao, 443 Mass. 770, 780 (2005) (evidence sufficient based on evidence of motive to kill coupled with identification of defendant standing, at approximate time of killing, outside residence where wife was killed).

The evidence also allowed a rational jury to infer that the defendant had the means (one of the tools lying around the victim's house) and opportunity to kill the victim. Based on the testimony of the forensic pathologist who conducted the autopsy, the victim likely died on Saturday, September 30, or Sunday, October 1. The last witness to have seen the victim alive saw her at approximately 5:30 P.M. on September 30, when the witness left the victim alone with the defendant. The jury reasonably could have inferred that the victim was killed within the three-hour time frame between 5:30 P.M., when McCarthy left the victim's house, and 8:25 P.M., when the last activity for the victim's cellular telephone was posted and the victim ceased responding to calls. When Welch, who did not know the defendant, attempted to telephone the victim around 6:00 P.M., the call was answered by a male who told Welch that the victim was asleep. Based on this, the jury could have inferred that the defendant hit the victim repeatedly in the head when she woke up unexpectedly as he was reaching into her pockets to take the cash and cocaine. Cf. Commonwealth v. Fitzpatrick, 463 Mass. 581, 593 & n.21 (2012) (evidence established that fatal shots fired shortly before 8:00 A.M.; based on reasonable inferences, jury could have concluded that defendant had driven distance from his home to location of shooting shortly before 8:00 A.M., providing evidence of opportunity, and that he had taken gun from victim's house).

Witnesses present at Young's James Street house differed about when the defendant was there. While a number of witnesses testified that the defendant was at the house after 9 P.M., none of the witnesses saw the defendant present at Young's house throughout the period from 2 or 3 P.M. to 9 P.M. on September 30. Several witnesses said that the defendant was at Young's house sometime in the afternoon, arriving around 4 or 5 P.M., and staying for from one-half hour to an hour before leaving and returning later in the evening. Others testified that the defendant only arrived sometime after 9 P.M. According to Wolfe, who arrived around 8 P.M., after his release on bail, the defendant arrived after he did.

The jury took a view and traveled the distance between the victim's house and Young's house; they also heard testimony that walking between the houses took approximately thirty to forty minutes. The jury could have considered this evidence, along with evidence that some of the DNA in the victim's pockets matched the defendant's, that there was no money in any of the pockets when the victim's body was found, and that the defendant was in sudden possession of a large amount of cash, to infer that the defendant remained at the victim's house after McCarthy left; the victim, who has been sleepy, fell asleep; and, sometime between 5:30 and 8:25 P.M., the defendant reached into the victim's pockets and robbed her.

ii. Extreme atrocity or cruelty. To convict a defendant of murder in the first degree on a theory of extreme atrocity or cruelty, the jury must consider the Cunneen factors and determine that the manner of the killing met one or more of them: "(1) whether the defendant was indifferent to or took pleasure in the victim's suffering; (2) the consciousness and degree of suffering of the victim; (3) the extent of the victim's physical injuries; (4) the number of blows inflicted on the victim; (5) the manner and force with which the blows were delivered; (6) the nature of the weapon, instrument, or method used in the killing; and (7) the disproportion between the means needed to cause death and those employed." Commonwealth v. Linton, 456 Mass. 534, 546 & n.10 (2010), citing Commonwealth v. Cunneen, 389 Mass. 216, 227 (1983).

The evidence here was sufficient to support the defendant's conviction of murder on a theory of extreme atrocity or cruelty because there were sufficient facts from which the jury reasonably could infer that at least one of the criteria established in Commonwealth v. Cunneen, supra, was met. The forensic pathologist testified that the victim suffered at least fourteen blows to the head, and other evidence indicated that at least some of the blows were delivered with so much force that there was brain matter on the victim's pillow. Defensive wounds indicated that the victim attempted to ward off those blows with her hands, and blood spatter evidence suggested that she had been sitting up when the blows were delivered, and then slid down the wall at some point. Thus, the victim was conscious, and the jury could conclude that she endured great suffering as she was beaten to death.

iii. Consciousness of guilt. The Commonwealth argued that the defendant's actions and his inconsistent statements after the victim was killed showed consciousness of guilt.14 "In conjunction with other evidence, a jury may properly consider actions and statements of a defendant that show a consciousness of guilt." Commonwealth v. Woods, 466 Mass. 707, 715 (2014), quoting Commonwealth v. Rojas, 388 Mass. 626, 629 (1983). See Commonwealth v. Best, 381 Mass. 472, 483 (1980); Commonwealth v. Montecalvo, 367 Mass. 46, 52 (1975). The jury reasonably could have concluded that a number of the defendant's statements indicated consciousness of guilt.

