
146 Wis.2d 554 (1988)
431 N.W.2d 716
STATE of Wisconsin, Plaintiff-Respondent,
v.
Jerry Wayne THOMPSON, Defendant-Appellant.[]
No. 87-1493.
Court of Appeals of Wisconsin.
Submitted on briefs June 24, 1988.
Decided September 22, 1988.
*556 For the defendant-appellant the cause was submitted on the briefs of John E. Tradewell, assistant state public defender.
For the plaintiff-respondent the cause was submitted on the brief of Donald J. Hanaway, attorney general, and David J. Becker, assistant attorney general.
Before Gartzke, P.J., Dykman and Eich, JJ.
*557 EICH. J.
Jerry Wayne Thompson appeals from a judgment convicting him of arson and from an order denying his motions for postconviction relief. The issues are: (1) whether exclusion of evidence of a police officer's opinion that the conditions under which Thompson lived were such as to justify his temporary detention under the mental health laws denied Thompson the "right to present a defense" to the charge that he intentionally set fire to his apartment; (2) whether the trial court erred in failing to submit a jury instruction on criminal damage to property as a lesser included offense of arson; and (3) whether the fact that the court had been informed of the pretrial sentence credit to which Thompson was entitled prior to imposing sentence warrants remand for resentencing. We resolve all questions against Thompson and affirm.
Thompson, a man with a history of mental health problems, lived in a storage room in the London Hotel and Pub in the City of Janesville. His quarters were filled with large piles of garbage and generally were in a filthy condition. On June 26, 1985, a fire broke out in Thompson's room and spread to other areas of the hotel and tavern. Shortly thereafter, Thompson entered the Rock County Sheriff's office and told those present that he had "set the London Pub on fire." He later told Janesville police the same thing. He was charged with arson. At trial, Thompson testified that he set the fire in "self defense" because people had been "trying to cause my death, with suicide or malicious harassment."
The jury found Thompson guilty and the trial court denied his motions for postconviction relief. Other facts will be referred to below.


*558 I. EXCLUSION OF EVIDENCE
While Thompson has not particularized in his brief the evidence he claims was erroneously excluded, we assume it was that summarized in an offer of proof concerning the testimony of a police officer:
The testimony of [the officer] would be that in April he examined a kitchen of a house ... where Mr. Thompson, according to the landlady had been living. That there was garbage piled in the kitchen two feet, three feet high in one corner. The apartment had no lights that were working. The place was filthy, a mess, and not suitable for human inhabitants. That as a result of that he detained Mr. [Thompson] at the Rock County Health Care Center.
[1]
Thompson argues that rejection of this evidence denied him "the right to present a defense." We agree that a defendant's right to due process of law includes "the right to a fair opportunity to defend against the State's accusations ... to confront and cross-examine witnesses and to call witnesses in one's own behalf ...." Chambers v. Mississippi, 410 U.S. 284, 294 (1973). But a defendant has no right, constitutional or otherwise, to place irrelevant evidence before the jury. State. v. Bolstad, 124 Wis. 2d 576, 584, 370 N.W.2d 257, 261 (1985). The real question is whether the proffered evidence was relevant.
[2, 3]
Determinations of relevancy are committed to the broad discretion of the trial court. State v. Denny, 120 Wis. 2d 614, 626, 357 N.W.2d 12, 18 (Ct. App. 1984). And we will not reverse a discretionary determination if the record shows that discretion was in fact exercised *559 and we can perceive a reasonable basis for the court's decision. Prahl v. Brosamle, 142 Wis. 2d 658, 667, 420 N.W.2d 372, 376 (Ct. App. 1987). Generally, we look for reasons to sustain a trial court's discretionary ruling. Id.
The prosecutor objected to the offer of proof, arguing that the officer's testimony related to an event remote in time and place from the hotel fire (it had occurred some two months earlier), and that the fact that Thompson had lived under squalid conditions at another time and location was irrelevant to whether he intended to set fire to the hotel on the night in question. Thompson's counsel argued that the testimony was "evidence of a mental condition ... that, I believe, rendered him incapable of forming an intent." The court sustained the state's objection to the testimony.
Thompson sums up his position on appeal as follows: "[The evidence] would have ... provided the jury with insight into the mental processes of the defendant of a type they could evaluate without expert testimony and shown the jury that defendant's rambling, often incoherent[,] trial testimony was not faked for the purposes of pulling the wool over the jury's eyes." But Thompson did not plead not guilty by reason of mental disease or defect, and he does not suggest that he was mentally incompetent to testify or to stand trial. And we do not believe that the officer's testimony would provide any basis for establishing that Thompson lacked the requisite intent to start the fire. Indeed, as the state points out, the thrust of Thompson's own testimony was that he had deliberately set the fire in order to "defend himself" from persons or institutions he believed were trying to kill him.
*560 Evidence that a police officer was once sufficiently concerned about the squalor in which Thompson lived that he took him to a mental health facility for observation would serve no purpose other than to reinforce a conclusion that Thompson may have been mentally unbalanced. And that conclusion was starkly apparent from his own rambling and frequently incoherent testimony. While the reason Thompson set the fire may have been the result of his mental problems, his intent to start the fire is a different matter.
