
93 Wis.2d 682 (1980)
287 N.W.2d 774
ROGERS, Plaintiff in error,
v.
STATE, Defendant in error.
No. 77-289-CR.
Supreme Court of Wisconsin.
Submitted on briefs December 5, 1979.
Decided February 7, 1980.
*685 For the plaintiff in error the cause was submitted on the briefs of Howard B. Eisenberg, state public defender, Mel S. Johnson and Marcus T. Johnson, assistant state public defenders.
For the defendant in error the cause was submitted on the brief of Bronson C. La Follette, attorney general, and Pamela Magee-Heilprin, assistant attorney general.
DAY, J.
The principal question presented for review is whether it was an abuse of discretion for the trial court to grant the prosecution's motion in limine prohibiting the defendant from cross-examining the complaining witness on the witness's failure to appear at two prior trial dates. We conclude that it was not and affirm.
The plaintiff in error (hereinafter the defendant), Samuel Rogers, was found guilty of armed robbery pursuant to sec. 943.32(1) (b) and (2), Stats. 1973, after a trial by jury and was sentenced to an indeterminate term of not more than twenty-five years in prison on December 4, 1975. A motion for a new trial was submitted to the trial court and by order dated February 18, 1977, the motion was denied. Writs of error were issued by this court to review the judgment and order.
Shortly after 1:05 a.m. on August 23, 1975, Samuel Robinson, a cab driver, was robbed at gunpoint of forty-six dollars by a passenger he had picked up on the 2700 block of North Third Street in Milwaukee.
Mr. Robinson identified the defendant at the trial as the man who robbed him. He testified that he had the opportunity to observe the defendant as he approached the cab and entered the backseat. Mr. Robinson also glanced back at the defendant a number of times during the six block trip. The defendant pulled a revolver, *686 pointed it at Mr. Robinson's head and said, "Give me your money." Mr. Robinson handed over his wallet and the defendant got out of the cab and ran away.
After giving the police a description of the man who robbed him, Mr. Robinson went to the police station and identified the defendant from a series of pictures shown to him. He testified that the defendant was wearing a short-sleeved blue-flowered shirt and a pair of blue jeans at the time of the robbery.
The trial was originally scheduled for November 10, 1975, but Mr. Robinson failed to appear. The case was adjourned until November 11, 1975, but once again Mr. Robinson did not show up. The trial court ordered that Mr. Robinson be taken into custody and that bail be set at $5,000 with sureties. The trial was rescheduled for December 2, 1975. It was on that date that Mr. Robinson finally appeared to testify.
Prior to the commencement of the trial, the prosecution made a motion in limine requesting the court to order defense counsel not to question Mr. Robinson about his failure to appear on the previous two trial dates. The assistant district attorney asserted that to allow cross-examination on the subject would be unfair and unnecessarily prejudicial. The trial judge concluded that any reference to Mr. Robinson's earlier failure to appear was completely irrelevant to the question of credibility. Defense counsel was instructed not to refer to the subject on cross-examination.
Nevertheless, the subject did arise during trial and outside the presence of the jury the trial judge questioned Mr. Robinson as to whether he ever told the district attorney that he did not wish to testify in the case. Mr. Robinson said that he did not make any such statement to the prosecutor.[1]
*687 At trial, the defendant attempted to establish an alibi during the armed robbery. The defendant testified that he was home playing cards on the evening of the robbery. He produced four other witnesses who testified that they were with him that evening playing cards. Those witnesses included his father, his nephew, and two friends. According to these witnesses, they played cards with the defendant from 10:30 p.m. until approximately 2 a.m. on August 23, 1975. The defendant did not leave the house after the card game had begun.
Detective Hugh Thompson of the Milwaukee Police Department arrested the defendant at his home in the early morning hours of August 23, 1975. The defendant's father answered the door and told Detective Thompson that his son had been home sleeping all evening. As the defendant was being advised of his right to remain silent, he told the arresting officer that he had been home sleeping all night. The defendant was told to get dressed, and he put on a long-sleeved green shirt with white flowers and green slacks. The defendant did not mention to the police officers that he had been playing cards.
