delivered the opinion of the court:
Defendant John Allison appeals from his conviction by a jury of first degree murder and armed violence, charging that the trial court (1) erroneously prohibited him from cross-examining the State’s only eyewitness as to who did the shooting, regarding her refusal to be interviewed by the defense, (2) impermissibly qualified an expert in gunshot residue analysis, and (3) improperly admitted irrelevant and prejudicial evidence.
The victim, Richard Barnett, was shot and killed in front of 154 North Pine in the City of Chicago in the early morning hours of July 31, 1987.1 Sometime prior to the shooting, Lavette Davis and Jennifer Myrick were riding in their car looking for a place to eat. At trial, Davis testified that two men in a brown Cadillac Seville started talking to Myrick and her at a traffic light, and although Myrick at first testified that there were only two people in the Seville, she later admitted on cross-examination that there were three. The two men made crude remarks to Myrick and Davis, followed them, and partially blocked their car from exiting the parking lot of a Wendy’s fast-food establishment which was closed. The men asked the women for dates, but the women refused. The men then followed them to a White Castle restaurant, and before entering the restaurant, defendant “felt on [Davis’] behind.” Myrick and Davis testified that they left the restaurant before ordering their food because of their being annoyed by the men. Myron Tucker, the security guard at the White Castle that evening, testified that the women remained in the restaurant after the men left, placed their order and left with it. Upon leaving the White Castle, Myrick saw Tyrone Ward (also known as Smooth), whom she had known for seven or eight years as a friend of her brother’s, leaning up against the Seville. Davis and Myrick then drove to Myrick’s brother’s house at 154 North Pine.
Myrick and Davis walked up to a gate at which a group of people were standing, including Myrick’s brother Ollie and the victim, Richard Barnett. The Cadillac pulled up and defendant got out. Myrick testified that after she told Barnett that defendant had been harassing her, he hit defendant, and that her brother also swung at defendant but missed. However, on cross-examination she could not say who, besides the victim, swung at defendant. After defendant ran *178away, the victim yelled “stop him” and ran after him. According to Myrick, when defendant got to the car, he turned around with a gun in his hand, which she had not seen until that time, and began to “fire and fire and fire.” After the first or second shot, her brother pushed her to the ground. She testified that she heard no more than three or four shots and that she could not remember whether she told a detective at the police station that she heard five or six shots. Myrick said she did not see any weapons on anyone else in the group. At trial she identified the gun by its handle, although her description of the manner in which defendant held the gun would mean that defendant’s hand necessarily concealed the handle. According to Myrick, defendant had his right hand around the “palm” of the gun and his left hand covered part of his right hand. She also testified that there was a streetlamp giving light across the street from where the car was parked and that a light inside the car was on.
The parties stipulated, however, that Myrick spoke to Officer Callahan at the scene immediately after the shooting and told him she saw nothing as defendant returned to the car. Further, in her initial statement to Detective Tapkowski on the day of the incident, Myrick did not mention that there were three persons in the car or that she knew one of them. She did not relate that defendant was struck by anyone; nor did she describe how the shooter held the gun. Tapkowski testified that when he arrived at the scene Davis and Myrick were upset and shaken, and that he had difficulty communicating with Myrick because she was so upset. He also stated that the weather was clear and that a streetlight located directly across the street from where the victim lay provided good artificial lighting. Officer John Gargul, whose car was the first to arrive at the scene, testified that after he had asked Myrick to calm down, she gave him a description of the offenders and their car, which was broadcast over the police radio system. He, too, observed that the streetlight across the street from where the victim lay was on.
Davis testified that she saw defendant approach the group alone at Myrick’s brother’s house and heard words being exchanged between him and members of the group. Davis also testified that Myrick’s brother and possibly the victim, Richard Barnett, struck defendant. She then saw defendant run back to the Cadillac and heard the sound of three or four shots being fired and of a car driving off; her testimony is silent, however, as to who fired the shots or where they were fired from. Davis did not mention that there was a third occupant in the car.
*179Tapkowski testified further that he and his partner interviewed a father and son, both named John Sims, who lived at 162 North Pine and that the father told him that he heard six or seven shots. At trial, the father, a Cook County deputy sheriff, testified that he heard about five shots, got out of bed and saw a man lying on the ground with five or six men standing over him. He stated that the streetlight on the northwest corner of North Pine and West End, where the body lay, was off, but that the lights across the street were on. On cross-examination he testified that he heard more than four shots being fired.