In his initial, unrecorded statement to police on October 3, 2006, the defendant asserted that he had been at the victim's house on September 30, consumed cocaine with her beginning at about 8:30 A.M., and left at approximately 2 or 3 P.M.15 He then took a walk on a specific route he described to police, which included a park, during which he consumed a single remaining gram of cocaine in his possession. After he consumed the cocaine, it was night and he returned home and went to bed. At that point, he had no money and no energy, following three days of drug use, and stayed home Sunday and Monday. The defendant did not make any reference to his trip to James Street. A number of these statements were inconsistent with the defendant's later statements to police, and with the testimony of other witnesses.

During his second interview at the police station, the defendant told police that, after he had been "partying" for two days at the victim's house, from Friday into Saturday, his son and nephew came to the victim's house looking for him, sometime between 2 and 3 P.M.;16 and after they had gone, he left, walking a particular route to a location with a wooden tower, where he ingested a gram of cocaine. He then walked into Somerville. He had no money to get more cocaine,17 so he went to the homes of several friends, ending up at the home of a friend named Gary, where he "mooched" drugs provided by others throughout the night, finally using heroin provided by Gary, fell asleep, and slept there all day Sunday. The defendant said that when he woke up Sunday it was dark and he was hungry and cold; he used someone else's cellular telephone to call his son, telling him he was walking home and would meet him on the way. The defendant, his son, and his nephew met up and walked home together.

As stated, other testimony at trial did not accord with the defendant's assertions regarding the time of his arrival at the James Street residence and his statement that he had had very little money with him at the James Street house and could not afford to purchase any drugs. Contrary to the defendant's statements, several witnesses testified that the defendant did not arrive at the James Street residence until well after 9 P.M. No witness testified to seeing the defendant there between 6 and 8:30 P.M., including Young, the victim's childhood friend. Several witnesses testified to the defendant's purchases of cocaine after his arrival at the James Street house; his leaving the house to purchase more cocaine, which he brought back to the house; and, on one occasion, his trip into Boston in an attempt to locate a prostitute. Moreover, telephone records indicate that, at 11 P.M. on Sunday night, a call was made to the defendant's house from a landline telephone number assigned to Milonopoulos's residence, and not from an unidentified cellular telephone. Thus, the jury could have viewed the defendant's statements to police as an attempt to conceal his whereabouts from 5:30 to 8:25 P.M. on Saturday evening, and to deflect police attention from his possession of large amounts of cash. See Commonwealth v. Woods, supra at 715-716. On that basis, the defendant's statements properly "could be seen as an attempt to hamper the police officers' investigation by preventing them from locating witnesses." See id. at 715.

In sum, the evidence supports the reasonable inference that it was the defendant who answered Welch's telephone call and then attempted to rob the sleeping victim of the cash and cocaine in the pockets of her jeans; that she was awakened by this action and sat up on the mattress to confront the defendant; and that the defendant at some point picked up a crowbar or similar implement from among the tools lying around the house, and used it to strike the victim in the head as she turned away from the blows toward the wall, raising her hands in an effort to protect herself. Based on the DNA evidence, the jury could have inferred that the defendant reached into at least three of the victim's pockets. The jury also reasonably could have inferred that the defendant took the victim's cellular telephone, which police were unable to locate, and disposed of it and the murder weapon, which was also never located, as he walked from the victim's Fellsway residence to the James Street residence of his friends Young and Osborne, where he arrived sometime after 9 P.M., flush with cash and in possession of cocaine.

The defendant contends that this case is like Commonwealth v. Mazza, 399 Mass. 395, 399 (1987), in which we held that the circumstantial evidence was insufficient to convict the defendant of murder. In that case, the defendant went to a restaurant where he planned to meet the victim. The victim's body was discovered about an hour later, lying facedown in a vehicle parked in the restaurant lot. Id. at 396. Although acknowledging evidence of the defendant's presence at the crime scene "together with the evidence of motive and consciousness of guilt," id. at 398, we noted also that there was no evidence of the time of death, or evidence that the particular vehicle had been in the restaurant parking lot when the defendant arrived, or that the defendant had had a gun when he entered the parking lot. Id. at 399.

