A Bristol County grand jury returned two indictments charging the defendant, Elizabeth Roderiques, with offenses that resulted in severe injuries to her infant child. The first indictment charged her with committing an assault and battery upon a child under fourteen years of age causing substantial *516bodily injury. See G. L. c. 265, § 13J(¿>), second par. The second charged her with wantonly and recklessly permitting an assault and battery upon a child that caused the child substantial bodily injury. See G. L. c. 265, § 13J(¿>), fourth par.1 At the defendant’s request and with the Commonwealth’s agreement, the trial judge charged the jury that reckless endangerment of a child, see G. L. c. 265, § 13L, was a lesser included offense of the offense charged in the second indictment.
After trial, a Superior Court jury acquitted the defendant of the two offenses charged in the indictments but found her guilty of reckless endangerment of a child. The defendant then filed a motion to vacate the conviction, claiming that reckless endangerment was not a lesser included offense and that the charge she had requested was erroneous and should not have been given. The judge denied the motion and the defendant appeals, asserting that (1) reckless endangerment is not a lesser included offense of wantonly or recklessly permitting an assault and battery on a child causing substantial bodily injury; (2) there was no rational basis in the evidence to present the charge of wantonly or recklessly creating a risk of serious bodily injury to a child; and (3) the Commonwealth’s expert impermissibly offered an opinion on an ultimate issue in the case. We affirm.
Facts. When the record is viewed in the light most favorable to the Commonwealth, Commonwealth v. Latimore, 378 Mass. 671, 676-677 (1979), the jury could have found that, in December, 2003, the seventeen year old defendant lived with her boyfriend, Shawn Cambria, and her infant son in a New Bedford apartment. On the afternoon of December 23, 2003, the defendant took the baby, then seven weeks of age, to a pediatrician because he was displaying flu-like symptoms and had kept her awake throughout the previous evening with his fussiness and refusal to eat. The treating physician gave her some medication, and she returned *517to her apartment. Apart from the flu symptoms and a small bruise on his cheek, nothing out of the ordinary about the infant was discovered during the visit.
During the night of December 23 and the early morning hours of December 24, the defendant, Cambria, and the baby were alone in the apartment. At some point, the defendant fell asleep with Cambria on a pull-out sofa in the apartment’s living room. The baby was in a recliner on the floor close by the defendant’s head. Several times during the night, the baby awakened the defendant with his fussing, and she got up to feed and change him. At one point, the defendant was awakened by the baby, who was crying because he had lost his pacifier. The defendant asked Cambria to put the pacifier back in his mouth. Cambria complied, although he told the defendant that the baby was a “crybaby” and told the infant to “stop fussing.”
At approximately 9:00 a.m. on December 24, the defendant telephoned her father and, in an hysterical voice, told him that the infant’s arm had been dislocated. The father and his girlfriend’s daughter arrived at the apartment within minutes of the call and discovered the infant lying on a bed crying, with Cam-bria sitting beside him. The baby’s arm was bent and red. They rushed him to a local hospital where he was examined and later airlifted to Boston Children’s Hospital.
Before the airlift, two New Bedford police officers observed the baby and saw that he had a large red bruise on his upper right arm, a bruise on his nose, a bruise on his left cheek that extended to his left ear, and bruising on his abdomen and upper thighs. When the infant was finally examined at Children’s Hospital, doctors discovered that he had suffered a fracture of the right upper arm, or humerus; multiple fractures to both legs; rib fractures; a compression fracture of the spine; and a fractured clavicle.
The infant’s injuries fell into at least three distinct categories. The break in his right lower right leg was a so-called “bucket handle fracture,” produced by a forceful pulling or twisting at the end of the limb and a frequent component of what is known as shaken baby syndrome. The compression fracture to the spine was produced by a force that traveled along the spine vertically, such as the force generated when a child is slammed down on his buttocks. The remaining fractures were of general *518traumatic origin. All of the injuries would have required a significant amount of force and would have produced significant pain, producing an outcry from the baby and making him difficult to console.2
When interviewed by the social workers and the police, the defendant first said that the baby had slept in his bassinet that night, that she fed him at 2 a.m. and 6 a.m., and that she noticed nothing out of the ordinary until she awoke up at 9 a.m. and discovered the significant bruising on his arm. Later, the defendant said that she had slept on the sofa bed with Cambria and that the infant had been in a recliner on the floor near her head. When asked by a State police investigator if she knew who had injured the baby, the defendant responded “something to the effect of ‘It wasn’t me. It must have been Shawn’ ” (Cambria), who, she indicated, had been yelling at the baby that evening to stop crying and sometimes would “handle the baby a little more aggressively than appropriate.”
For his part, Cambria said that the defendant must have hurt the baby because he had not done so. However, he did say that he had been playing “air drums” with the baby on the evening of December 23, describing “air drums” as a maneuver in which he grabbed the infant’s arms and waved them around in the air as if the baby were playing drums. Cambria, who claimed to suffer from periodic blackouts, also said that it was possible that he had stepped on the baby on the recliner when he got up during the evening to use the bathroom or get a drink of water, though he did not think that had happened.
