Following a jury-waived trial in Superior Court, the defendant was convicted of possession with intent to distribute cocaine, in violation of G. L. c. 94C, § 32(A)(c), and with committing this offense within one thousand feet of a school, in violation of G. L. c. 94C, § 321. At issue was whether the defendant intended to distribute a 2.71 gram piece of crack cocaine found in his sock, or whether it was intended for personal use.
*840Moments before the trial which resulted in these convictions, the trial judge accepted the defendant’s guilty pleas to three other indictments: two charging him with possession with intent to distribute cocaine and a third charging him with conspiring to violate the controlled substance laws over a three-month period in late 1997 and early 1998. On appeal from the judgments of conviction, the defendant argues (1) that it was error to admit on the issue of intent (a) the opinion testimony of a police officer who testified that the facts were consistent with drug distribution; and (b) the incidents of prior drug distribution and conspiracy to which he had just pleaded guilty; and (2) that, in light of one or both of these alleged errors, the evidence was insufficient to permit a finding beyond a reasonable doubt that the defendant intended to distribute or to do so within one thousand feet of a school. We reverse on the ground that, in the circumstances of this case, it was an abuse of discretion to admit the incidents of prior drug distribution and conspiracy, and the remaining evidence was insufficient to support the guilty findings.
1. Evidence of intent to distribute. The Commonwealth presented the following evidence. On February 17, 1998, shortly before 10 p.m., two police officers spotted the defendant sitting with a female companion in a parked car in a commercial section of Pittsfield and arrested him on an outstanding warrant for distribution of cocaine. The defendant was found to possess a pager and a single piece of what appeared to be crack cocaine contained in a plastic bag and hidden in his right sock. No other drug paraphernalia or smoking apparatus was found on the defendant, and no money was found on him, on his companion, or in the car. The State laboratory later confirmed that the substance in the plastic bag was a cocaine derivative weighing 2.71 grams.
(a) One of the arresting officers, Glenn Civello, testified that, at the time of the defendant’s arrest, the most common way that crack cocaine was sold on the street was in packages of one-tenth of a gram selling for twenty dollars apiece. According to Civello’s calculation, the amount of cocaine found in the defendant’s possession was equivalent to twenty-seven such packages, with a total potential street value of $540. In his *841opinion, this amount together with the other circumstances of the arrest were “consistent with distribution.” Civello noted that the defendant had no smoking apparatus but had an operational pager “so he never misses a sale or a person never misses a sale. They are always in contact with their customers.” The defendant’s objection and motion to strike this testimony were denied.1
Civello further opined that the cocaine found on the defendant was not consistent with personal use because “if it was for personal use, it would have been in a smaller increment.” He explained that a crack cocaine user normally would consume a tenth of a gram in one session and, although a user might engage in six to ten such sessions a day, it would not be common for a user to possess a full day’s supply at one time because “people have trouble getting . . . that much money for crack cocaine.” Instead, “[pjeople usually just go out for more” by finding their “connection” five or six times per day.
On cross-examination, Civello acknowledged that it is “quite common” for sellers of crack cocaine to be users as well, and that the piece found on the defendant’s person would have cost only $140 or $150 even though it would have been worth substantially more if divided for sale. He further acknowledged that “it really pays” for a user to buy cocaine in volume and that, in his experience, users, including dealer-users, may consume $100 worth of crack cocaine in a day. On redirect, Civello testified that dealer-users, who are “the only ones that could afford it,” may smoke an entire “eight ball” (a piece weighing roughly 3.5 grams or an eighth of an ounce) by themselves over a period of three or four days.
(b) Other evidence elicited at trial that bore on the issue of *842intent to distribute consisted of the factual statements by the Commonwealth to which the defendant agreed when he entered his guilty pleas in the prior cases.2 Before the opening statements and before receiving any evidence, the trial judge ruled that these prior bad acts would be admitted because they were close enough in time to the offenses being tried to be relevant to the defendant’s intent or state of mind.