The facts in that case differ significantly from the circumstances here. As in Commonwealth v. Mazza, supra, the time of the victim's death was uncertain, others could have had means, motive, and opportunity to kill her, and the evidence was almost entirely circumstantial. The theory of the defense was to point to other possible perpetrators who might have entered the victim's room, including the victim's former boy friend, who had been convicted of an assault and battery against her and who had been ordered to keep away from her house, and a real estate broker and business associate of the victim to whom she owed substantial amounts of money. Nonetheless, the evidence in this case established that the defendant was the last person seen with the victim, in the bedroom of her locked apartment, and that he had the opportunity to commit the crime during the approximately three-hour window thereafter before the victim's cellular telephone ceased accepting calls. In addition, DNA matching the defendant's was found in the victim's pockets and, along with his sudden possession of a large amount of cash, and the absence of any cash on the victim's person where she normally kept it, is sufficient for the jury to have found that the defendant robbed and killed her.

b. Expert testimony on blood spatter. The defendant claims error in the admission of testimony by Martin, the blood spatter expert, over the defendant's objection, that there would "not necessarily" be any blood found on the victim's assailant. The defendant argues that this line of questioning did not aid the jury because they could have understood the evidence without the expert testimony, and that the testimony culminated in a conclusion by the expert that invaded the province of the jury.18 We review a judge's decision concerning the admission of expert testimony for abuse of discretion. Commonwealth v. Federico, 425 Mass. 844, 847 (1997). Commonwealth v. Colin, 419 Mass. 54, 59 (1994). Where the error is preserved, we consider whether the admission was harmless error. Commonwealth v. Federico, supra at 852.

Expert testimony "is admissible whenever it will aid the jury in reaching a decision, even if the expert's opinion touches on the ultimate issues that the jury must decide." Commonwealth v. Dockham, 405 Mass. 618, 628 (1989), quoting Simon v. Solomon, 385 Mass. 91, 105 (1982). There was no abuse of discretion in the decision to permit Martin's testimony.

Martin explained to the jury that bloodstain analysis or blood spatter analysis is "the study of blood once blood leaves the body and a force has acted on it." He explained further that, if a strike with a weapon is of sufficient force to break the skin, blood from the wound would be projected in a certain direction, based on the rules of physics. He testified that in the area of bloodstain pattern analysis, it is generally accepted that if a person is struck and the skin is lacerated, a subsequent strike would result in projected blood and there would potentially be cast-off from the blood found on the implement. When the implement is brought back, as a result of centrifugal force, blood is projected off the weapon and onto a surface such as a wall. Demonstrating, Martin testified that the shape of the tails on the bloodstains would be different depending on the manner in which the implement was swung.

The prosecutor asked Martin, without objection, whether, if there were cast-off, "it necessarily mean[s] that the person swinging the implement is going to get cast-off onto them?" to which Martin replied, "Not all the time. No, sir." Martin explained that the type of weapon used and the shape of the implement would dictate how the blood was distributed, and that it also would depend on the direction in which someone swung the weapon and the position of the victim; Martin demonstrated different directions of strike and the resulting direction of projection. Martin then described the victim's bedroom and the observed bloodstains, concluding that "the bloody event itself took place in [the] corner by [the] mattress in the southwest corner of the room." Over defense counsel's objection, the prosecutor asked: "Based on your training and experience and education in the field of bloodstain analysis, would you expect to see blood in this situation that you described on the perpetrator? ... [W]ould you expect to see any type of impact spatter or cast-off on the perpetrator of the crime?" Martin answered, "Not necessarily."19

Although the defendant argues that the expert testimony was not necessary and the jury could have understood the evidence without such testimony, Martin's explanation regarding cast-off spatter could have assisted the jury in understanding the various directions in which blood may travel after a person is struck with an instrument. Without this explanation, the jury might have believed, for example, that the perpetrator of such an attack will always end up covered with blood spatter. Cf. Commonwealth v. Federico, supra at 851 (in case involving child sexual abuse where there is no evidence of physical injury, "a medical expert may be able to assist the jury by informing them that the lack of such evidence does not necessarily lead to the medical conclusion that the child was not abused"). Martin did not opine whether the perpetrator in this case would have had cast-off blood on his person. Rather, Martin testified to observations he made at the scene, and explained the variables that could affect whether cast-off might be found on a person wielding a weapon and striking another in a position similar to that in which the victim was found.