[4]
Evidence is relevant when it has a "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. The fact that Thompson may have been mentally unbalanced has no tendency to make the formation of the requisite intent more or less probable than it would have been without the evidence. The trial court properly exercised its discretion when it sustained the prosecutor's objection to the offer of proof.

II. LESSER INCLUDED OFFENSE
[5]
Thompson requested an instruction on criminal damage to property as a lesser included offense of arson. Wisconsin courts use the "elements only" test to determine whether one crime is a lesser included offense of another. The test focuses on the language of the statutes defining the offenses, and the "paramount inquiry" is the meaning of the words of the statutes. State v. Carrington, 134 Wis. 2d 260, 265, 397 *561 N.W.2d 484, 487 (1986). We place the statutes "side by side" to differentiate and compare the elements of the crimes. Id. at 265-66, 397 N.W.2d at 487. Then, if the lesser crime is "statutorily included in the greater offense and contain[s] no [additional] element[s]," the lesser crime is an included offense of the greater. Id. at 265, 397 N.W.2d at 486. Section 939.66(1), Stats., codifies the rule in its definition of a lesser included offense as: "A crime which does not require proof of any fact in addition to those which must be proved for the crime charged." In simplest terms, "for one crime to be included in another, it must be `utterly impossible' to commit the greater crime without committing the lesser." Hagenkord v. State, 100 Wis. 2d 452, 481, 302 N.W.2d 421, 436 (1981), quoting Randolph v. State, 83 Wis. 2d 630, 645, 266 N.W.2d 334, 341 (1978) (citation omitted).
[6]
Before a defendant is entitled to an instruction on the lesser offense, however, there must be a reasonable basis for conviction on the lesser charge and acquittal on the greater. State v. Zdiarstek, 53 Wis. 2d 776, 786, 193 N.W.2d 833, 838 (1972).
The trial court ruled that the criminal damage charge was not included in the arson charge because it required proof of an additional element to those which must be proved to establish arson. Section 943.01(1), Stats., makes it a Class A misdemeanor to "intentionally cause[] damage to ... physical property of another without the person's consent ...." Under sec. 943.01(2)(d), if the property is diminished or reduced in value by more than $1,000, the offense becomes a Class D felony, subject to greater penalties. The trial court ruled that proof of the monetary amount of the *562 damage was an "additional element" within the meaning of the rules just discussed, and thus criminal damage to property could not be a lesser included offense of arson. We believe this was error, for the monetary provision is a penalty enhancer, not an element of the crime.
In Block v. State, 41 Wis. 2d 205, 212, 163 N.W.2d 196, 199 (1968), the supreme court held that another common penalty enhancerthe defendant's status as a repeateris not in itself part of a criminal charge, but "only renders the defendant eligible for an increase in penalty for the crime of which he [or she] is convicted." The court so held in spite of its recognition of the requirement that recidivism, like the value of the property in a theft charge, or, as here, the reduction in value of the damaged property, must be proved at trial. Id. (See also Harms v. State, 36 Wis. 2d 282, 285, 153 N.W.2d 78, 80 (1967), where the court recognized that "[t]he habitual criminality statute increases the penalty for a particular [offense], but in no way changes the [general] nature of the crime.") And, in Moore v. State, 55 Wis. 2d 1, 5-6, 197 N.W.2d 820, 822-23 (1972), the court, although not discussing the effect of the "value of the property" provisions increasing the punishment for theft, held that theft was a lesser included offense of robbery. That result could not have obtained if, as the state urges here, the property value provision was considered to be an additional element of the lesser crime. We hold, therefore, that criminal damage to property is a lesser included offense of arson.
That does not end the inquiry, however; nor does it necessarily require reversal. As we have said, even if the lesser offense is included in the greater, the defendant is not entitled to an instruction on the *563 lesser charge unless there is a reasonable basis in the evidence for acquittal on the greater. Thompson argues that such a basis exists with respect to the arson charge because one of the elements of that offense is that he intentionally damaged the building by means of fire. Sec. 943.02(1)(a), Stats. He asserts that the jury could reasonably conclude from the evidence that he did not intend to damage the building when he started the fire in his room. We reject the argument.
Thompson testified that the crumpled some newspapers, placed them along the wall under a set of drapes and ignited them with his cigarette lighter. He then left the premises.
The pattern jury instructions for arson defines the "intent" element of the offense as follows:
The term "intentionally" means that the defendant must have had the mental purpose to damage the building ... by means of fire [] or a belief that the act, if successful, will cause damage to the building ..., even though the defendant did not desire that result to occur.
Wis J ICriminal 1404 (1980) (footnote omitted). An explanatory comment states: "The defendant may set fire to furniture with mental purpose to damage only the furniture; he may be found guilty of arson of the building though indifferent to that result." Id. at n. 2.
[8]
Applying these principles to Thompson's self-described actions, we conclude that those actions manifest an intent to damage the building (as opposed to an intent to damage only the newspaper he ignited or the draperies hanging above). Even though he may have lacked the specific intent to damage the structure, the *564 law holds him responsible for damage to the building under the circumstances of this case.