Subsequent to the shooting, Sergeant Helen De Witte stopped a car with three occupants. After stopping the car, which was driving erratically, De Witte noticed that the car and two of its occupants matched a description which had been broadcast in the police radio report of the homicide. De Witte testified that after ordering the occupants out of the car, she found a .357 Smith and Wesson revolver, which had two live cartridges in it, under the front seat of the car on the passenger side. During the stop, the driver of the car fled the scene and was never apprehended. At trial, De Witte identified defendant as the front seat passenger.
While De Witte was waiting to transport the remaining two suspects to the police station, a police car arrived carrying Davis, who placed defendant and the car at the scene. At the station, Davis and Myrick identified defendant as the front seat passenger. Tucker, the security guard employed by the White Castle, identified Tyrone Ward as the person creating the disturbance there. Subsequent to the lineup, defendant was released from custody at 10:40 a.m., on July 31, 1987, after having posted bond on misdemeanor weapons charges. Chicago police department detective Richard Schak testified that a mistake had been made when defendant was released from custody, but that he secured an arrest warrant for him on July 31, 1987, and placed him under arrest for murder on August 1, 1987. Pamela Steel, defendant’s aunt, testified that defendant’s mother owned a brown, four-door Cadillac which she had seen defendant driving at different times.
Dr. Michael Chambliss of the Cook County medical examiner’s office testified that he recovered a bullet, which had entered the victim’s right eye adjacent to the right side of the nose, from the victim’s brain, and that the cause of his death was a gunshot wound to the face. Dr. Chambliss also testified that in forming his opinion he reviewed a report prepared by an investigator for the medical exam*180iner’s office which contained information that multiple gunfire was exchanged between the two groups of men that were on the street.
Officer Joseph Moran of the Chicago police department, an evidence technician who investigated the scene of the crime, collected blood standards from a pool of blood on the sidewalk and recovered two fired bullets. Moran testified that after defendant indicated to him that he was right-handed, he conducted a gunshot residue test on him, which consisted of his wiping a separate swab treated with nitric acid and water on the back and palm of each of defendant’s hands. He also testified that there were no lacerations or abrasions on defendant’s face. Officer Robert Smith, a firearms examiner, test-fired four bullets from the .357 Smith and Wesson six-shot revolver which was recovered from the Cadillac and compared them to the three bullets he had received, two from the scene and the other from the victim’s brain. Smith concluded that the bullet which was recovered from the victim had been fired from the recovered weapon. However, he was unable to form an opinion about the other two bullets because they were mutilated. There was no fingerprint evidence.
Dr. Krishan Kaistha, called by the State as an expert gunshot residue analyst, testified that the threshold figures established by the FBI for the three substances found in gunshot residue (in micrograms) are 0.3 for barium, 0.05 for antimony and 1.0 for lead. The threshold figures equate to the figures that could be found on a blank or control swab containing only the nitric acid and water solution. The concentrations found on the back of defendant’s right hand were 2.58 for barium, 0.11 for antimony and 0.46 for lead; while those found on defendant’s right palm were 3.32 for barium, 0.10 for antimony and 0.47 for lead! The concentrations found on the back of defendant’s left hand were 1.58 for barium, 0.09 for antimony and 0.37 for lead; and those found on defendant’s left palm were 0.45 for barium, 0.19 for antimony and 0.77 for lead. The concentrations found on the back of Ward’s right hand were 1.45 for barium, 0.19 for antimony and 0.052 for lead; while those found on his right palm were 1.52 for barium, 0.230 for antimony and 0.66 for lead. The concentrations found on the back of Ward’s left hand were 1.35 for barium, 0.095 for antimony and 0.24 for lead; while those found on his left palm were 1.54 for barium, 0.095 for antimony and 0.50 for lead. Dr. Kaistha calculated ratios by dividing the concentration of barium by antimony. The ratio for defendant’s right back was 23.45 and it was 33.20 for his right palm. The ratio for defendant’s left back was 17.56 and it was 2.37 for his left palm. The ratio for Ward’s right back was *1817.63 and it was 6.61 for his right palm. The ratio for Ward’s left back was 14.21 and it was 16.21 for his left palm.
Dr. Kaistha testified that if a right-handed person fired a gun “his left palm should have less [gunshot residue] and the right back and left back should have more [gunshot residue].” According to Dr. Kaistha, the right palm could also have more depending on how close he held the weapon to his hands. In Dr. Kaistha’s opinion, the concentrations found on defendant’s hands were consistent with the amounts detected on a person who had discharged or handled a firearm or was in close proximity to a firearm when it was discharged. He testified that it was more likely that defendant either discharged or handled a weapon rather than being in close proximity to one. Although he found that Ward either fired or handled a gun, in his opinion it was more likely that defendant fired and that Ward simply handled a gun. On cross-examination, however, Dr. Kaistha admitted that it is very hard to prove whether someone discharged or merely handled a gun. He then said, “I’m not telling anything here. I’m just giving the concentration of the residue on the right back and left.”
