Wilkins, C.J.
This appeal, here on further appellate review, requires us to consider whether the evidence warranted a find[844]*844ing that the Commonwealth had met its burden of proving beyond a reasonable doubt that the defendant was criminally responsible. We conclude that the evidence warranted a finding that the defendant was criminally responsible and that the Appeals Court should not have ordered a directed verdict of not guilty by reason of insanity. Commonwealth v. Keita, 45 Mass. App. Ct. 550 (1998).
Additionally, the court has chosen this case as a vehicle to consider whether we should abandon our common-law rule that the Commonwealth must prove sanity (i.e., criminal responsibility) beyond a reasonable doubt in favor of a rule that a criminal defendant, asserting insanity as a defense, must prove his lack of criminal responsibility by a preponderance of the evidence.
A judge, at the end of a brief jury-waived trial in the Quincy District Court, found the defendant guilty of indecent assault and battery on a person over the age of fourteen years. G. L. c. 265, § 13H. The defendant had raised insanity as a defense, pursuant to Mass. R. Crim. P. 14 (b) (2), 378 Mass. 874 (1979). The sole issue on appeal is whether the evidence was sufficient to warrant a finding beyond a reasonable doubt that the defendant was sane. Although the defendant did not move for a required finding of not guilty by reason of insanity, we agree with the Appeals Court that, if the evidence did not permit a finding of criminal responsibility, his conviction would create a substantial risk of a miscarriage of justice. Id. at 551.
The victim testified that on November 21, 1996, she was a passenger on a moderately crowded Massachusetts Bay Transportation Authority (MBTA) subway train headed toward Quincy. The defendant boarded the train and sat across from her. The Appeals Court’s summary of the testimony continues as follows:
“[F]or about twenty minutes, [the defendant] stared at her while making obscene gestures and touching his clothes in the genital area, and saying, ‘Oh baby, you’re nice.’ She did not react to his conduct or acknowledge his' presence and, instead, feigned being engrossed in her book. When the victim arrived at her destination and attempted to disembark from the train, the defendant lunged for her, pushed her against the car doors of the train, groped her, and uttered obscenities, T want you. I want to fuck you.’ As the car doors opened and the victim broke to run, the [845]*845defendant told her, Tm gonna get you.’ As she ran from the train to summon police assistance, a man grabbed and held the defendant on the station platform. From what the victim could see as she ran, the man appeared as if he were going to punch the defendant. When she quickly returned with three uniformed MBTA officials, the defendant offered them no resistance.
“MBTA officer Miguel Rosario testified that he, another MBTA officer, and an MBTA inspector, all three in uniform, arrested the defendant. He was cooperative and his arrest uneventful. Rosario also recounted that the defendant, during the booking process immediately following his arrest, was docile and responsive to questions concerning his personal history.”
Id. at 552.
The Commonwealth then rested, and the defense called a well-qualified forensic psychologist who gave his opinion of the defendant’s mental condition. Based in part on the defendant’s medical history, which included ten admissions to Bridgewater State Hospital since 1982, and the opinion of a court psychologist that, on the day after his arrest, the defendant was suffering from a mental illness, the psychologist testified that the defendant was mentally ill. He testified that in his opinion the defendant was acutely mentally ill on the day of the attack and that the defendant would have had “substantial difficulties conforming his behavior to the requirements of the law.” On cross-examination, the witness provided information concerning the defendant’s perception of the events on the subway train, some of which we discuss when we consider the adequacy of the evidence to support a finding of sanity.
The Commonwealth offered no rebuttal evidence. The judge found the defendant guilty. On appeal, the Appeals Court set aside the guilty finding and ordered the entry of a judgment of acquittal by reason of the defendant’s lack of criminal responsibility. Id. at 558. We then granted the Commonwealth’s application for further appellate review.
1. The defendant was not entitled to a directed verdict of not guilty by reason of insanity. We have never taken away from a trier of fact the determination whether a defendant was criminally responsible when the evidence raised the issue. [846]*846Moreover, the evidence warranted the finding that the defendant was criminally responsible.