The first of the prior bad act incidents took place on December 5, 1997, shortly before 8 p.m., at a residence at 39 Springside Avenue, in Pittsfield. An undercover State trooper went to this location to meet with a woman identified as Charlene Crockwell, who had agreed to sell him an eighth of an ounce of cocaine which was about to be delivered by her supplier. The defendant then arrived, and after he spoke privately with Crockwell in another area of the apartment, Crockwell handed a package to the trooper and asked him for $150. The trooper turned to the defendant and told him that he wished to pay only $140. The defendant initially insisted on the full amount but eventually agreed to take $140. The trooper handed the money to Crockwell and took the package, which later proved to contain crack cocaine.
The second prior bad act incident took place on January 2, 1998, at approximately 4 p.m., at a residence at Riverview West Apartments in Pittsfield. Earlier that day, a different undercover *843State trooper had called the apartment and spoken to an individual named Christine Hebert about exchanging a stereo for drugs. When the trooper brought the stereo over, he was met at the door by the defendant who was holding a bag of what appeared to be packages of crack cocaine. The defendant invited the trooper inside and examined the stereo. Hebert then produced a package of crack cocaine for the trooper. When the trooper indicated that he thought he was entitled to a larger quantity, the defendant advised Hebert as to how much more she should provide, and she did as he directed. Tests later confirmed that the items provided to the trooper were crack cocaine.
The facts pertaining to the defendant’s guilty plea on the conspiracy charge were that on a number of occasions between November 1, 1997, and February 6, 1998, he acted in concert with eight other individuals to distribute crack cocaine out of two Pittsfield residences: 39 Springside Avenue and an apartment at Riverview West. The defendant’s companion at the time of his arrest was not named as one of these coconspirators; nor was she identified as being present or playing any role whatsoever with respect to any of the prior bad acts.
2. Admission of prior bad act evidence. Our consideration of this issue begins, as it must, by recognizing the overarching principle that “the prosecution may not introduce evidence that a defendant previously has misbehaved, indictably or not, for the purposes of showing his bad character or propensity to commit the crime charged,” even though such evidence may be admissible for another purpose. Commonwealth v. Helfant, 398 Mass. 214, 224 (1986). See Commonwealth v. Jackson, 417 Mass. 830, 835-836 (1994); Commonwealth v. Kater, 432 Mass. 404, 414 (2000). The exclusion of propensity evidence is grounded in a fundamental assumption of our criminal law: that a defendant should have a fair trial on the offenses charged and should not be convicted principally because of previous antisocial behavior. As Justice Cardozo observed, “In a very real sense a defendant starts his life afresh when he stands before a jury . . . Inflexibly the law has set its face against the endeavor to fasten guilt upon him by proof of character or experience predisposing to an act of crime.” People v. Zackow*844itz, 254 N.Y. 192, 197 (1930). This observation is no less pertinent when a defendant is tried not by a jury, but by a judge. Commonwealth v. Welcome, 348 Mass. 68, 71 (1964) (refusing to draw distinctions between jury and jury-waived cases with respect to the application of the rule). See Commonwealth v. Darby, 37 Mass. App. Ct. 650, 655-656 (1994).
To be sure, notwithstanding this general principle, prior bad acts find their way into criminal trials in a number of different contexts. Such evidence may be admitted, in the trial judge’s discretion, to show, for example, “a common scheme, pattern of operation, absence of accident or mistake, identity, intent or motive.” Commonwealth v. Helfant, 398 Mass. at 224. See Commonwealth v. Hanlon, 44 Mass. App. Ct. 810, 817-818 (1998), and cases cited.3 These uses of prior bad act evidence have been endorsed even though, as noted in Hanlon, there are those who have questioned the logic and coherence of allowing prior bad acts to show intent or “inclination” when they are not allowed to demonstrate a defendant’s propensity to commit the crime charged. Id. at 818 n.5. See United States v. Rubio-Estrada, 857 F.2d 845, 856 (1st Cir. 1988), in which the majority opinion upheld the admission under Federal Rule of Evidence 404(b) of a prior conviction for drug distribution to prove that the defendant knew drugs were present in his house and intended to distribute them, while the dissent opined that “bad character, the forbidden inference, provided the only logical link between the prior bad act and the fact[s] to be proved.”