Two police officers who had been patrolling in the area of the robbery testified that they saw the defendant on the street at 1:30 a.m. on the evening of the robbery. Both officers testified that the defendant was wearing a multiprint flowered shirt with long sleeves, with a green vest and green trousers.
The defendant argues that it was reversible error for the trial judge to prohibit defense counsel from cross-examining Mr. Robinson regarding his absence from the earlier scheduled trial because the evidence sought to be *688 elicited was relevant to Mr. Robinson's credibility as a witness. If the evidence was relevant, as defined by the statutory rules of evidence, it was admissible, unless its introduction was otherwise prohibited by another rule or the constitutions of the United States or Wisconsin. Sec. 904.02, Stats. 1973.[2]
[1-3]
Relevant evidence is defined as ". . . 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." Sec. 904.01, Stats. 1973; State v. Sarinske, 91 Wis.2d 14, 44, 280 N.W.2d 725 (1979). The criterion of relevancy is whether the evidence sought to be introduced would shed any light on the subject of inquiry. Zdiarstek v. State, 53 Wis.2d 420, 428, 192 N.W.2d 833 (1972). Evidence is relevant when it indicates that a fact in controversy did or did not exist because the conclusion in question may be logically inferred from the evidence. Any fact which tends to prove a material issue is relevant. Oseman v. State, 32 Wis.2d 523, 526, 145 N.W.2d 766 (1966), citing Anderson, 1 Wharton's Criminal Evidence, sec. 148 (12th ed.).
[4, 5]
Impeaching the testimony of a witness tends to make the factual assertions of the witness less probable than they would be without the impeaching testimony. 3A Wigmore, Evidence, sec. 874 (Chadbourn rev. 1970). In addition, each item of evidence offered to discredit a witness "must first pass the gauntlet of the relevancy principles; but it may also be obnoxious to some principle *689 of auxiliary policy which may after all exclude it." Wigmore, supra, sec. 877.
[6-9]
The proper standard for the test of relevancy on cross-examination is not whether the answer sought will elucidate any of the main issues in the case but whether it will be useful to the trier of fact in appraising the credibility of the witness and evaluating the probative value of the direct testimony. McCormick, Law of Ill. p. 690 Evidence, sec. 30 (2d ed. 1972). The scope of cross-examination allowed for impeachment purposes is discretionary with the trial court. Chapin v. State, 78 Wis.2d 346, 352, 254 N.W.2d 286 (1977); State v. Becker, 51 Wis.2d 659, 667, 188 N.W.2d 449 (1971). This court adheres to the rule that any material or relevant matters may be inquired into on cross-examination and that cross-examination is not limited to the scope of direct examination. McClelland v. State, 84 Wis.2d 145, 155, 267 N.W.2d 843 (1978); see, Boller v. Cofrances, 42 Wis.2d 170, 166 N.W.2d 129 (1969). An abuse of discretion warranting reversal will not be found unless the ruling of the trial judge restricting cross-examination impinges upon a substantial right of a party. Sec. 901.03 (1), Stats. 1973, provides in relevant part, that "[e]rror may not be predicated upon a ruling which admits or excludes evidence unless a substantial right of the party is affected. . . ."
[10]
Professor McCormick has summarized the five main lines of attack on the credibility of a witness. He states:
"The first, and probably the most effective and most frequently employed, is an attack by proof that the witness on a previous occasion has made statements inconsistent with his present testimony. The second is an attack by a showing that the witness is biased. . . . The third is an attack upon the character of the witness. The fourth is an attack by showing a defect of capacity in the witness to observe, remember or recount the matters *690 testified about. The fifth is proof by other witnesses that material facts are otherwise than as testified to by the witness under attack." McCormick, Law Of Evidence, sec. 33 (2d ed. 1972). See also, Anderson, 2, Wharton's, Criminal Evidence, sec. 430 (13th ed. 1972).
Unless the testimony sought to be elicited on cross-examination was relevant to the issue of Mr. Robinson's credibility on one of the above-mentioned grounds, the trial court properly excluded the evidence.