Dr. Kaistha also testified on cross-examination that he calculated the ratio between barium and antimony found on defendant, but that he did not calculate the ratio between barium and antimony on the control swab. He explained that although he calculated ratios in his report, he subsequently found that the ratios were not important, but that the concentrations were. Nevertheless, he stated that whatever he wrote in his report was correct. After admitting that he had testified on an earlier occasion that ratios were important, he clarified his position on ratios by stating that they are used to help the defendant and not against the defendant. And although he also admitted that both his control levels for barium and antimony had a higher value than the corresponding threshold levels, he explained that that fact was irrelevant and that the control has nothing to do with the ratios.
He further testified on cross-examination that it was possible to transfer the residue to different parts of the same hand or to another hand through touching due to handcuffing, “high-fiving” or shaking hands. He also testified that an individual who fired a gun would have a higher concentration than someone he passed the gun to after firing it. When asked, “Now an individual who fired a gun could have a significantly higher concentration than any of the ones you have tested?” Dr. Kaistha answered, “It should have.” When asked, “It could be even higher then [sic] the concentrations on either Tyrone Ward or John Allison, correct. You could have higher concentrations?” Dr. Kaistha answered, “Depending on how many shots the guy fired.” *182Earlier he had testified that he believed more than one shot was fired.
Defendant was convicted and sentenced to 26 years in the custody of the Illinois Department of Corrections. On appeal, he seeks reversal of his conviction and a remand for a new trial.
I
Defendant’s first assignment of error is that the trial court erroneously prohibited him from cross-examining Myrick, the State’s only eyewitness as to who did the shooting, regarding her refusal to be interviewed by defense counsel prior to trial. The State responds that the judge, in doing so, acted within his discretion. The cross-examination at issue is as follows:
“[DEFENSE COUNSEL]: Now, do you remember back in September of 1987,1 came out to talk to you?
[WITNESS]: Sure, I do.
[DEFENSE COUNSEL]: And you refused to talk to me?
[PROSECUTOR]: Objection, Judge. I have been given no discovery.
[DEFENSE COUNSEL]: There wasn’t — why don’t we continue?
THE COURT: I’ll sustain the objection.
[PROSECUTOR]: Thank you.
[DEFENSE COUNSEL]: Judge if I could continue? She refused to talk to me.
[PROSECUTOR]: Objection.
THE COURT: Let’s have a sidebar on this.”
During the sidebar the State argued that it was given no discovery and that Myrick’s refusal to talk to the defense was irrelevant. Defense counsel responded that there was no discovery because she refused to talk to him and that if she had nothing to hide, she should have been subject to being interviewed by anybody. He also argued that he, as an attorney and officer of the court, had a right to interview her, to ask her about her refusal to be interviewed by him, and that he was going to argue it in closing argument. At the conclusion of the sidebar, the judge upheld the State’s objection.
The immortal Shakespeare depicted the issue of confrontation as one of elemental fairness when he had King Richard II, some 400 years before there was a United States Constitution, command John of Gaunt, in connection with an accusation made by Henry Herford against the Duke of Norfolk:
“Then call them to our presence.
*183Face to face,
And frowning brow to brow, ourselves will hear
The accuser and the accused freely speak.”
(William Shakespeare, Richard II act 1, sc. 1, lines 17 through 21 (Yale University Edition).)
Centuries later the United States Supreme Court expressed much the same sentiment thus:
“We think that a criminal defendant states a violation of the Confrontation Clause by showing that he was prohibited from engaging in otherwise appropriate cross-examination designed to show a prototypical form of bias on the part of the witness, and thereby ‘to expose to the jury the facts from which jurors [***] could appropriately draw inferences relating to the reliability of the witness.’ ” Delaware v. Van Arsdall (1986), 475 U.S. 673, 680, 89 L. Ed. 2d 674, 684, 106 S. Ct. 1431, 1436, quoting Davis v. Alaska (1974), 415 U.S. 308, 318, 39 L. Ed. 2d 347, 355, 94 S. Ct. 1105, 1111.