In ruling on the admissibility of prior bad acts, the analysis required of the trial judge will vary depending upon the nature *845and purpose of the evidence being offered.4 However, ail cases where prior bad acts are offered invite consideration of the potency of this type of evidence, the risk that it may be misused, and the importance, in jury trials, of delivering careful limiting instructions. Although the ruling is committed to the trial judge’s discretion, it will be reviewed on appeal for palpable error. See Commonwealth v. Fordham, 417 Mass. 10, 22 (1994); Commonwealth v. Hubbard, 45 Mass. App. Ct. 277, 279 (1998).
In a case such as this one, where the prior bad acts are offered to establish an element of the crime, namely intent to distribute, the trial judge must take particular care to determine that there is a sufficient factual nexus between the charge being tried and the prior bad acts so that their probative value outweighs the considerable and inevitable prejudice to the defendant. See Commonwealth v. Helfant, 398 Mass. at 224-225. Factors to consider when prior drug involvement is offered to prove an element of a drug charge include temporal proximity, location, and the form of the conduct. See Commonwealth v. Luna, 410 Mass. 131, 134, 140 (1991) (prior controlled purchases of cocaine from the defendant at his house deemed admissible to prove that he was involved as a joint venturer in distribution of cocaine found within a week or so in another part of the premises occupied by a codefendant); Commonwealth v. Delrio, 22 Mass. App. Ct. 712, 715, 719 (1986) (street sales to undercover troopers which took place both the day before and the morning of the defendant’s arrest in a raid on a heroin-filled apartment three blocks from the site of the street sales held admissible to prove defendant’s intent to distribute drugs seized in the raid, even though charges stemming from the street sales had been severed for separate trial); *846Commonwealth v. Velasquez, 48 Mass. App. Ct. 147, 153 (1999) (prior offense involving the same accomplices, the same maimer of conducting business out of an apartment, and the same predilection for stashing drugs in the basement deemed admissible to prove the defendant’s “method of operation”). See also Commonwealth v. Montanez, 410 Mass. 290, 304 (1991) (upholding joinder of two offenses, four months apart, because even if offenses had been severed, prior undercover sale at defendant’s apartment would have been admissible at trial on trafficking charge stemming from seizure of drugs at the same premises to establish defendant’s intent to distribute).
Here the trial judge relied heavily, if not exclusively, on the temporal relationship of the charged offenses to the prior acts, concluding that the incidents of December 5, 1997, and January 2, 1998, and the existence of a conspiracy between November 1, 1997, and February 6, 1998, were close enough in time to be probative as to the defendant’s intent at the time of the charged offenses on February 17, 1998.5 However, unlike the facts in Delrio, supra, the prior acts in this case were not so immediate that timing alone strongly suggested a unified course of conduct or purpose. And unlike the facts in Montanez, supra, which involved a comparable time frame, this case lacks other significant indicia of nexus, such as identity of locale.
Indeed, except for the fact that the relevant events took place within weeks of each other, there is little connection or similarity between the prior acts and the offenses being tried. The prior acts introduced in the instant case consisted of two hand-to-hand sales to undercover troopers by the defendant or an accomplice in the defendant’s presence. These episodes took place in the two residences that were identified in the conspiracy charge as being centers for cocaine distribution by the defendant *847and eight other named individuals in the late afternoon and early evening. On these prior occasions, the defendant worked in tandem with others and possessed varying amounts of cocaine, including multiple packages. In contrast, the charged offenses stemmed from the defendant’s possession of a single piece of crack cocaine while sitting in a car in a commercial part of town, late in the evening, with a companion who had no connection to the prior acts. Thus, the facts of the instant case differed significantly from the prior acts with respect to location, form of conduct, and other attendant circumstances.
When due regard is given to all of the relevant factors, it cannot fairly be said that the defendant’s prior misdeeds were sufficiently related to the charged offenses that their probative value outweighed the unfair prejudice of admitting them, particularly when the proof of the defendant’s intent to distribute was otherwise extremely thin. Although “the trial judge’s discretion in weighing the balance is broad,” Commonwealth v. Englehart, 27 Mass. App. Ct. 1201, 1203 (1989), we are constrained to conclude that the admission of the prior bad act evidence in this case was palpable error. See Commonwealth v. Emence, 47 Mass. App. Ct. 299, 304 (1999).