[11]
The defendant contends that Mr. Robinson's failure to appear on the first two scheduled trial dates were specific acts of misconduct reflecting on the witness's character for truthfulness and is thus admissible under sec. 906.08 (2), Stats. 1973.[3] This type of conduct standing alone does not reflect on the truthful character of the witness. The failure to appear does not show a tendency to lie or fabricate on the part of the absent witness. It is true that the conduct of the witness, may indicate, among other things, irresponsibility, fear of courts, or of the defendant. There may also have been a number of legitimate reasons for the non-appearance. The witness did not make any assertion at trial that in any way conflicted or which would be deemed inconsistent with his prior conduct with regard to his non-appearance. Standing alone, we do not find the witness's conduct in this case to be relevant as to his character for truthfulness.
[12]
Secondly, the assertion is made that from the failure to appear the jury could have inferred that Mr. Robinson *691 was fearful of perjuring himself. The defendant has advanced no reason or motive for Mr. Robinson to falsify his testimony. An inquiry based upon this theory is too far afield of any rational relationship to the truthful character of the witness or his testimony to consider it an abuse of discretion to exclude the proferred testimony.
Whether Mr. Robinson failed to testify when called is completely irrelevant to his character for truthfulness. It is also irrelevant for proving that he was not relating the events of the robbery as he perceived them in a truthful manner. Another argument advanced by the defendant is that a jury is less likely to give the same weight to the testimony of a witness who fails to appear on two trial dates than it would a witness who appears promptly at trial.
[13]
The credibility of Mr. Robinson was an important factor in this case. He was both the victim of and the sole witness to this crime. This court has stated that more latitude should be given on cross-examination where the state's case depends upon the testimony of a single witness. State v. Buss, 273 Wis. 134, 139, 76 N.W.2d 541 (1956); Desjarlais v. State, 73 Wis.2d 480, 502, 243 N.W.2d 453 (1976). However, there must still be some reasonable relation between the evidence sought to be introduced and proposition to be proved before the evidence is admissible. Although we have already rejected the defendant's assertion that the evidence reflects on the truthfulness of the testimony, or the witness' truthful character, the defendant asserts that the failure to appear shows insincerity, uncertainty or unreliability on the part of Mr. Robinson.
[14]
We conclude that any bearing that the failure to appear could possibly have had upon the credibility of Mr. Robinson, was so remote that it was not an abuse of discretion for the trial court to exclude the testimony. *692 The unreliability of Mr. Robinson was not relevant to his credibility, nor was it a material issue in the case because it had no bearing on the truthfulness of his testimony, or his capacity to perceive the events on the evening of the robbery. Neither can we discern any probative value in the testimony which would demonstrate bias. Any uncertainty in the witness's testimony was capable of being explored through detailed cross-examination regarding the events surrounding the robbery and subsequent identification of the defendant. The fact that Mr. Robinson did not appear for two earlier trial dates does not in itself make it any more probable that the facts as he related them at trial were not as he observed them because of a defect in memory or perception.
[15]
The process by which the attendance of a witness is procured at trial is not probative of the general credibility of the witness. The evidence was not relevant and was not admissible. Sec. 904.02, Stats. 1973.
The defendant contends that because the court refused to permit the cross-examination question he was impermissibly denied his right to confront witnesses against him under the Sixth Amendment to the United States Constitution. Because we conclude that the testimony which the defendant sought to elicit was irrelevant, by definition, the defendant's confrontation right under the Sixth Amendment was not infringed.
[16, 17]
The Sixth Amendment secures to the accused the right to "be confronted with the witnesses against him." The right applies to the states through the Fourteenth Amendment. Pointer v. Texas, 380 U.S. 400, 85 S. Ct. 1065, 13 L. Ed.2d 923 (1965).
[18]
This court has emphasized that cross-examination is the cornerstone of the right of confrontation. State v. *693 Lenarchick, 74 Wis.2d 425, 437, 247 N.W.2d 80 (1976). However, the confrontation right secured under the Sixth Amendment does not encompass an obligation upon the courts to allow a party to question witnesses as to irrelevant matters.
