The defendant, Carlos A. Palacios, was convicted by a jury of operating a motor vehicle after his license had been suspended for operating a motor vehicle while under the influence of intoxicating liquor. See G. L. c. 90, § 24D. On appeal, he asserts that his conviction should be reversed on multiple grounds, including that (1) the judge, in initial jury instructions, omitted one element of the offense, and shifted the burden of proof to the defendant on another; (2) the judge and the prosecutor referred to the defendant throughout as having been “convicted” of operating under the influence, whereas the defendant had instead admitted to sufficient facts, and the judge erred also in instructing that suspension by virtue of a previous conviction of operating under the influence was an element of the offense; (3) the judge erred both in denying a motion to dismiss on the ground of racial profiling, and in excluding racial profiling as a defense at trial; and (4) there was ineffective assistance of counsel. We conclude that there was neither error that requires reversal nor ineffective assistance of counsel, and we accordingly affirm the judgment of conviction.
From the evidence presented at trial, the jury could permissibly have found the following facts. Charged in the Boston Municipal Court with operating a motor vehicle while under the influence of alcoholic beverages, the defendant admitted to sufficient facts for a finding of guilty, and the case was continued without a finding. In connection with that disposition, the Registry of Motor Vehicles (registry), on July 10, 2003, forwarded to the defendant written notice that his license to operate a motor vehicle had been suspended for forty-five days.
On July 27, 2003, Officer Richard DiPerri of the Wilmington police department, while on patrol on Lowell Street in Wilmington, observed a white Toyota Corolla automobile pass his cruiser. He entered the vehicle’s license plate number into a laptop computer, which accessed the registry’s database. Registry *15information for the license plate number revealed that the defendant was the registered owner of the Corolla, and that his license was suspended. Officer DiPerri stopped the vehicle and observed the defendant in the driver’s seat. The defendant identified himself by name and date of birth, and told Officer DiPerri that he knew his license was suspended and that he had made a mistake. The officer then placed the defendant under arrest.
The jury could also permissibly have credited the testimony of Estavelle Yoloski, the defendant’s sole witness. Yoloski testified that she was a passenger in the defendant’s car when he was stopped and arrested. She claimed that after the arrest, Officer DiPerri approached her as she sat in the car and asked her what a nice girl such as herself was doing with a “Spanish kid.”1
1. Jury instructions. The defendant first takes issue with the judge’s initial instructions to the jury, in which he described elements of the charged offense. The judge told the jury that the Commonwealth had to prove that the defendant’s license was suspended, and added, “which I think is fairly self-evident.” The defendant claims that this statement in effect informed the jury that the defendant’s license had in fact been suspended, thereby relieving the Commonwealth of its burden to prove that element of the offense. The defendant argues also that the initial jury instructions were deficient because the judge failed to include a reference to the element that the defendant must have had notice of the suspension of his license. The defendant acknowledges that the judge, in his final instructions, did not include the “self-evident” comment, and did include the required element of notice.
We agree that, in a criminal trial, the Commonwealth is required to prove every element of a charged offense beyond a reasonable doubt, and a judge’s instructions must communicate *16to the jury that this burden exists. See Sandstrom v. Montana, 442 U.S. 510, 520 (1979), quoting from In re Winship, 397 U.S. 358, 364 (1970); Commonwealth v. Pickles, 393 Mass. 775, 778 (1985). A judge’s instructions may not shift the burden of proof with respect to any fact necessary to constitute the crime. Ibid. Whether given instructions have impermissibly shifted the burden depends on how “a reasonable juror could have interpreted the instruction.” Ibid., quoting from Sandstrom v. Montana, 442 U.S. at 514.
Here, we conclude that the judge’s initial instructions did not impermissibly shift the burden of proof. The judge’s remark that the Commonwealth must prove that the defendant’s license was suspended, “which I think is fairly self-evident,” taken in context by any reasonable juror, communicated that it is self-evident that an element of the charge of operating after suspension is that the defendant’s license was in fact in suspension at the time of such operation. The statement in no way indicated that the Commonwealth had been relieved of its burden on the issue. Given that the judge did not include similar language in his final instructions, there was little likelihood of uncertainty regarding allocation of the burden of proof. Likewise, omission from the initial instructions of a reference to notice of the suspension was insignificant. The element of notice was included in the judge’s final instructions, and it was clear to any reasonable juror that notice of the suspension was an element of the charged offense which the Commonwealth had the burden to prove.
2. Improper use of the term “conviction. ” The defendant next assigns as error references by both the judge and the prosecutor to the defendant having been “convicted” of operating a motor vehicle while under the influence of intoxicating liquor. In fact, the defendant had admitted to sufficient facts in the prior proceeding, thereby avoiding a “conviction.” In his instructions to the jury, the judge erroneously stated that the defendant was charged with “operating his motor vehicle while his license was suspended for an operating under the influence conviction,” and instructed further that, in order to prove the defendant’s guilt, the Commonwealth had to show that his license had been suspended as a result of a previous conviction of operating *17under the influence. Likewise, in her opening and closing statements, the prosecutor asserted several times that the evidence showed that the defendant’s license had been suspended as the result of a conviction of operating under the influence.