c. DNA from victim's back left pocket. Pursuant to our duty under G. L. c. 278, § 33E, we consider an error in the prosecutor's closing argument that was not raised by the defendant. In his closing, the prosecutor told the jury that the DNA profile found in all four of the victim's jeans pockets "matched the profile of the defendant ... to an exclusion rate of ... 99.8 percent," and that for "all four of the pockets, the known standard from [the defendant] was collected and analyzed and compared to the swabs of all four pockets and to a 99.8 percent exclusion. [Ninety-nine point eight] percent of society is excluded but for [the defendant] and his paternal relatives." Although Drugan, the Commonwealth's DNA expert, testified that 99.8 per cent of the population could be excluded as a source of the DNA found in three of the victim's jeans pockets, there was no direct testimony about the exclusion rate for the DNA found in the back left pocket. The defendant did not object to the closing argument, or to Drugan's testimony about the back left pocket.20

Because "DNA evidence that a particular individual could not be excluded as a potential contributor of the DNA at issue should not be admitted without accompanying statistical evidence of the likelihood that the test could not exclude other individuals in a given population," Commonwealth v. Bizanowicz, 459 Mass. 400, 409-410 (2011), citing Commonwealth v. Mattei, 455 Mass. 840, 851-855 (2010), we consider the issues raised by the lack of such evidence to determine whether "there is a substantial likelihood that a miscarriage of justice has occurred." Commonwealth v. Wright, 411 Mass. 678, 681 (1992). See Commonwealth v. Riley, 467 Mass. 799, 807 (2014).

Drugan testified that Y-STR testing of swabs of the victim's pockets showed a mixture of DNA. At least three men contributed to the DNA found in the front right pocket of the victim's jeans, the front left pocket, and the back right pocket; Drugan testified that she identified a "major" profile within the mixture, that is, the contributor of one profile who contributed more cellular material than the other contributors. A major profile was found at sixteen loci for the front left and back right pockets, and at ten loci for the front right pocket. Explaining the significance of this match as to these three pockets, Drugan testified that, apart from the defendant's paternal relatives, 99.8 per cent of the population could be excluded as a source of the DNA with respect to DNA from these three pockets.21

As to the back left pocket, Drugan testified that her analysis of the DNA detected a major profile at three of the sixteen loci which matched the DNA profile of the defendant, and that "at the [thirteen] locations where there was not a major profile detected... I still observed [the defendant's] alleles" and "could not exclude him." She did not testify as to the "statistical evidence of the likelihood that the test could not exclude other individuals in a given population." Commonwealth v. Bizanowicz, supra at 409-410, citing Commonwealth v. Mattei, supra at 851-855. It is not apparent from the record whether, in light of the differences between the DNA findings as to the back left pocket and the findings as to the other three pockets, the statistical evidence would have been different from that of the other three pockets.22

Because it was based, in part, on evidence that was not before the jury, the prosecutor's argument should not have been made. See Commonwealth v. Beaudry, 445 Mass. 577, 580 (2005), quoting Commonwealth v. Coren, 437 Mass. 723, 730 (2002). In closing arguments, prosecutors may not misstate the evidence, but must tailor their remarks to ensure they remain properly grounded in the evidence. See Commonwealth v. Roy, 464 Mass. 818, 831-832 (2013). Nonetheless, the improper argument did not create a substantial likelihood of a miscarriage of justice. Whether the defendant's DNA matched that of the major profile in three of the victim's pants pockets, or four of those pockets, was not likely to have influenced the jury's conclusion. See Commonwealth v. Wright, supra at 682. It was not essential to the Commonwealth's case that the evidence establish that the defendant put his hand into four of the victim's pockets.23 Even if it had been established that the defendant's DNA matched that of the major profile in only three of the pockets, the jury could have inferred that the victim woke up before the defendant completed the search of her pockets.

Having reviewed the entire record pursuant to G. L. c. 278, § 33E, we discern no reason to reduce the conviction of murder in the first degree to a lesser degree of guilt or to order a new trial.

3. Conclusion. The order dismissing the defendant's conviction of armed robbery is vacated and set aside. The convictions of armed robbery and murder in the first degree are affirmed.

So ordered.