3. The sufficiency of the evidence. Stripped of the erroneously admitted prior bad acts, the Commonwealth’s evidence on the issue of intent to distribute consisted of the 2.71 gram piece of crack cocaine found in the defendant’s sock, his possession of a pager, the absence of smoking paraphernalia in the car, and the opinion expressed on direct examination by Trooper Civello that these facts were consistent with drug distribution. However, even when viewed in the light most favorable to the Commonwealth, this evidence, singly and in the aggregate, was equally consistent with distribution and with personal use. Consequently, the conviction cannot stand. See Commonwealth v. Latimore, 378 Mass. 671, 676 (1979); Commonwealth v. Wooden, 13 Mass. App. Ct. 417, 422-424 (1982); Commonwealth v. Tripp, 14 Mass. App. Ct. 997, 998 (1982). Compare Commonwealth v. Evans, 50 Mass. App. Ct. 846, 850 (2001).
This is not a case where the sheer amount of the drugs provided sufficient evidence of intent to distribute. Compare *848Commonwealth v. Ridge, 37 Mass. App. Ct. 943, 945 (1994) (possession of 636.8 grams of cocaine was “alone an amount sufficient to warrant the inference beyond a reasonable doubt that the defendant intended to distribute cocaine”). Indeed, we have recently observed that the possession of 2.73 grams of cocaine (a slightly larger quantity than that found in the instant case), even when packaged in eleven envelopes, “does not, without more, clearly tend towards showing an intent to distribute.” Commonwealth v. Andrews, 49 Mass. App. Ct. 201, 204 (2000). Here, where the cocaine was a single piece that was not packaged for distribution, the inference is even weaker. Compare Commonwealth v. Martin, 48 Mass. App. Ct. 391, 392-393 (1999) (eighteen individually packaged rocks of cocaine weighing a total of 2.04 grams, together with other evidence probative of intent, held sufficient to support finding of intent to distribute).
Because the quantity of drugs was relatively small, it was not packaged for distribution, and no cash was found on the defendant, his companion, or in the car, we do not attach dis-positive significance to the defendant’s possession of a pager. Compare Commonwealth v. Clermy, 421 Mass. 325, 331 (1995) (defendant’s possession of a pager, one of the “traditional accoutrements of the illegal drug trade,” was one of a number of circumstances, including quantity of drugs, manner of packaging, and presence of cash, that in the aggregate were sufficient to establish the defendant’s intent to distribute cocaine). Even if having a pager marked the defendant as a drug dealer, it did not blunt the alternative, equally plausible, inference that he was a dealer-user who had reserved a piece of cocaine for himself. See Commonwealth v. Wooden, 13 Mass. App. Ct. at 422-424; Commonwealth v. Tripp, 14 Mass. App. Ct. at 998. This ambiguity was not dispelled by the absence of smoking apparatus in the car, since the defendant could well have planned to consume the drugs at home or at some other location where smoking supplies were available.
Trooper Civello’s opinion that the circumstances were consistent with drug distribution did not add anything further to the Commonwealth’s case, especially since his later testimony supported the conclusion that the circumstances were just as *849consistent with personal consumption by a dealer-user. A mere guess or conjecture by an expert witness in the form of a conclusion from basic facts that do not tend toward that conclusion anymore than toward a contrary one has no evidential value. See Nass v. Duxbury, 327 Mass. 396, 401 (1951). See also Commonwealth v. Club Caravan, Inc., 30 Mass. App. Ct. 561, 563 (1991) (trooper’s testimony regarding alleged gaming offenses was “properly disregarded as expert opinion in discord with the subsidiary facts on which it was based”). Civello’s testimony did not rescue an otherwise insufficient case.
The judgment on the part of the indictment charging intent to distribute is reversed, that verdict is set aside, and judgment is to enter for the defendant. The case is remanded to the Superior Court for entry of a new judgment on the lesser included offense of possession of cocaine and resentencing as appropriate. See Commonwealth v. Tripp, supra at 999; G. L. c. 278, § 12. The judgment as to intending to distribute cocaine within a school zone is reversed, that verdict is set aside, and judgment is to enter for the defendant.