Discussion. Against that backdrop, the defendant first argues that reckless endangerment of a child, an offense requiring proof that the defendant “wantonly or recklessly engage[d] in conduct that create[d] a substantial risk of serious bodily injury . . . to a child or wantonly or recklessly fail[ed] to take reasonable steps to alleviate such risk where there is a duty to act,” G. L. c. 265, § 13L, inserted by St. 2002, c. 322, § 2, is not a lesser included offense of G. L. c. 265, § 13J(¿»), fourth par., the *519offense with which the defendant was actually charged in the second indictment.3
Although the Commonwealth and the defendant are sharply divided on the question, we find it unnecessary to resolve it. In our view, even if the trial judge erred in giving the instruction because § 13L is not, strictly speaking, a lesser included offense of any of the offenses set out in § 13J(¿>), the defendant invited the error, and no substantial risk of a miscarriage of justice arose when the judge accepted the invitation.4
We have discussed the concept of invited error in earlier decisions. In Commonwealth v. Knight, 37 Mass. App. Ct. 92, 99-100 (1994), for example, we faced a claim that a manslaughter conviction should be reversed because the manslaughter instruction was flawed and, although requested by the defendant, was premised on a theory our jurisprudence did not recognize. In rejecting that claim, we explained that
“[a]s the challenged instruction was given upon the specific request of defense counsel at trial, to the extent that the issue is reviewable at all,[5] . . . the defendant on appeal bears a heavy burden in attempting to have his conviction *520overturned. He must demonstrate at least a substantial risk of a miscarriage of justice.”
See Commonwealth v. Simcock, 31 Mass. App. Ct. 184, 196 (1991) (“The consequences of trial tactics may not be converted after conviction into alleged errors by the judge. . . . The less is this so if the tactics produce some measure of success, as they did here”); Commonwealth v. Grant, 49 Mass. App. Ct. 169, 171 (2000) (“Where the error [in giving an instruction] was invited by the defendant, our review is limited to whether a substantial risk of a miscarriage of justice occurred”). See also Commonwealth v. Vinnie, 428 Mass. 161, 180 (1998) (conviction of murder in first degree affirmed even though judge did not instruct on murder in second degree because, in part, defendant asked that instruction on murder in second degree be omitted).
Because the defendant requested the instruction she now challenges, we limit our review, in accordance with the cited cases, to determining whether the instruction, if improper, created a substantial risk of a miscarriage of justice. In approaching that question, we do not look at a theoretical case tided in some theoretical fashion on theoretical issues and ask whether a miscarriage of justice were possible. Instead, we look at this case and the issues this case presented, asking whether a substantial risk of a miscarriage of justice in fact existed. We think it did not.
It was uncontested that the baby’s injuries occurred during a period when the defendant and Cambria were alone with him. It was uncontested that the injuries were extensive and traumatic. And it was uncontested that infliction of the injuries would have caused the baby to “cry out loud ... for some period of time.” Those uncontested facts were accompanied by strong evidence that one of the fractures resulted from someone twisting the infant’s leg forcefully enough to break it, that another resulted from a force like that produced by slamming the infant down on his buttocks hard enough to compress a vertebra to the point of fracture, and that the remaining fractures resulted from the application of other forces. The nature of the injuries suggested, therefore, that they occurred serially, not from application of a single force. Finally, strong evidence of consciousness of guilt flows from the defendant’s claim that, although awakened by the baby’s fussiness at various points throughout the night, she did not hear what all experts agreed would have been the *521infant’s loud cries as someone engaged in a process of breaking his bones.
That evidence, albeit circumstantial, was sufficient to support a conviction on the second indictment as charged on a theory that the defendant knew Cambria was committing assault and batteries on the child and that she wantonly or recklessly failed to take any steps to rescue him or otherwise intervene in Cambria’s as-saultive onslaught. See Commonwealth v. Garcia, 47 Mass. App. Ct. 419, 422-423 (1999). See generally Commonwealth v. Robinson, 74 Mass. App. Ct. 752, 759 (2009).
The essential difference between the offense as charged in the second indictment and the “lesser included offense” on which the defendant requested an instruction is that the lesser offense did not require proof that anyone battered the infant. In theory, conviction of that offense could rest on any wanton or reckless conduct by the defendant that created or failed to alleviate a substantial risk of serious bodily harm to the infant. But, as noted earlier, in assessing the likelihood of a substantial risk of a miscarriage of justice, theory gives way to reality. On this record, there was no evidence of any risk-creating conduct by the defendant apart from her failure to protect the baby from the force of Cambria’s blows. Consequently, what the defendant labeled as the lesser included offense was simply a vehicle for penalizing less severely conduct that would have warranted conviction of a greater offense and imposition of a greater penalty.6 Even if erroneously charged, therefore, the lesser included offense instruction created no substantial risk of a miscarriage of justice.7
*522The defendant next argues that the Commonwealth’s expert witness, a pediatrician named Jennifer Denton, impermissibly offered an opinion on an ultimate issue in the case when she testified that, in her opinion, the baby had not suffered “accidental injuries” and that all of his injuries could not have been caused by someone stepping on him while he slept in the recliner.