The Commonwealth had the burden of proving beyond a reasonable doubt that the defendant was criminally responsible at the time of the crime. See Commonwealth v. Kappler, 416 Mass. 574, 578 (1993); Commonwealth v. Kostka, 370 Mass. 516, 526 (1976). The Commonwealth, however, may prove sanity without presenting expert testimony. Commonwealth v. Brennan, 399 Mass. 358, 364 (1987). A trier of fact may reject the testimony of experts that a defendant lacked criminal responsibility and may infer sanity from the defendant’s conduct and the facts of the crime. See Commonwealth v. Kappler, supra at 579; Commonwealth v. Lunde, 390 Mass. 42, 47 (1983). We have also permitted the trier of fact to consider as evidence the so-called presumption of sanity. Commonwealth v. Kappler, supra at 583, citing Commonwealth v. Kostka, supra at 536. This inference or presumption is based on the trier of fact’s “common knowledge that a great majority of people are sane, and the probability that any particular person is sane.” Commonwealth v. Brennan, supra. A jury instruction concerning the presumption of sanity should be given in every case in which the question of the defendant’s criminal responsibility is raised.
We recognize the inconsistency between placing the burden of proof of sanity on the Commonwealth and, at the same time, allowing a presumption of sanity to satisfy, or even to support, that burden. See Commonwealth v. Kappler, supra at 590 (O’Connor, J., dissenting). That inconsistency, however, has been the law of the Commonwealth for decades. The tension created by that inconsistency becomes greater as the facts of the crime and the defendant’s conduct provide less and less of a basis for finding mental competence.
The Appeals Court found “nothing in the victim’s account of the defendant’s grotesque and bizarre conduct which bespeaks sanity.” Commonwealth v. Keita, supra at 555. Nor did that court see significant support for a finding of sanity in the defendant’s conduct after the crime was committed. Id. at 556. That court concluded that “[s]landing alone, the presumption is an insufficient basis upon which to conclude that a defendant is sane beyond a reasonable doubt.” Id. at 557. There is no doubt that this court has taken comfort in the fact that, in most cases, there was “other evidence which [the] jury [were] permitted to weigh in reaching their conclusion on the sanity issue.” Com[847]*847
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Wilkins, C.J.
This appeal, here on further appellate review, requires us to consider whether the evidence warranted a find[844]*844ing that the Commonwealth had met its burden of proving beyond a reasonable doubt that the defendant was criminally responsible. We conclude that the evidence warranted a finding that the defendant was criminally responsible and that the Appeals Court should not have ordered a directed verdict of not guilty by reason of insanity. Commonwealth v. Keita, 45 Mass. App. Ct. 550 (1998).
Additionally, the court has chosen this case as a vehicle to consider whether we should abandon our common-law rule that the Commonwealth must prove sanity (i.e., criminal responsibility) beyond a reasonable doubt in favor of a rule that a criminal defendant, asserting insanity as a defense, must prove his lack of criminal responsibility by a preponderance of the evidence.
A judge, at the end of a brief jury-waived trial in the Quincy District Court, found the defendant guilty of indecent assault and battery on a person over the age of fourteen years. G. L. c. 265, § 13H. The defendant had raised insanity as a defense, pursuant to Mass. R. Crim. P. 14 (b) (2), 378 Mass. 874 (1979). The sole issue on appeal is whether the evidence was sufficient to warrant a finding beyond a reasonable doubt that the defendant was sane. Although the defendant did not move for a required finding of not guilty by reason of insanity, we agree with the Appeals Court that, if the evidence did not permit a finding of criminal responsibility, his conviction would create a substantial risk of a miscarriage of justice. Id. at 551.