Defendant relies on People v. Van Zile (1977), 48 Ill. App. 3d 972, and People v. Timmons (1983), 114 Ill. App. 3d 861, in support of the proposition that the refusal of a witness to talk to the other side is germane to an inquiry into the bias and credibility of the witness and is therefore a proper subject of cross-examination. In Van Zile the court held that the State had a right to cross-examine the defense witnesses about their refusal to talk to the State’s Attorney. (Van Zile, 48 Ill. App. 3d 972.) The court reasoned:
“The credibility of a witness is always an issue — more correctly, in issue. A refusal to talk in advance of trial to the other side reasonably could indicate hostility by the witness to the inquiring side, or at least a bias for, or an interest in, a favorable outcome for the side calling him. We say ‘could’ because triers of the fact need not invariably so conclude, but they reasonably can do so. ***
Under our present system of liberal discovery, both sides at a minimum know the witnesses who will oppose them. Admittedly, both sides have the right to attempt to interview the other’s witnesses. Admittedly too, witnesses have a corollary right not to be interviewed if they so choose. But this refusal, in our opinion, can be used against them to argue bias, hostility, interest in outcome, all of which look to credibility. It is a risk the witness or his side takes. That there are reasonable inferences from such conduct cannot be gainsaid. Although they are not inexorable, they are reasonable. It is up to the trier of the fact *184to accept or reject them.” (Emphasis in original.) Van Zile, 48 Ill. App. 3d at 977.
Timmons, 114 Ill. App. 3d at 869; see also People v. Smith (1977), 52 Ill. App. 3d 583, 591, cert. denied (1978), 436 U.S. 961, 57 L. Ed. 2d 1127, 98 S. Ct. 3079.
In response, the State relies on People v. Williams (1985), 131 Ill. App. 3d 597, 609, for the proposition that “prosecution witnesses are not obligated to talk to defense counsel prior to trial, and it is not an abuse of discretion to exclude cross-examination regarding a witness’ refusal to talk to defense counsel.” In reaching its decision, the court in Williams relied on People v. Peter (1973), 55 Ill. 2d 443, 451-52, cert. denied (1974), 417 U.S. 920, 41 L. Ed. 2d 225, 94 S. Ct. 2627. (Williams, 131 Ill. App. 3d at 609.) Similarly, we note that the court in People v. Brown (1980), 87 Ill. App. 3d 368, 372, held, on the authority of Peter, that the fact that a witness refused to be interviewed by counsel prior to trial is not impeaching because a witness has a right to refuse to submit to such questioning. In Peter, defense counsel contended that the refusal of the police officers to discuss the case with him was part of a prosecutorial plot and that the trial court erred in prohibiting him from eliciting on cross-examination that the police had refused to talk to him. (Peter, 55 Ill. 2d at 450-51.) Notwithstanding its decision in People v. Glover (1971), 49 Ill. 2d 78, and its adoption of Rule 415(a) (87 Ill. 2d R. 415(a)), which provide that neither counsel nor prosecution or defense personnel should advise witnesses to refrain from discussing the case with opposing counsel, the court noted that the general proposition that a prosecution witness need not grant an interview to defense counsel remained valid. (Peter, 55 Ill. 2d at 450-51.) According to the court, defense counsel was unable to establish to the satisfaction of the trial court that there was such a plot. (Peter, 55 Ill. 2d at 451.) With respect to defendant’s contention that the trial court erred in prohibiting him from eliciting the fact that the police had refused to talk to him, the court stated the general rule to be that “ ‘the latitude to be allowed in cross-examination of witnesses rests largely in the discretion of the trial court. Such cross-examination should be kept within fair and reasonable limits, and it is only in a case of clear abuse of such discretion, resulting in manifest prejudice to defendant, that a reviewing court will interfere.’ [Citations.]” (Peter, 55 Ill. 2d at 451-52.) Accordingly, the court in Peter held that the trial court, in refusing to permit the defense on cross-examination to elicit the fact that the witnesses had refused to talk to defense counsel, “did not abuse its discretion to the prejudice *185of the defendant by its failure to permit this line of questioning.” Peter, 55 Ill. 2d at 452.
In addition, the State argues that the jury was informed of Myrick’s refusal to talk to defense counsel by defense counsel’s statement to the trial judge, “she refused to talk to me,” and of other factors which allowed them to assess adequately her credibility. In support of its position the State cites People v. Shinkle (1987), 160 Ill. App. 3d 1043, 1056, rev’d on other grounds (1989), 128 Ill. 2d 480, in which the court stated that “when a defendant alleges denial of the right of confrontation, the issue is whether the jury was made aware of adequate factors to determine the witness’ credibility, not whether any particular limitation has been placed on the defendant’s ability to cross-examine him or whether the jury has knowledge of any specific fact.”