So ordered.
The defendant contends that Civello essentially testified that the defendant was guilty and impermissibly vouched for the Commonwealth’s case. We agree that the witness’s personalized references to the defendant should have been struck. See Commonwealth v. Woods, 419 Mass. 366, 374-375 (1995); Commonwealth v. Barbosa, 421 Mass. 547, 554-555 (1995); Commonwealth v. Tanner, 45 Mass. App. Ct. 576, 579-582 (1998). However, we find no prejudice because the judge, who was the trier of fact, immediately admonished Civello to “stop there” and clearly understood that the expert was not permitted to express an opinion as to the defendant’s guilt. See Commonwealth v. Bonner, 33 Mass. App. Ct. 471, 477. (1992); Commonwealth v. Darby, 37 Mass. App. Ct. 650, 655 (1994).
Defense counsel objected to the admission of this evidence on the ground that the prior bad acts were not relevant except to show propensity and thus were inadmissible under the principles set forth in Commonwealth v. Helfant, 398 Mass. 214, 224-228 n.13 (1986), and Commonwealth v. Hanlon, 44 Mass. App. Ct. 810, 817-819 (1998). The objection was voiced not only when the issue was first called to the judge’s attention after the defendant waived his right to jury trial, but also, appropriately, at the time the evidence was formally offered by the Commonwealth. Compare Commonwealth v. Diaz, 49 Mass. App. Ct. 587, 588 n.2 (2000). However, counsel agreed that, if the court found the evidence to be admissible, “the Commonwealth need not produce the individual witnesses to put those facts before the Court.” In other words, the recitation of facts made by the Commonwealth at the plea hearing, coupled with the defendant’s acknowledgment that he had in fact committed the acts recited, were stipulated to be an appropriate method of receiving the prior bad act evidence. In light of this stipulation, we do not question the form in which the evidence was introduced. Compare Commonwealth v. Hubbard, 45 Mass. App. Ct. 277, 278-282 (1998) (reversing conviction because prosecutor’s repeated references to a prior bad act were based upon excluded hearsay and not founded in the evidence).
Prior bad act evidence also may be admitted if it is “inextricably intertwined with the description of events” on the day of the crime charged. Commonwealth v. Gunter, 427 Mass. 259, 263 (1998), quoting from Commonwealth v. Hoffer, 385 Mass. 244, 269 (1982). It may come in to rebut a defendant’s entrapment defense. See Commonwealth v. Vargas, 417 Mass. 792, 794-796 (1994); Commonwealth v. Coyne, 44 Mass. App. Ct. 1, 5-6 (1997). And, in the form of prior criminal convictions, evidence of prior bad acts may be admitted to impeach the credibility of a testifying defendant pursuant to G. L. c. 233, § 21. See Commonwealth v. Riccard, 410 Mass. 718, 723-724 (1991); Commonwealth v. Rivera, 425 Mass. 633, 646 (1997).
Depending upon the context, the tests for admissibility can be contradictory. For example, similarity to the charged offense militates against the admission of a prior bad act when it is a conviction offered for impeachment purposes. Commonwealth v. Roucoulet, 22 Mass. App. Ct. 603, 608, 610 (1986) (probability for prejudice from use of prior convictions of controlled substance offenses similar to charge being tried outweighed any possible insight they may have provided as to the defendant’s credibility). However, close similarity is a prerequisite to the admission of a prior bad act when it is offered to rebut the defendant’s entrapment defense. Commonwealth v. Vargas, 417 Mass. 792, 796-797 (1994) (crime of possession not similar enough to crime of distribution to be admitted for purpose of proving predisposition to distribute).
Before hearing defense counsel on his grounds for objection, the judge ruled that the prior bad acts could be introduced because they were sufficiently close in time to the charged offenses. Only after announcing this ruling, did the judge allow counsel to give a thumbnail sketch of the case and to state for the record his position that the evidence of defendant’s prior distribution was not similar enough to shed light on his intent in the instant case. The judge reiterated his ruling that the prior acts were admissible, indicating that he would consider defense counsel’s points in determining how much weight to give the evidence.