The victim testified that on November 21, 1996, she was a passenger on a moderately crowded Massachusetts Bay Transportation Authority (MBTA) subway train headed toward Quincy. The defendant boarded the train and sat across from her. The Appeals Court’s summary of the testimony continues as follows:
“[F]or about twenty minutes, [the defendant] stared at her while making obscene gestures and touching his clothes in the genital area, and saying, ‘Oh baby, you’re nice.’ She did not react to his conduct or acknowledge his' presence and, instead, feigned being engrossed in her book. When the victim arrived at her destination and attempted to disembark from the train, the defendant lunged for her, pushed her against the car doors of the train, groped her, and uttered obscenities, T want you. I want to fuck you.’ As the car doors opened and the victim broke to run, the [845]*845defendant told her, Tm gonna get you.’ As she ran from the train to summon police assistance, a man grabbed and held the defendant on the station platform. From what the victim could see as she ran, the man appeared as if he were going to punch the defendant. When she quickly returned with three uniformed MBTA officials, the defendant offered them no resistance.
“MBTA officer Miguel Rosario testified that he, another MBTA officer, and an MBTA inspector, all three in uniform, arrested the defendant. He was cooperative and his arrest uneventful. Rosario also recounted that the defendant, during the booking process immediately following his arrest, was docile and responsive to questions concerning his personal history.”
Id. at 552.
The Commonwealth then rested, and the defense called a well-qualified forensic psychologist who gave his opinion of the defendant’s mental condition. Based in part on the defendant’s medical history, which included ten admissions to Bridgewater State Hospital since 1982, and the opinion of a court psychologist that, on the day after his arrest, the defendant was suffering from a mental illness, the psychologist testified that the defendant was mentally ill. He testified that in his opinion the defendant was acutely mentally ill on the day of the attack and that the defendant would have had “substantial difficulties conforming his behavior to the requirements of the law.” On cross-examination, the witness provided information concerning the defendant’s perception of the events on the subway train, some of which we discuss when we consider the adequacy of the evidence to support a finding of sanity.
The Commonwealth offered no rebuttal evidence. The judge found the defendant guilty. On appeal, the Appeals Court set aside the guilty finding and ordered the entry of a judgment of acquittal by reason of the defendant’s lack of criminal responsibility. Id. at 558. We then granted the Commonwealth’s application for further appellate review.
1. The defendant was not entitled to a directed verdict of not guilty by reason of insanity. We have never taken away from a trier of fact the determination whether a defendant was criminally responsible when the evidence raised the issue. [846]*846Moreover, the evidence warranted the finding that the defendant was criminally responsible.
The Commonwealth had the burden of proving beyond a reasonable doubt that the defendant was criminally responsible at the time of the crime. See Commonwealth v. Kappler, 416 Mass. 574, 578 (1993); Commonwealth v. Kostka, 370 Mass. 516, 526 (1976). The Commonwealth, however, may prove sanity without presenting expert testimony. Commonwealth v. Brennan, 399 Mass. 358, 364 (1987). A trier of fact may reject the testimony of experts that a defendant lacked criminal responsibility and may infer sanity from the defendant’s conduct and the facts of the crime. See Commonwealth v. Kappler, supra at 579; Commonwealth v. Lunde, 390 Mass. 42, 47 (1983). We have also permitted the trier of fact to consider as evidence the so-called presumption of sanity. Commonwealth v. Kappler, supra at 583, citing Commonwealth v. Kostka, supra at 536. This inference or presumption is based on the trier of fact’s “common knowledge that a great majority of people are sane, and the probability that any particular person is sane.” Commonwealth v. Brennan, supra. A jury instruction concerning the presumption of sanity should be given in every case in which the question of the defendant’s criminal responsibility is raised.
We recognize the inconsistency between placing the burden of proof of sanity on the Commonwealth and, at the same time, allowing a presumption of sanity to satisfy, or even to support, that burden. See Commonwealth v. Kappler, supra at 590 (O’Connor, J., dissenting). That inconsistency, however, has been the law of the Commonwealth for decades. The tension created by that inconsistency becomes greater as the facts of the crime and the defendant’s conduct provide less and less of a basis for finding mental competence.