[9]
There was, therefore, no reasonable basis in the evidence for the jury to conclude that Thompson lacked intent to damage the building. As a result, the trial court correctly, if for the wrong reason, declined to instruct the jury on the lesser included offense of criminal damage to property.

III. THE SENTENCING
During his statement to the court at the sentencing hearing, the prosecutor, who was recommending a sentence of eight years in prison, remarked that Thompson would be entitled to approximately eighteen months' credit on his sentence for pretrial detention and then stated: "[W]ith all that credit, I think the eight-year sentence is in order[] [b]ut he would have to do a few more years in prison." The court did not refer to pretrial jail credit in its sentencing remarks and proceeded to sentence Thompson to an indeterminate term not to exceed ten years.
At the hearing on Thompson's postconviction motions, his attorney pointed out the supreme court's admonition in State v. Walker, 117 Wis. 2d 579, 586, 345 N.W.2d 413, 416 (1984), that "time previously served should not be a factor in the exercise of sentencing discretion: and contended that the prosecutor's remark so "tainted" the sentencing proceedings that he should be granted a new hearing. The trial court denied the request, stating that there was nothing in its statements at the sentencing hearing to suggest that the prosecutor's comments were "[taken] *565 into consideration at all." The court went on to state: "And the plain fact of the matter is I didn't [take them into consideration]. ... That did not enter into my thinking .... I would agree with you that ... comments like that are improper. ... But that certainly did not enter into my thinking here."
We start with "the presumption that the trial court acted reasonably and with the requirement that the [appellant] must show some unreasonable or unjustifiable basis in the record for the sentence complained of." Krueger v. State, 86 Wis. 2d 435, 444, 272 N.W.2d 847, 851 (1979), quoting Jung v. State, 32 Wis. 2d 541, 548, 145 N.W.2d 684, 688 (1966), cert. denied, 386 U.S. 999 (1967).
Thompson argues that we should disregard the trial court's statement that the prosecutor's remarks had no effect on the sentence and order a new hearing because "improper argument by the prosecutor at sentencing offends due process even if the trial judge truthfully believes it had no effect," citing Santobello v. New York, 404 U.S. 257 (1971). We do not share Thompson's view of that case.
In Santobello, a substitute prosecutor, who was unaware of a colleague's earlier plea bargain promise to refrain from recommending any sentence for the defendant, recommended a one-year sentence, which the court imposed. And the supreme court held only that the prosecutor's breach of the plea agreement by recommending a specific sentence to the court warranted a new hearing, whether or not that recommendation was felt by the court to have influenced the sentencing decision. The court's opinion emphasizes the breach of the plea agreement, not the substance of the prosecutor's remarks to the trial court: "[W]e conclude that the interests of justice and appropriate *566 recognition of the duties of the prosecution in relation to promises made in the negotiation of pleas of guilty will be best served by remanding the case ... for further consideration." Id., 404 U.S. at 262-63.
In this case, we are dealing with an offhand remark by the prosecutor, not a violation of a plea agreement or an improper, unbargained-for sentence recommendation. Santobello centers not on the improper nature of the prosecutor's argument at sentencing or its possible effect on the sentencing judge, but on the court's own view of the social and judicial utility of plea bargaining and the sanctity which must be accorded plea agreements if this "essential" and "highly desirable" part of the judicial process is to operate efficiently. Id., 404 U.S. at 260-61. Under the circumstances of this case, we believe Wisconsin precedent is more instructive.
In Moore v. State, 83 Wis. 2d 285, 265 N.W.2d 540, cert. denied, 439 U.S. 956 (1978), the defendant argued that the trial court was improperly influenced by the prosecutor's statement at sentencing that he (the defendant) had fabricated an alibi. The supreme court looked to the record, finding it "barren of any reference by the trial court to the truthfulness or falsehood of the defendant's testimony," and concluded that there was "nothing in the record which would lead us to conclude that the trial court abused its discretion when imposing sentence." Id. at 310, 265 N.W.2d at 550. And in State v. Schael, 131 Wis. 2d 405, 388 N.W.2d 641 (Ct. App. 1986), the defendant contended that the trial court, when sentencing him for robbery, relied on erroneous information that he had fathered two children out of wedlock. On appeal, we were "persuaded by the trial judge's comments during sentencing as well as his statement at the postconviction *567 motion hearing that this had `nothing to do with the sentence that was imposed in [the] case,'" and we rejected the defendant's argument, stating: "It is evident that the comment was an isolated, casual reference and not a factor utilized in passing sentence." Id. at 414, 388 N.W.2d at 645.
[10]
In this case, we have not only a sentencing record barren of any reference to the prosecutor's remarks, as in Moore, but also the trial court's unequivocal statement that the remarks had no effect on the sentence imposed. Nor do we find Thompson's suggestion, that despite all this, "some subconscious effect may have in fact been present," to be at all persuasive. There is no suggestion of improper influence on this record, and we decline Thompson's invitation to delve into the trial court's subconscience.
By the Court.Judgment and order affirmed.
NOTES
[]  Petition to review denied.
