The defendant appeals from his conviction by a jury of rape of a child under sixteen years of age, without force (G. L. c. 265, § 23). On appeal, the defendant claims that the judge abused his discretion in (1) refusing to allow evidence of the victim’s prior sexual intercourse with a person other than the defendant and (2) excluding a letter that the victim had written *973to the defendant’s brother. He also contends that certain comments by the prosecutor in her closing argument require reversal.
We summarize the Commonwealth’s evidence as background for our discussion of the evidentiary issues. The victim testified that as of the date of the crime, June 10, 1987, she was fourteen years old. On that date, she received a telephone call from the defendant inviting her to accompany him to a lake where they would meet the defendant’s brother-and other friends. The victim had been dating the defendant’s brother and, during the course of that relationship, had met the defendant two or three times. The victim agreed to the defendant’s plan, but when they arrived at the lake the persons whom she expected to meet were not there. After about twenty-five minutes, during which the defendant. and the victim drank some beer, the defendant suggested that they drive to a “camp” to look for their friends. The victim agreed. The defendant drove to the camp, passed it, and parked on a deserted road.
After they both drank some more beer, the defendant told the victim that he would not take her home unless she had intercourse with him. The victim was scared and wanted to go home. At the defendant’s suggestion, the victim got into the back seat and they had intercourse. The defendant, according to the victim, ejaculated during the course of the sexual act.
Afterwards, the defendant started to drive the victim home. The automobile got stuck in the mud and, after a long wait, a tow truck freed the automobile. By that time, it was the afternoon of June 11. After the truck left, the automobile got stuck in the mud again. This time, however, the defendant telephoned his mother, and she arrived with his father, brother, and a friend to remove the automobile. They failed, and a tow truck pulled the automobile out of the mud again at about 6:00 p.m. The victim did not complain to anyone at this time regarding the defendant’s actions.
The victim arrived home at approximately 7:30 p.m. on June 11. After being confronted by her mother as to her whereabouts during the previous twenty-four hours, she ran to her friend’s house, crying. She told her friend what had happened, and the friend urged the victim to tell her mother. She did, and the mother took her to the police station and then to a hospital for an examination.
The examining physician testified that he took fluid by a swab from the victim’s vagina. He stated that the laboratory report showed the presence of rare non-motile sperm in the victim’s vagina and that its presence was “certainly consistent with intercourse that might have taken place within twenty-four hours prior to [the examination].” He testified that such sperm can be found in the vagina up to five days after intercourse. The doctor considered in his assessment of when the intercourse may have occurred that the victim was menstruating at the time of the sexual act.
The defendant conceded that he was with the victim on the night in question but denied that any intercourse had taken place.
*9741. Evidence of the victim’s prior sexual conduct. Through discovery, the defendant learned that the victim had told the examining physician that she had had intercourse with another person two weeks before the alleged incident but also told a police officer that the prior sexual intercourse had taken place two months prior to the incident. As a result, the defendant filed a motion, as required by G. L. c. 233, § 21B (the rape-shield statute), requesting that he be allowed to cross-examine the victim regarding her prior sexual conduct.
The judge held an in camera hearing on the motion during the presentation of the Commonwealth’s case. The only evidence presented by the defendant in support of his motion were the two statements of the victim to the physician and the police officer. The defendant contended that the statements showed that the victim had sexual intercourse with another person close to the time that she claimed that the defendant had sexual intercourse with her. He argued that he was entitled to cross-examine the victim about her prior sexual conduct in order to show an alternative source of the sperm found in the victim’s vagina.
The judge noted that, of the two statements made by the victim, the one most favorable to the defendant placed her prior sexual intercourse with another person two weeks before the date she claimed that the defendant had sexual intercourse with her. The judge then observed that uncontra-dicted evidence showed that sperm would be present in the victim’s vagina only up to five days after intercourse. He ruled that, in view of the defendant’s offer of proof taken in context of the evidence, cross-examination of the victim concerning her prior sexual conduct was not relevant. There was no error.