[19]
A primary function of the right of confrontation is the right to cross-examine witnesses so that their credibility may be explored and evaluated by the jury. Barber v. Page, 390 U.S. 719, 721, 88 S. Ct. 318, 20 L. Ed.2d 255 (1968). The defendant seeks to compare this case with the United States Supreme Court's decision in Davis v. Alaska, 415 U.S. 308, 94 S. Ct. 1105, 39 L. Ed.2d 347 (1974). There it was held that a state's interest in protecting the anonymity of juvenile offenders was not sufficient to preclude a defendant from exploring through cross-examination the potential bias of a key prosecution witness. The witness in Davis was a juvenile on probation at the time he assisted the police in identifying the defendant. The excluded evidence involved in that case was clearly relevant to the credibility of the witness. The prior juvenile convictions of the prosecution witness were admissible "to afford a basis for an inference of undue pressure because of . . . [the witness's] vulnerable status as a probationer . . . as well as of . . . [the witness's] possible concern that he might be a suspect in the investigation." 415 U.S. at 318.
The confrontation right of the defendant under the Sixth Amendment required that he be allowed to cross-examine the witness as to the potential bias arising from his probationary status.
The juvenile offender status of the witness in Davis v. Alaska was clearly probative of subtle influences on the witness and it exposed a motive to falsify testimony. The mere failure to appear for a trial date, without more, *694 has none of the impeaching qualities present in the excluded testimony in Davis.
The defendant urges this court to grant a new trial in the interest of justice because the real controversy in the case was not tried.[4] It is alleged that the real controversy was not tried because the defendant was not allowed to challenge the credibility of the key prosecution witness and because the trial court did not allow the defendant to testify a second time following the state's rebuttal to explain the reasons for his actions and statements after his arrest.
[20]
A new trial in the interest of justice is to be granted only in the event of a probable miscarriage of justice, and only with some reluctance and great caution. Zebrowski v. State, 50 Wis.2d 715, 731, 185 N.W.2d 545 (1971); Garcia v. State, 73 Wis.2d 651, 245 N.W.2d 654 (1976). This is not a case where there has been a miscarriage of justice, or where the defendant "should not have been found guilty." Berg v. State, 41 Wis.2d 729, 746, 165 N.W.2d 189 (1969), quoted with approval in Zebrowski v. State, supra at 731, see also, State v. Sarinske, 91 Wis.2d 14, 58-60, 280 N.W.2d 725 (1979).
By the Court.  Judgment and order affirmed.
NOTES
[1]  The trial judge asked the following questions:

"The Court: . . . Mr. Robinson, did you at any time ever tell the District Attorney you did not wish to testify in this case?
"Witness: No. No, I 
"The Court: Did you ever, because of having told untruths with regard to this, advise the District Attorney that you would not testify?
"Witness: No."
[2]  "904.02. Relevant evidence generally admissible; irrelevant evidence inadmissible. All relevant evidence is admissible, except as otherwise provided by the constitutions of the United States and the State of Wisconsin, by statute, by these rules, or by other rules adopted by the supreme court. Evidence which is not relevant is not admissible."
[3]  "906.08. Evidence of character and conduct of witness. . . .

(2) SPECIFIC INSTANCES OF CONDUCT. Specific instances of the conduct of a witness, for the purpose of attacking or supporting his credibility, other than conviction of crimes as provided in s. 906.09, may not be proved by extrinsic evidence. They may, however, if probative of truthfulness or untruthfulness and not remote in time, be inquired into on cross examination of the witness himself or on cross examination of a witness who testifies to his character for truthfulness or untruthfulness."
[4]  Sec. 751.06, Stats. 1977, provides:

"Discretionary reversal. In an appeal in the supreme court, if it appears from the record that the real controversy has not been fully tried, or that it is probable that justice has for any reason miscarried, the court may reverse the judgment or other appealed from, regardless of whether the proper motion or objection appears in the record, and may direct the entry of the proper judgment or remit the case to the trial court for the entry of the proper judgment or remit the case to the trial court for the entry of the proper judgment or for a new trial, and direct the making of such amendments in the pleadings and the adoption of such procedure in that court, not inconsistent with statutes or rules, as are necessary to accomplish the ends of justice."