In general, expert testimony is admissible when it bears on a factual issue that is “beyond the jury’s common knowledge and [the testimony] may aid them in reaching a decision.” Commonwealth v. Colin C., 419 Mass. 54, 60 (1994). See Mass. G. Evid. §§ 701, 702 (2010). “The admission of expert testimony lies ‘largely in the discretion of the trial judge,’ ” Commonwealth v. Hudson, 417 Mass. 536, 540 (1994), quoting from Commonwealth v. Maltais, 387 Mass. 79, 93 (1982), and as a consequence, “[a] judge’s decision to admit expert testimony is subject to review only for abuse of discretion.” Commonwealth v. Shanley, 455 Mass. 752, 762 (2010).
Whether the injuries suffered by the baby could have been caused by someone stepping on him on a recliner was squarely within the area where professional expertise was both helpful and appropriate. While Dr. Denton’s opinion that the injuries were not “accidental” is more judgmental, that testimony simply summarized testimony that could have been elicited through a long series of entirely proper hypothetical, and it did not purport to assign responsibility for causing the injuries. In any event, “[a]n opinion within the domain of the expert’s professional knowledge may be admissible even if the expert’s testimony touches on the ultimate issues before the jury.” Commonwealth v. Woods, 419 Mass. 366, 374-375 (1995). The judge did not abuse his discretion by allowing admission of the challenged testimony.
Judgment affirmed.
We note that the statute uses the disjunctive “or” to join “wantonly” and “recklessly,” but the indictment uses the conjunctive “and.” “Where a crime can be committed in any one of several ways, an indictment properly charges its commission in all those ways, using the conjunction ‘and’ in joining them.” Commonwealth v. Dowe, 315 Mass. 217, 219-220 (1943). “In that case, the defendant may be convicted if it is proved that he committed the crime in any of those ways.” Smith, Criminal Practice and Procedure § 15.9 (3d ed. 2007).
The Commonwealth’s expert and the defendant’s both agreed that the injuries would have produced pain sufficient to make the baby “cry out loud hard for some period of time,” though they differed in their assessment of the length of time the crying would have lasted and the point at which the baby, who was not crying by the time he arrived at the hospital, could have been consoled.
General Laws c. 265, § 13J(Z>), inserted by St. 1993, c. 340, § 2, describes a number of offenses. The offense charged in the second indictment required proof that the defendant, “having care and custody of a child, . . . wantonly or recklessly permitted] another to commit an assault and battery upon such child, which assault and battery cause[d] substantial bodily injury” to him.
The offense proscribed by G. L. c. 265, § 13L, is a misdemeanor and, therefore, does not require prosecution by indictment. See Mass.R.Crim R 3(b), as appearing in 442 Mass. 1502 (2004). Consequently, even if § 13L does not contain a lesser included offense, inquiry into whether the instruction created a substantial risk of a miscarriage of justice is both necessary and appropriate. See Commonwealth v. Bynoe, 49 Mass. App. Ct. 687, 692-693 (2000).
At this point in Knight, we cited Lannon v. Commonwealth, 379 Mass. 786, 792-793 (1980) (“The petitioner cannot now object to the judge’s use of wording which his own counsel proposed for inclusion in the instructions”), and Commonwealth v. Gladney, 34 Mass. App. Ct. 151, 158 n.3 (1993) (“Ordinarily, we would not review an instruction requested by defense counsel. We do so here out of an abundance of caution and fairness and because the defendant claims that the incorrect instruction resulted from trial counsel’s ineffectiveness”). In a footnote in Knight, 37 Mass. App. Ct. at 100 n.2, we also observed that “there is abundant Federal case law to the effect that invited error is not reviewable,” citing several Federal decisions. As in Gladney, we proceed with our review out of an abundance of caution and fairness.
In fact, the Commonwealth’s closing invited the jury to draw from the evidence an inference that the young defendant was exhausted and overwhelmed by a number of circumstances on the night that the baby was injured.
The defendant also argues that even if reckless endangerment is a lesser included offense, there was no rational basis for giving the instruction because, in line with cases such as Commonwealth v. Santo, 375 Mass. 299, 305-306 (1978), such an instruction is appropriate only if there is a rational basis for acquitting the defendant of the greater charge and convicting her of the lesser. Here, she appears to maintain, the evidence provided no such rational basis. If the defendant is correct, and we might agree that she is, then the effect of the instruction under the circumstances this record reveals was to give her a benefit she sought but to which she was not entitled. She cannot now complain that bestowal of the benefit was error. See generally Commonwealth v. Curtis, 417 Mass. 619, 632 (1994); Commonwealth v. Allen, 76 Mass. App. Ct. 9, 10 n.3 (2009).