The State also argues that defendant’s reliance on Timmons is misplaced because in Timmons, unlike in the case at bar, defense counsel made an offer of proof. However, diming the sidebar in the instant case, defense counsel stated, “That’s — that’s the question. You refused to talk to me? She’s going to say, yes, and that’s it.” “Although formal offers of proof, where the proposed evidence or testimony is formally offered in a question and answer manner outside the presence of the jury, are generally required to preserve the issue of whether preclusion of the evidence was proper, an informal offer of proof, where counsel summarizes what the proposed evidence or testimony may show, may be sufficient to preserve the error if it is specific enough in nature, and if it is not based merely on speculation or conjecture.” (People v. Phillips (1989), 186 Ill. App. 3d 668, 678-79, appeal denied (1989), 128 Ill. 2d 670.) “ ‘Where it is obvious that the witness is competent to testify to a fact, and it is obvious what his testimony will be if he is permitted to give it, a brief statement by counsel may suffice.’ ” People v. Rosa (1977), 49 Ill. App. 3d 608, 614, quoting Hession v. Liberty Asphalt Products, Inc. (1968), 93 Ill. App. 2d 65, 71.
There is no question that during cross-examination a lawyer must be permitted to ask whether a witness has refused to talk to him. Indeed, we find it difficult to understand why, in light of such a longstanding, well-established rule, a prosecutor would raise an objection to such a query, and, moreover, why a judge would even entertain it.
However, contrary to defendant’s argument that the court’s impermissible restriction imposed on the cross-examination of State witnesses is reversible error per se (see Smith v. Illinois (1968), 390 U.S. 129, 19 L. Ed. 2d 956, 88 S. Ct. 748; Davis v. Alaska (1974), 415 U.S. *186308, 39 L. Ed. 2d 347, 94 S. Ct. 1105), the Supreme Court has made it clear in Van Arsdall that Davis, which quotes Smith, when “[r]ead properly *** does not support an automatic reversal rule.” (Van Arsdall, 475 U.S. at 683, 89 L. Ed. 2d at 685, 106 S. Ct. at 1437.) In Van Arsdall the court held that the “improper denial of a defendant’s opportunity to impeach a witness for bias, like other Confrontation Clause errors, is subject to Chapman harmless-error analysis.” (Van Arsdall, 475 U.S. at 684, 89 L. Ed. 2d at 686, 106 S. Ct. at 1438.)
“The correct inquiry is whether, assuming that the damaging potential of the cross-examination were fully realized, a reviewing court might nonetheless say that the error was harmless beyond a reasonable doubt. Whether such an error is harmless in a particular case depends upon a host of factors, all readily accessible to the reviewing courts. These factors include the importance of the witness’ testimony in the prosecution’s case, whether the testimony was cumulative, the presence or absence of evidence corroborating or contradicting the testimony of the witness on material points, the extent of cross-examination otherwise permitted, and, of course, the overall strength of the prosecution’s case.” Van Arsdall, 475 U.S. at 684, 89 L. Ed. 2d at 685-86,106 S. Ct. at 1438.
Accordingly, a proper harmless error analysis, which must take into account the entire record, requires affirmance.
In People v. Harris (1988), 123 Ill. 2d 113, our supreme court provided the following standards for review of a trial court’s limitation on cross-examination:
“As a reviewing court, we are not required to isolate the particular limitation on cross-examination to determine whether reversible error has occurred. [Citation.] Rather, ‘the question in each case must finally be whether defendant’s inability to make the inquiry created a substantial danger of prejudice by depriving him of the ability to test the truth of the witness’s direct testimony.’ [Citations.] In answering this question the court must look to the record as a whole and the alternative means open to the defendant to impeach the witness. [Citations.] Thus, if a review of the entire record reveals that the jury has been made aware of adequate factors concerning relevant areas of impeachment of a witness, no constitutional question arises merely because the defendant has been prohibited on cross-examination from pursuing other areas of inquiry.” (Harris, 123 Ill. 2d at 145.)
*187In Harris, the trial court had erroneously sustained the State’s objection to defense counsel’s inquiry into a witness’ expectation of the restoration of good-time credits for purposes of showing bias. The supreme court found that the error was harmless beyond a reasonable doubt. In so doing, the court emphasized the latitude afforded defense counsel to establish the witness’ potential bias and the effective closing argument by defense counsel that the witness’s testimony was not credible.
The rationale of Harris is fully applicable here: Defense counsel fully and strenuously argued the witness’ lack of credibility. Further, other than the unanswered question, there was no limitation on defense counsel’s opportunity to establish the witness’ bias. Indeed, the issue of Myrick’s bias in this case was pursued vigorously in many different ways, most of them listed above. They include that Myrick was a close friend of Barnett and that she was angry and scared as a result of the White Castle incident. To paraphrase the standard supplied by Harris: because the jury in this case had been made aware of adequate factors concerning the bias of Myrick, there is no constitutional question merely because defendant had been prohibited from pursuing another area of inquiry concerning bias. Harris, 123 Ill. 2d at 145.
