Charged by complaint and tried by a jury in District Court the defendant was convicted of assault and battery upon his then girlfriend, Maria Levesque. He was acquitted of larceny. He appeals the conviction.
Maria’s testimony went thus.1 She and the defendant had been dating for some four months. On the night of April 22, *8781998, the defendant was moving his clothes and effects from a rooming house on Ferry Street to his mother’s house at 20 Pleasant View Avenue, Everett. Maria was helping at the rooming house. About 2:30 a.m. Maria made her way to the mother’s house and joined the defendant there. They were on the sofa in the TV room. The defendant asked Maria harshly for a gold chain she had let him wear on some earlier date. She said she had given the chain to a cousin to take home (in fact she had the chain wound around her ankle and had made the excuse to avoid the defendant’s badgering her about it). The defendant became enraged. He seized her by the hair, threw her to the floor, got on top of her, struck her, and bit her on the cheek. She was screaming. Stirred by the noise, the defendant’s mother, Isabel Martin, came downstairs to the room and intervened and tried to draw the defendant off her. Finally, weeping, with blood on her face, and “pus” running from her nose, Maria went to the kitchen where the defendant’s niece, Shawna Martin, also attracted downstairs, helped her clean up with a wet towel.
Maria tried to quit the house by the front door but was stopped by the defendant. The mother (again trying to ward off the defendant) told her to go out the back door; when she did so, he stopped her at the driveway. She returned to the house, and ultimately left by way of the front door. The defendant followed, wrested her pager from her pants belt and smashed it to the ground. She walked for perhaps fifteen minutes to a police station on Ferry Street.
Police officer Gregory Derosher was at the desk in the station’s front office. Maria appeared there about 3:30 a.m. He described her condition as shaken, crying, covering her face with her hand. There was blood on her cheek, redness around her nose and head area. She refused medical treatment. He took two pictures of her face. (These were received in evidence. On inspection, the pictures seem of poor quality; some redness can be discerned on her right cheek.2)
Isabel and Shawna Martin, testifying for the defense, said in substance there was a loud argument going on between the defendant and Maria, but they observed no violence, no laying on of hands. Maria was crying when she went to the kitchen, but there was no blood or discharge from her nose. A wet towel *879was applied but it showed no trace of redness. Maria left the house without incident.
Elizabeth Lopes, eighty-seven years old, residing with her daughter Isabel, testified that Maria appeared at the house the morning after the fracas and asked for her beeper. It was on the coffee table, intact. Maria took it and left.
As appears from the foregoing summary, the evidence was more than adequate to support the guilty verdict on the charge of assault and battery.
The defendant argues — it is his main contention on appeal — that the judge erred in ruling that he could not cross-examine Maria with a view to showing she had particular animus or bias against him that might have inspired her to charge him falsely in the present case. The defense wanted the jury to hear that the defendant had earlier lodged two criminal complaints against Maria which were open and pending when Maria testified herein.3 Maria’s sponsoring the present prosecution as principal witness, the defense could say, may have been a payback for those complaints, or, perhaps, the manufacture of a bargaining chip by which she might hope to get all the prosecutions settled and withdrawn. Possibly Maria was testifying against the defendant in the expectation that the Commonwealth would treat her kindly in disposing of the pending complaints. At all events, the defendant claimed a right to cross-examine Maria to develop the theme of bias.
The cross-examination of a witness to show bias (as motivation to give false testimony) is, indeed, often spoken of in the decisions as a “right.” Thus Chief Justice Hennessey in Commonwealth v. Ahearn, 370 Mass. 283, 287 (1976), wrote: “A basic rule states that reasonable cross-examination for the purpose of showing bias and prejudice of the witness is a matter of right.” See Commonwealth v. Hamilton, 426 Mass. 67, 72 (1997); Commonwealth v. Moore, ante 730, 736 (2000), and cases cited.4 Were we presiding at the present trial we think we would have been inclined, out of abundant caution, to let the fact of the complaints come in during the cross-examination of Maria for such effect on her credibility as counsel and the jury could make of it.
*880The decisions, however, speak of the “materiality” or strength of proffered evidence of bias, see Commonwealth v. Haywood, 377 Mass. 755, 761 (1979); Commonwealth v. Johnson, 16 Mass. App. Ct. 935, 936-937 (1983); Commonwealth v. Quegan, 35 Mass. App. Ct. 129, 132 (1993), and this suggests that if its strength is low in relation to the rest of the case its exclusion may not constitute error, or error serious enough to warrant reversal of a conviction otherwise well supported. See Commonwealth v. Haywood, 377 Mass. at 761; Commonwealth v. Hamilton, 426 Mass. at 73. Here the testimony of an outsider, Officer Derosher, seems to settle there was an assault, even disregarding Maria’s testimony to like effect. Contrast Commonwealth v. Moore, supra at 735-736. Consider also that the jury would anyway, in the nature of the case, have seen Maria, the complaining witness, as parti pris and biased in that sense, to which the circumstance of the complaints would not add much. Counsel as well as the judge had impressed on the jury the importance of assessing the credibility of witnesses with attention to their individual interests in the conduct and outcome of the prosecution.
The trial transcript has Maria saying during her cross-examination that the defendant “when he was released from jaaaa — .” Apparently defense counsel then broke in with a motion for a mistrial and motion to strike. The prosecutor said, “She didn’t say it” (meaning jail) and the judge said he thought she did not say it. The motions may be taken to have been denied. Even assuming the jury heard such a reference, we cannot think it more than a minor incident in the trial as a whole, with the jury duly instructed against wandering from the relevant.
As the defendant is black and Maria white, the judge, after inquiring whether the defendant wanted the prospective jurors questioned about their racial attitudes, put questions in that behalf that seem to us sufficient. See Commonwealth v. Sanders, 383 Mass. 637, 641 (1981); Commonwealth v. LaFaille, 430 Mass. 44, 51-53 (1999). The defendant complains that the judge declined to ask specifically how the jurors viewed interracial dating, but the judge in reasonable discretion could prefer to avoid setting up the narrower proposition.
Judgment affirmed.