The Appeals Court found “nothing in the victim’s account of the defendant’s grotesque and bizarre conduct which bespeaks sanity.” Commonwealth v. Keita, supra at 555. Nor did that court see significant support for a finding of sanity in the defendant’s conduct after the crime was committed. Id. at 556. That court concluded that “[s]landing alone, the presumption is an insufficient basis upon which to conclude that a defendant is sane beyond a reasonable doubt.” Id. at 557. There is no doubt that this court has taken comfort in the fact that, in most cases, there was “other evidence which [the] jury [were] permitted to weigh in reaching their conclusion on the sanity issue.” Com[847]*847monwealth v. Walker, 370 Mass. 548, 581, cert. denied, 429 U.S. 943 (1976), and cases cited. See Commonwealth v. Lunde, supra at 48-49; Commonwealth v. O’Brien, 377 Mass. 772, 781 (1979). The fact that there was evidence beyond the presumption in support of a finding of criminal responsibility tells us nothing, however, about the right answer when there is no such evidence.1
This court has never held that the presumption of sanity is alone insufficient to meet the Commonwealth’s burden. To the contrary, the court intimated in Commonwealth v. Clark, 292 Mass. 409 (1935), that “the fact that a great majority of men are sane, and the probability that any particular man is sane, may be deemed by a jury to outweigh, in evidential value, testimony that he is insane.” Id. at 415. We were explicit in Commonwealth v. Smith, 357 Mass. 168 (1970), that the jury have the right to “infer that the defendant is sane from their common knowledge of the fact that a great majority of men are sane, and of the probability that any particular man is sane. It is for the jury to decide in each case whether they draw that inference.” Id. at 180. The judge “cannot direct the jury how they shall decide.” Id2 See Commonwealth v. Gould, 380 Mass. 672, 679 (1980). In his dissent in Commonwealth v. Kappler, supra, Justice O’Connor correctly noted that “a jury may rely on the so-called ‘presumption of sanity’ to conclude that a defendant was sane beyond a reasonable doubt.” Id. at 589 (O’Connor, J., dissenting).
There are circumstances in which the court has ordered, or one or more Justices would have ordered, a new trial because the Commonwealth’s case on criminal responsibility appeared weak. It may be significant that all these cases involved appeals [848]*848from convictions of murder in the first degree, reviewed pursuant to G. L. c. 278, § 33E. In Commonwealth v. Cox, 327 Mass. 609, 615 (1951), the only expert testimony was that the defendant was not criminally responsible and the defendant’s conduct lent no support for a finding of criminal responsibility. A majority of the court, acting pursuant to G. L. 278, § 33E, ordered a new trial because the verdict was against the weight of the evidence. In doing so, the court said, “[t]he fact that most men are sane, and a rational probability that the defendant, too, may have been sane on [the date of killing] notwithstanding what he then did and later said about it, seem to us inadequate reasons upon which to disregard this unanimous medical opinion that he was not.” Id. Two Justices in dissent in Commonwealth v. Francis would have ordered a new trial under G. L. c. 278, § 33E, because all experts concluded that the defendant was not criminally responsible, but the jury may have misunderstood some of the expert medical opinion. Commonwealth v. Francis, 355 Mass. 108, 112 (1969) (Whittemore and Cutter, JJ., dissenting). See Commonwealth v. Kostka, supra at 539 (Hennessey, C.J., dissenting in part, with whom Kaplan, J., joined) (new trial should be ordered pursuant to G. L. c. 278, § 33E); Commonwealth v. Mutina, 366 Mass. 810, 816 (1975) (pursuant to § 33E, new trial ordered, in part, because finding of sanity “was against the weight of the evidence”). Cf. Commonwealth v. Cullen, 395 Mass. 225, 231 n.4 (1985) (in case not governed by § 33E, defendant authorized to file motion for new trial to seek consideration of weight of evidence on insanity). We are aware of no case in which we have ordered the entry of a judgment of not guilty by reason of the defendant’s lack of criminal responsibility.
The question then, at most, would be whether we should order a new trial because, as the defendant argues, the Commonwealth had no evidence other than the presumption of sanity in support of its burden of proof. The Commonwealth argues to the contrary that there was evidence of sanity. We agree with the Commonwealth. We concur with the Appeals Court that there is nothing in the defendant’s conduct prior to his arrest that would support a finding of sanity. The Commonwealth points to police testimony that, when arrested, the defendant did not struggle, did not act in an erratic way, and was cooperative. When the defendant was booked at the police station, he was again cooperative, answered all the questions, and presented no [849]*849difficulty. In an interview with the psychiatrist who testified on his behalf, the defendant denied that he did anything criminally wrong but said that his memory was fuzzy as to what happened on the train. The defendant’s version of the alleged offense was that he accidentally brushed up against a woman passenger.3 This suggests that the defendant knew what lawful conduct was. An inference was warranted that he lied about the incident. This inference, if made, would tend to suggest that he appreciated the wrongfulness of his conduct.