In People v. Peter (1973), 55 Ill. 2d 443, discussed at some length above, our supreme court held that the trial court’s refusal to allow defense counsel to elicit the fact that police officers had refused to talk to him did not constitute an abuse of discretion and did not prejudice the defendant. In Peter, and in many cases before and since, the supreme court stated that the latitude to be allowed in cross-examination rests largely in the discretion of the trial court and that reversal should occur only when there is a clear abuse of discretion, resulting in manifest prejudice to the defendant. (Peter, 55 Ill. 2d at 451-52.) For the reasons that follow, the record in this case demonstrates no “manifest prejudice” to the defendant.
Although the defendant denigrates the quality of the evidence presented at trial, this was not a closely balanced case. All of the defendant’s claims as to the shortcomings in the State’s case were before the jury. Indeed, an analysis of those shortcomings shows that they were not directly related to the central issue, which was who shot Richard Barnett. As to the identity of the shooter, the defendant claims that there was no corroborating or contradictory testimony. While we agree that there was no testimony that contradicted Myrick’s statement that defendant was the shooter, there certainly was ample corroborating evidence.
*188The record reflects important facts overlooked by the defendant, facts that corroborate that he was the shooter and which establish that neither of his companions could have been, contrary to his contention. Myrick testified that defendant wore a red T-shirt, was the front-seat passenger in the brown Cadillac Seville, and shot Barnett. Davis corroborated this evidence by her testimony that defendant wore a red T-shirt and was the front-seat passenger in the car. When defendant was arrested a short time after the shooting, police found him seated in the front passenger seat (under which the pistol linked to this homicide was recovered) of the described car, and he was shirtless; in the back seat of the car was a red T-shirt. The driver of the car, the man to whom the defendant refers as missing since almost immediately following the commission of the offense and later identified as Patrick Gibbons, was wearing a light colored dress shirt. The person in the back seat of the car, Tyrone Ward, was wearing a blue jogging suit. Thus, the defendant’s implication that one of his companions might be the actual perpetrator is not only unsupported by the evidence, it is inconsistent therewith.
The defendant argues that the jury might have received a significantly different impression of Myrick’s credibility had Myrick been permitted to answer his counsel’s question, and there was admittedly only one question. In the sidebar that followed the State’s objection to defense counsel’s question, defense counsel said, “That’s all I’m going to ask. *** That’s — that’s the question. You refused to talk to me? She’s going to say, yes, and that’s it.”
Defendant was bound by this offer of proof. (People v. Andrews (1992), 146 Ill. 2d 413.) There was to be no Perry Mason-like breakdown of the witness; there was to be no exculpatory evidence; there was to be no follow-up questioning at all. Instead, there was to be only one question, then “yes” as an answer, and on to another area of inquiry.
As we have already noted, in Van Arsdall, the Court said, “The correct inquiry is whether, assuming that the damaging potential of the cross-examination were fully realized, a reviewing court might nonetheless say that the error was harmless beyond a reasonable doubt.” (Van Arsdall, 475 U.S. at 684, 89 L. Ed. 2d at 686, 106 S. Ct. at 1438.) We must therefore ask, applying the limitations imposed by defendant’s own offer of proof, what would have been the full damaging potential of the disallowed cross-examination. Myrick’s refusal to talk to defense counsel, in itself, was neutral — witnesses are under no obligation to talk to an attorney representing an opposing side. (Peter, 55 Ill. 2d at 451.) Thus, the full potential damage that *189could be realized from the question and answer was at best an inference, the most favorable of which was that Myrick was biased against defendant, a fact abundantly established by other evidence.
That Myrick would cover for the actual shooter and falsely implicate defendant strains credulity. Nevertheless, assuming the relevance of the disallowed question to establish bias, and assuming that the court’s refusal to allow the one question to be answered kept from the jury some evidence concerning bias, the effect of the court’s ruling here was insignificant because Myrick’s bias was adequately developed. The answer to the one question would have changed none of the evidence that corroborated Myrick’s identification of defendant as the shooter. Even if improper, the disallowance of that simple question, whose one-word answer had limited value for defendant, could not have affected the outcome of the trial, and thus was harmless beyond a reasonable doubt. Reversal of defendant’s conviction on that basis cannot be justified; and by declining to reverse, we extol no principle that we could not adequately honor by simply stating that the trial court erred and that the question that was not permitted should always be allowed.