The question is not whether the defendant was operating a motor vehicle following a “conviction” of operating under the influence, but rather whether such operation took place while the defendant’s license was suspended for an alcohol-related reason. How the defendant’s suspension otherwise came about is unimportant. Once it was established that (1) there was an alcohol-related suspension, (2) the suspension was in effect, and (3) the defendant was given notice of it, his operation of a motor vehicle was a criminal offense. See G. L. c. 90, §§ 23, 24D. Because there were no objections at trial, we review the error to determine whether it created a substantial risk of a miscarriage of justice. See Commonwealth v. Vinnie, 428 Mass. 161, 163-164, cert. denied, 525 U.S. 1007 (1998). While use of the term “conviction” was incorrect, and while it was not accurate to instruct that proof of a conviction was required, neither mistake constitutes reversible error under the applicable standard.
Whether a prosecutor’s mischaracterization of evidence during final argument requires reversal depends on a number of factors, including whether the defendant objected to the argument; whether the error went to the heart of the case; whether the judge’s instructions to the jury mitigated the prosecutor’s mistake; and whether the error in the circumstances possibly made a difference in the jury’s conclusions. See Commonwealth v. Kozec, 399 Mass. 514, 518 (1987); Commonwealth v. Quinn, 61 Mass. App. Ct. 332, 335-336 (2004). Here, the erroneous labeling of the disposition of the prior proceeding did not go to the heart of the case, nor could it have made a difference in the jury’s conclusions. In order to find the defendant guilty, the jury had to find, among other things, that his license had been suspended for operating a motor vehicle while under the influence of intoxicating liquor. Whether that suspension came about pursuant to a conviction or to an admission to sufficient facts is a collateral matter that would not affect a determination whether the Commonwealth had proved the required elements of the offense.
*18For the same reason, the reference by the judge to the defendant’s “conviction” did not create a substantial risk of a miscarriage of justice. A judge’s misstatement of the law injury instructions poses a substantial risk of a miscarriage of justice where the instruction may have materially influenced the jury’s appraisal of the evidence. See Commonwealth v. Gendraw, 55 Mass. App. Ct. 677, 687 (2002). Here, however, the jury needed to decide only whether the defendant’s license was in fact under an alcohol-related suspension when he operated the motor vehicle, and that determination would not be influenced by the source of the suspension (i.e., conviction or admission to sufficient facts). Because the jury would come to the same conclusion regarding the status of the defendant’s license regardless of the disposition that led to the suspension, the judge’s apparently inadvertent use of the term “conviction” in the jury instructions did not create a substantial risk of a miscarriage of justice.
The defendant argues further that the use of the word “conviction” at trial gave the jury the impression that the defendant had been convicted of a criminal offense, thus labeling him a criminal and inviting the jury to draw negative inferences regarding his behavior. We conclude that any negative inference that the jury may have drawn from the mistaken belief that the defendant had been convicted of the prior offense rather than having admitted to facts sufficient to convict him of that offense was minimal. As a practical matter, there was evidence in either event that the defendant had driven while under the influence of intoxicating liquor. The erroneous assertion that the defendant had been “convicted” did not sink to the level of an error that “paint[ed] the defendant as a chronic criminal and a man at constant war with society.” Commonwealth v. Ford, 397 Mass. 298, 301 (1986).
3. Racial profiling. The defendant argues next that it was error first to deny his pretrial motion to dismiss the complaint on the ground of racial profiling,2 and then to allow the Commonwealth’s motion in limine prohibiting references to racial *19profiling at trial. Given the evidence of racial profiling offered by the defendant, we conclude that the rulings on the defendant’s motion to dismiss and the Commonwealth’s motion in limine were correct.
Racial profiling is not a substantive defense at trial. Rather, it is properly addressed in a pretrial motion to dismiss because of selective enforcement based on race. See Commonwealth v. Franklin, 376 Mass. 885, 891 (1978). In order to obtain a dismissal on the basis of selective enforcement, the defendant must initially offer evidence that reasonably permits an inference of unlawful discrimination by showing that (1) a broader group of persons than those prosecuted has violated the law; (2) the failure to prosecute others was either consistent or deliberate; and (3) the decision not to prosecute others was based on an impermissible classification factor such as race, religion, or sex. See id. at 894; Commonwealth v. Franklin Fruit Co., 388 Mass. 228, 230 (1983). If the defendant satisfies that initial burden, the Commonwealth must then rebut the inference that there has been selective enforcement, or the case will be dismissed. See Commonwealth v. Franklin, 376 Mass. at 895.