The evidence that we have recited, thin as it may be, is sufficient along with the presumption of sanity, not only to warrant the judge’s finding of guilt, but also to justify our not ordering a new trial. See Commonwealth v. Lunde, supra at 47-48. We conclude that the judgment should be affirmed.
2. When we allowed the Commonwealth’s application for further appellate review, we gave notice that “the court will consider whether to adopt a rule that the burden is on a criminal defendant to prove lack of criminal responsibility by a preponderance of the evidence, and whether, if such a rule were to be adopted, it may properly and should be applied to this case.” If we were to announce a new rule placing the burden on a criminal defendant to prove by a preponderance of the evidence that he or she lacked criminal responsibility, we would make the rule prospective only. The more difficult question is whether we should change the burden of proof on criminal responsibility from the prosecution (proof beyond a reasonable doubt that the defendant did not lack criminal responsibility) to the defendant (proof by a preponderance of the evidence that the defendant lacked criminal responsibility). We conclude that we should not.
Currently, we place the burden on the Commonwealth to prove a defendant’s criminal responsibility if the defendant asserts an “insanity defense” and the evidence permits a reasonable doubt about the defendant’s criminal responsibility at the time of the alleged crime. In this process, we require the Commonwealth to prove negatives beyond a reasonable doubt: that [850]*850the defendant did not have a mental disease or defect at the time of the crime and, if that is not disproved beyond a reasonable doubt, that no mental disease or defect caused the defendant to lack substantial capacity either to appreciate the criminality of his conduct or to conform his conduct to the requirements of law. Commonwealth v. McHoul, 352 Mass. 544, 546-547 (1967). In the McHoul case, this court adopted the definition of criminal responsibility of the Model Penal Code § 4.01 (Proposed Official Draft 1962). Id. at 555.4 When the burden of proof is on the Commonwealth, jury instructions according to these principles are unavoidably complicated. We grant that it would be easier to instruct a jury, and for the jury to understand, that a defendant has the burden of proving, by a preponderance of the evidence, that he or she had a mental disease or defect that resulted in his or her lack of a substantial capacity either to appreciate the wrongfulness of his or her conduct or to conform his or her conduct to the requirements of the law, or both.
Just over five years ago, Justice Abrams, concurring in Commonwealth v. Kappler, supra, stated a strong preference for placing the burden of proving the lack of criminal responsibility on the defendant, as thirty-six jurisdictions, including the Federal government, then did.5 Id. at 601 (Abrams, J., concurring). Now, thirty-eight jurisdictions, including the Federal court system, place the burden of proof of insanity on the defense. Most do so by statute.6 Eight States have done so by common-[851]*851law rule.7 Expert commentary tends to disagree with the majority view and favors placing the burden on the prosecution to prove criminal responsibility. See, e.g., Model Penal Code §§ 1.12(3)(a), 4.03(1); Underwood, The Thumb on the Scales of Justice: Burdens of Persuasion in Criminal Cases, 86 Yale L.J. 1299 (1977); Ashford, Presumptions, Assumptions, and Due Process in Criminal Cases: A Theoretical Overview, 79 Yale L.J. 165 (1969). For an exhaustive list of authorities rejecting the shift of the burden of persuasion to the defendant on the issue of insanity, see State v. James, 393 N.W.2d 465, 471 (Iowa 1986) (Lavorato, J., dissenting).