II
Defendant also contends that the trial court erred in qualifying Dr. Krishan Kaistha as an expert in gunshot residue analysis. Although defendant acknowledges Dr. Kaistha’s ability to operate the atomic absorption spectrophotomat machine, which performs the gunshot residue test, he maintains that the doctor was not qualified to analyze the results of the test. According to defendant, Dr. Kaistha’s assertion that he did not need any training indicates his confusion between the training required to run the machine and to analyze the results. Defendant argues that Dr. Kaistha’s failure to testify about distribution patterns between the palm and the back of the hand as well as his failure to discuss “hand blanks,” which are samples taken from people who have not fired guns, also illustrate his lack of knowledge.
“[T]he burden of establishing the qualifications of an alleged expert witness is that of the proponent of his testimony.” (People v. Park (1978), 72 Ill. 2d 203, 209.) “[T]he question of whether the State ha[s] met that burden [is] a matter within the discretion of the trial court.” (Park, 72 Ill. 2d at 209.) However, “its decision is subject to reversal if it constituted an ‘abuse of discretion.’ (People v. Fiorita (1930), 339 Ill. 78, 89.)” (Park, 72 Ill. 2d at 209.) “[T]he degree and manner of knowledge and experience of an alleged expert is directly *190related to the complexity of the subject matter and the corresponding likelihood of error by one insufficiently familiar therewith.” Park, 72 Ill. 2d at 209-10.
In People v. Cole (1988), 170 Ill. App. 3d 912, 928-29, appeal denied (1988), 122 Ill. 2d 582, the appellate court held that the trial court did not err in qualifying a police department chemist who had received one day of formal training focusing on the interpretation of test results, as an expert. In addition to the brief training period, the chemist performed approximately 300 tests to establish baseline levels for use as testing guidelines. The tests were conducted on individuals who had fired guns as well as on those who had not fired them. However, the results of the tests were not published. (Cole, 170 Ill. App. 3d at 928-29.) “Although [the chemist] admitted that the majority of her formal training was concerned with these mechanical procedures,” the court said, “her formal training did, in fact, include the interpretation of data derived as a result. In view of the standard of review regarding challenges to an expert’s qualifications,” it continued, “we are satisfied that such matters go to the weight to be given testimony, rather than precluding that testimony entirely. We are unaware of any benchmark,” the court concluded, “to test the requisite extensiveness of formal training or the existence of any rule which requires that an individual have published material in the field for which he intends to testify in order to qualify as an expert.” (Cole, 170 Ill. App. 3d at 29-30.) “That the defendant had an opportunity to cross-examine [the witness] as to his qualifications therefore [sic\ did not eliminate or in any way reduce the State’s burden of establishing those qualifications.” Park, 72 Ill. 2d at 209.
Dr. Kaistha’s involvement in gunshot residue testing began in 1987 at the request of the Chicago police department when its machine broke down. He admitted that he had had no formal training in the detection of gunshot residue, but he stated also that he did not need any training and that the test results do not need interpretation. However, Dr. Kaistha appears to be an exceedingly well-educated scientist with many years of experience, and holds a Ph.D. degree in pharmaceutical chemistry and bio-chemistry. He is also a certified forensic scientist and a forensic toxicologist, and has received special post-Ph.D. training in analytical procedures and methodologies applicable to substances such as blood and urine. Despite the fact that it did not involve the substances contained in gunshot residue, Dr. Kaistha testified that his special training could be applied to those substances as well. Although the State did not show that he had any formal training in the analysis of gunshot residue results comparable to *191the day of formal training undertaken by the chemist in Cole, Dr. Kaistha testified that he had read articles by Dr. Krishnan, a noted expert in the field of gunshot residue analysis, that he had also conducted 60 gunshot residue tests and that he had been qualified as an expert on the subject 10 to 12 times. Despite Dr. Kaistha’s lack of formal training in the analysis of gunshot residue test results, in light of his familiarity with Krishnan’s work as well as his scientific training and experience, we cannot conclude that the trial court abused its discretion in qualifying him as an expert.
In connection with this issue, defendant also asserts that although the threshold levels used by the doctor were not “per se unreliable^] there should have been some foundation laid before Dr. Kaistha was allowed to testify using the unsupported scientific data of a Chicago Police Department manual concerning threshold levels.” In opposition, the State correctly maintains that defendant waived this objection by failing to raise it at trial. (People v. Enoch (1988), 122 Ill. 2d 176, 186, cert. denied (1988), 488 U.S. 917, 102 L. Ed. 2d 263, 109 S. Ct. 274.) Furthermore, because the claimed error does not affect the substantial rights of defendant, the plain error rule (107 Ill. 2d R. 615(a)) instructs us that we may properly disregard it. People v. Herrett (1990), 137 Ill. 2d 195, 209.