“In a prosecution for rape . .., the rape shield law, G. L. c. 233, § 21B, prohibits the introduction of evidence dealing with ‘the reputation of a victim’s sexual conduct.’ It also prohibits evidence of ‘specific instances of a victim’s sexual conduct,’ with exceptions available in two specified areas when the defendant follows a specified procedure.” Commonwealth v. Mosby, 11 Mass. App. Ct. 1, 13 (1980). One of the exceptions allows the admission of “evidence of recent conduct of the victim alleged to be the cause of any physical feature, characteristic, or condition of the victim.” G. L. c. 233, § 21B, as inserted by St. 1977, c. 110. The presence of sperm in the vagina is considered to be a “condition” under the rape-shield statute. See Commonwealth v. Elder, 389 Mass. 743, 753 (1983).
Before a defendant is entitled to present evidence to a jury about a rape victim’s prior sexual activity, he must first make a preliminary showing to the trial judge that “the theory under which he proceeds is based on more than vague hope or mere speculation.” Commonwealth v. Chretien, 383 Mass. 123, 138 (1981). Here, it was the defendant’s “theory” that the victim had had sexual intercourse with another person which accounted for the sperm found in her vagina. However, the defendant offered nothing to the judge that showed that the victim’s prior sexual conduct fit into the *975time frame put forth by the examining physician. “[T]he constitutional right to confront one’s accuser does not extend so far as to entitle the defendant to engage in an unbounded and free-wheeling cross-examination in which the jury are invited to indulge in conjecture and supposition. Neither does the rape-shield statute provide an opportunity for such cross-examination . . . .” Commonwealth v. Chretien, 383 Mass. at 138. In the circumstances, the judge was justified in concluding that the proffered evidence did not have sufficient relevance to the issues before the jury to warrant its admission.1 See Commonwealth v. Shaw, ante 39, 44 (1990).
2. Exclusion of the victim's letter. The defendant also requested that a letter written by the victim to the defendant’s brother, with whom she was romantically involved, be admitted in evidence. The letter was received by the brother about three weeks before the incident for which the defendant was on trial.
The defendant made a somewhat convoluted argument for the admission of the letter. He informed the judge that, as a key part of his defense, he would present evidence of lack of fresh complaint by the victim after the alleged incident. According to the defendant, the Commonwealth would attempt to rebut that evidence by arguing to the jury that the victim did not immediately complain because she was immature and lacked judgment. According to the defendant, however, the letter would dispute that explanation. The judge read the letter and denied the request on the ground that it was not material.
The letter graphically illustrated that the victim, at least as to her knowledge of sexual matters, was well advanced beyond her years. It does not follow from that fact alone that she would promptly complain about the defendant’s conduct, especially where, as here, the defendant was not charged with forcible rape but, rather, accused of having intercourse with a child under sixteen years of age. G. L. c. 265, § 23. Further, under the rape-shield statute, evidence, although admissible, may be excluded “if the judge finds that the weight and relevancy of the proffered evidence is not sufficient to outweigh the prejudicial effect to the victim.” Commonwealth v. Grieco, 386 Mass. 484, 489 (1982). In the circumstances, we hold that the judge did not abuse his discretion in excluding the letter.
3. The prosecutor’s closing argument. The defendant claims that the prosecutor, in her closing argument, misstated the examining physician’s testimony before the jury. Counsel is entitled to argue as to the evidence and the fair inferences from the evidence. Commonwealth v. Smith, 404 Mass. 1, 8 (1989). The prosecutor, in her summation, did no more than that. There is no merit to the defendant’s argument.
Judgment affirmed.
Mary Page Kelley, Committee for Public Counsel Services, for the defendant. Anne M. Kendall, Assistant District Attorney, for the Commonwealth.The defendant also argued that evidence of prior sexual intercourse was admissible because it would refute the Commonwealth’s explanation of the lack of fresh complaint. That argument is without merit. See part 2 of this opinion.