The Constitution of the United States does not bar placing on a criminal defendant the burden of proving that he lacked criminal responsibility at the time of the alleged crime. See Martin v. Ohio, 480 U.S. 228, 236 (1987); Rivera v. Delaware, 429 U.S. 877 (1976); Leland v. Oregon, 343 U.S. 790, 799 (1952). Cf. Patterson v. New York, 432 U.S. 197, 201-202 (1977). Almost every State that has considered the question [852]*852under its Constitution has concluded that due process of law does not require that the prosecution assume the burden of proving a criminal defendant’s criminal responsibility.8 If sanity were an element of the crime to be proved, it would, of course, be unconstitutional to place the burden on the defendant to prove his or her sanity. See Mullaney v. Wilbur, 421 U.S. 684, 699 n.24 (1975); In re Winship, 397 U.S. 358, 364 (1970).9
When the New York Court of Appeals considered the constitutionality, under its Constitution, of a 1984 statute that shifted the burden of proof on insanity to defendants, a divided court upheld the statute. People v. Kohl, 72 N.Y.2d 191, 199 (1988) (five-to-two decision). The court acknowledged that, if a defendant is unable to appreciate the nature and consequences of his conduct (i.e., does not appreciate the criminality of his conduct), “it may be difficult to support a finding, at least in some cases, that the person had ‘conscious objective’ [statutory language] to kill the victim.” Id. at 198. In such a case, “the affirmative defense statute suffers the potential of impermissibly shifting to defendant the burden of disproving the formation of [853]*853conscious objective to kill another human being, and the statute as applied could be unconstitutional.” Id. Although, “in a particular case, this potentiality could sow confusion and erroneous application of rules among juries with respect to the People’s burden of proving the element of intent and defendant’s burden of proving the affirmative defense of insanity,” id. at 198-199, the court concluded that the problem could be alleviated by jury instructions that emphasized the prosecution’s burden of proving all elements of criminal intent beyond a reasonable doubt. Id. at 199. The dissent took the position that, because “there can be no crime without a sane mind, the burden of proof on the issue of mental competency must be borne by the state.” Id. at 204 (Hancock, J., dissenting, with whom Kaye, J., joined).
We now state our reasons for continuing to require the Commonwealth to prove beyond a reasonable doubt that the defendant was criminally responsible for his conduct. A long-established tradition in our criminal law is that a person who was insane at the time of an alleged crime, that is, one who lacked criminal responsibility, should not be convicted of that crime. See Commonwealth v. Rogers, 7 Met. 500, 501 (1844); Commonwealth v. Kostka, supra at 532, and cases cited. Cf. Commonwealth v. Matchett, 386 Mass. 492, 507 (1982) (criminal liability not justified absent some culpable mental state). It is also a well-established tradition in our jurisprudence that the prosecution must prove each element of a crime beyond a reasonable doubt in order to assure, as far as is reasonably possible, that an innocent person is not convicted. On the same principle, we should require proof beyond a reasonable doubt that a criminal defendant is criminally responsible in order to assure, as far as is reasonably possible, that an insane person is not convicted. There is no theoretical justification for maintaining a lower standard for the proof of sanity than for the proof of guilt. ,
Almost one hundred years ago this court made clear for the first time “that the burden of proof was upon the Commonwealth to satisfy [the jury] beyond a reasonable doubt that [the defendant] was' legally responsible at the time, or in other words was sane.” Commonwealth v. Johnson, 188 Mass. 382, 388 (1905). In the absence of controlling legislation, we could change our judge-made rule that places the burden on the Commonwealth. Although we need not leave it to the Legislature to [854]*854act and although a change would not violate Federal due process requirements, the fact that the common-law rule has prevailed for almost one hundred years, without legislative change, in the face of the enactment of statutes in many other jurisdictions placing the burden of proof on the defendant, influences us not to shift the burden of proof of insanity to the defendant. The conflicting burdens noted by both opinions in People v. Kohl, supra, cause us further pause. There is no good reason to tolerate a lower burden on the Commonwealth when the question is the defendant’s sanity than when the question is the defendant’s guilt. A further, practical consideration is that experience in this Commonwealth has shown that it is most difficult for a defendant to prevail on a claim of insanity even with the burden on the Commonwealth to prove criminal responsibility beyond a reasonable doubt. A case for shifting the burden of proof to the defendant to prove his insanity has not been made.
Judgment affirmed.