Ill
Finally, defendant objects to a police investigator’s testimony that there was a spot of blood on defendant’s shoe and to the admission of the shoe in evidence. According to defendant, “the evidence was irrelevant, there was no evidence to tie the blood on defendant’s shoe to the offense, and any relevance that the shoe did have was based on an unprove[n] assumption.” Alternatively, the defense contends that “the prejudicial effect of admitting the shoe far outweighed its probative value.” In support of these allegations, defendant claims the “only relevance that the shoe could have would be to make the proposition that defendant shot Richard Barnett either more or less probable. This relevance however [is] based on the unprovefn] assumption that the spot on defendant’s shoe was Richard Barnett[’s] blood.” Defendant further asserts that the “State’s own eyewitness refutes that assumption” since she “testified that the fatal shot was fired from a distance of 15 feet.” Similarly, in his reply brief defendant argues that the “only way the State could have conclusively demonstrated a connection would be to have Officer Moran testify that the blood could have been the victim[’]s.” However, defendant continues, the State “failed to qualify Officer Moran as a ‘blood flight specialist.’ ” (See *192 People v. Knox (1984), 121 Ill. App. 3d 579; People v. Owens (1987), 155 Ill. App. 3d 990.) Therefore, defendant contends, the State introduced the shoe “in bad faith” based on the “unproven assumption that the blood belonged to Richard Barnett” and “to inflame the passions of the jury.”
The State responds that “the court properly allowed admission of defendant’s shoe into evidence and testimony concerning the shoe where the shoe was relevant to show that the defendant was in close proximity to. the victim at the time the victim was shot, thus providing additional evidence that defendant was the shooter,” and that “[t]he shoe was connected to both defendant and the crime. First, the shoe was recovered from defendant’s foot while defendant was at the police station shortly after the murder took place. *** [Second,] Jennifer Myrick, an eyewitness to the murder, testified that at the time defendant shot the victim, defendant was wearing gym shoes.” In addition, the State contends that a police officer may testify as to his observation of blood. See People v. Krone (1981), 98 Ill. App. 3d 619.
“Relevant evidence means ‘evidence having any tendency to make the existence of any fact that is of consequence to the determination of the action more probable or less probable than it would be without the evidence.’ ” (People v. Barrow (1989), 133 Ill. 2d 226, 261, cert. denied (1990), 497 U.S. 1011, 111 L. Ed. 2d 767, 110 S. Ct. 3257, quoting Fed. R. Evid. 401.) “Physical evidence must be connected to both the defendant and crime to be admissible, but the inquiry is one of relevance and not weight.” (People v. Harbold (1984), 124 Ill. App. 3d 363, 378.) “ ‘The factor of connection is met if the physical evidence is sufficiently connected with the crime and with the defendant so as to make the physical evidence relevant as evidence against the defendant.’ ” (People v. Fletcher (1978), 66 Ill. App. 3d 502, 514-15, quoting People v. Dixon (1976), 36 Ill. App. 3d 247, 253.) “Proof of such connection may be circumstantial.” (Fletcher, 66 Ill. App. 3d at 515.) “It is well established that questions concerning the admission of evidence are within the discretion of the trial court and that its decision should not be reversed unless such discretion has been clearly abused. [Citation.]” People v. Martinez (1979), 76 Ill. App. 3d 658, 663.
Joseph Moran, the evidence technician referred to above, testified that when he examined defendant after his initial arrest on July 30, he saw a spot on defendant’s shoe which appeared to be blood. Moran testified on cross-examination that it was possible that a person who shot at an individual from a distance of 15 feet could get blood on him if the bullet struck an artery. The medical evidence, *193however, is silent as to whether or not the bullet did in fact strike an artery. The only thing that is clear is that the blood is human blood. And although Dr. Chambliss testified that there were abrasions on the victim’s eye, knee, and hand consistent with a fall or a fight, Moran testified that he did not observe any abrasions or lacerations on defendant’s face. No matter. Even if we were to assume, arguendo, that the judge abused his discretion in admitting the shoe into evidence, in light of the more than substantial evidence of defendant’s guilt as the shooter, which has been extensively reviewed above, we are convinced that the error, if any, was harmless beyond a reasonable doubt.
For the foregoing reasons, we affirm the judgment of the circuit court.
Affirmed.
HARTMAN, P.J., and DiVITO, J., concur.