If the defendant’s charge of racial profiling is not established prior to trial, it may not subsequently be raised again as a defense. However, we distinguish between racial profiling and racial bias. Denial of the motion to dismiss does not by itself eliminate the right of either party to challenge at trial the testimony of a witness on the ground of racial bias. See Commonwealth v. Franklin, 376 Mass. at 904; Commonwealth v. Johnson, 431 Mass. 535, 538 (2000). The right to cross-examine a witness regarding racial bias is not unfettered, however, and the judge may reasonably limit the extent and scope of cross-examination on this, as on any other, subject. Ibid. Where the defendant makes no plausible showing to support his claim of racial bias, the judge may prohibit reference to a witness’s alleged bias altogether. Ibid.
Here, the judge correctly denied the defendant’s motion to dismiss because of a lack of any evidence at that time that warranted a finding of selective enforcement. The defendant’s offer of proof on the subject consisted only of evidence that he was Hispanic and that he had been stopped by a police officer. The *20defendant’s race by itself is not sufficient to make out a case of selective enforcement. There was no evidence that violators of other races had not been stopped, or that the defendant’s race was otherwise a motivating factor in the arrest. Yoloski’s testimony attributing a racial reference to the arresting officer was not offered in evidence at the hearing on the motion to dismiss. Even had it been offered, the alleged statement took place subsequent to the stop, and there was no indication whether Officer DiPerri was aware that the defendant was Hispanic before that time. Once the judge properly denied the motion to dismiss, it follows that it was also proper to allow the Commonwealth’s motion to preclude renewal of the racial profiling allegation at trial.
With respect to alleged racial bias on the part of Officer DiPerri, the judge did not limit the defendant in any meaningful way. Following the sustaining of an objection by the Commonwealth when defense counsel referred to racial profiling in his opening statement, nothing else on the subject that was admissible was restricted. Yoloski testified as indicated, and the judge permitted both cross-examination of Officer DiPerri and final argument on behalf of the defendant on the subject. There is accordingly no basis on which the defendant may contend that he was deprived of an opportunity to demonstrate that the arresting officer’s testimony might be the product of bias.3
4. Ineffective assistance of counsel. The defendant asserts that his trial counsel rendered ineffective assistance in multiple respects. See Commonwealth v. Saferian, 366 Mass. 89, 96 (1974). Chief among the defendant’s accusations is that counsel failed to use Yoloski’s testimony regarding an alleged racial statement by Officer DiPerri in support of the defendant’s motion to dismiss the complaint because of racial profiling. It is a fact that counsel was aware of Yoloski’s testimony because it had been given at an earlier suppression hearing, but did not make that testimony part of the record on the motion to dismiss.
*21There being no motion for new trial, and thus no affidavit of trial counsel, we have no way of knowing what counsel’s thinking on the subject may have been. Regardless, in order for there to be ineffective assistance of counsel, the defendant must show that counsel’s conduct likely deprived him “of an otherwise available, substantial ground of defence.” Commonwealth v. Peloquin, 437 Mass. 204, 209 (2002), quoting from Commonwealth v. Saferian, supra. In this case, even had defense counsel presented Yoloski’s testimony as evidence of racial profiling, he would not thereby have satisfied the burden of demonstrating selective enforcement. As we have indicated, there was no evidence suggesting that a class of persons other than the defendant had violated the law by driving with a suspended license in Wilmington during the relevant period, and therefore, even with Yoloski’s testimony, the motion to dismiss would properly have been denied. With respect to possible racial bias on the part of the arresting officer, the judge permitted the subject to be explored at trial, and the defendant was not deprived of any opportunity to exploit the issue.
The defendant’s suggestion that his trial counsel was unfamiliar with principles governing a police stop of a motor vehicle is, even if true, of no moment because the validity of the stop has not been challenged on appeal except as a product of selective enforcement. The defendant also asserts claims of ineffective assistance of counsel on other grounds, including allegations regarding defense counsel’s excessive argument with the judge; failure to object to, or request limiting instructions upon, the introduction of registry certifications; failure to move for a required finding of not guilty; failure to object to improper uses of the term “conviction”; and failure to object to improper jury instructions. Without pausing to consider whether counsel’s performance was in fact substandard in any of these respects, we conclude that there has been no showing that the defendant was deprived of any substantial ground of defense.
Judgment affirmed.
Yoloski’s testimony on the subject shifted somewhat on different occasions. At a hearing on the defendant’s motion to suppress, she testified that Officer DiPerri asked, “What’s a nice girl like you doing with a Spanish boy?” At trial, she testified first that the officer asked, “What is a nice girl like you doing with, with him. Like meaning Spanish kid.” Questioned again regarding the alleged comment, she stated, “[H]e said can you tell me why a nice girl is with, with, with this Spanish kid?” For the purposes of this case, we adopt the version most favorable to the defendant.
We adopt the defendant’s characterization of the fact that the defendant is Hispanic as a “racial” judgment. Whether we are concerned with a technically “racial” characteristic, or some other distinguishing feature, the outcome is not affected.
We see nothing in the defendant’s contention that it was improper for the motion judge to suggest that the Commonwealth submit a motion in limine on the subject of racial profiling. The issue had been raised by the defendant, and such a motion was an appropriate vehicle for deciding what could be presented at trial.