delivered the opinion of the court:
Following a jury trial, defendant Keith Allen Stanley was convicted of first degree murder and aggravated battery. (Ill. Rev. Stat. 1989, ch. 38, pars. 9 — 1, 12 — 4.) The trial court sentenced Stanley to concurrent terms of 95 years’ imprisonment for murder and 10 years’ imprisonment for aggravated battery. Stanley appeals the convictions and sentences, arguing: (1) the trial court erred in denying his motion attacking the propriety of the jury selection process; (2) the trial court erred in admitting blood-frequency probabilities; (3) the conviction for aggravated battery should be vacated as an included offense of first degree murder; and (4) defense counsel’s failure to present mitigating evidence at sentencing amounted to ineffective assistance of counsel. We affirm in part and vacate in part.
On April 18, 1991, defendant was charged by information with four counts of first degree murder (Ill. Rev. Stat. 1989, ch. 38, pars. 9 — 1(a)(1), (a)(2), (a)(3)) and aggravated battery (Ill. Rev. Stat. 1989, ch. 38, par. 12 — 4(a)). The charges stemmed from an incident that occurred on or about January 6, 1991, in which John Miletta was stabbed and killed. The incident occurred at Miletta’s home, *395where he lived alone. Miletta was 73 years old at the time of his death, suffered from Parkinson’s disease and Alzheimer’s disease, and walked with a cane.
Carolyn Madison testified she met John Miletta in 1985 or 1986, and did housework for him for four to five years prior to his death. Miletta paid her approximately $200 per month for housekeeping. After four to six months, the two developed a sexual relationship. Madison testified she met defendant at a rehabilitation center in October 1990 and they became intimately involved shortly thereafter. Defendant began going to Miletta’s house to help Madison with the housework. Madison testified that she and defendant forged some of Miletta’s checks.
On January 4, 1991, Madison held a birthday party for her son at her mother’s house, attended by both Miletta and defendant. She drove Miletta home sometime between 7:30 and 9 p.m. She stayed at Miletta’s home overnight and awoke at approximately 10:30 a.m. She and Miletta then got dressed and went to the bank. Miletta attempted to cash a check at the drive-in window but the teller informed him his account balance was extremely low. Miletta went inside the bank and was later joined by Madison. A bank officer told Miletta his account was almost empty and that someone was forging his checks. Madison then told Miletta that defendant was the person forging Miletta’s checks. Miletta appeared visibly upset when the two left the bank at approximately 1 p.m.
Madison returned home alone at approximately 3:30 p.m. where defendant was waiting for her. Madison accused defendant of stealing from Miletta and informed him that Miletta had discovered the forgeries. At approximately 7 p.m., she returned to Miletta’s house, where she received several phone calls from defendant. Madison told defendant she would meet him at a McDonald’s restaurant. She left Miletta’s house at approximately 9:30 p.m. to meet defendant but did not see him at the McDonald’s restaurant so she went home. At approximately 4 a.m., Madison was awakened by defendant, who told her he had driven to Miletta’s house but did not see the car so he left. Defendant was wearing jeans, a green army jacket, and black shoes. Defendant told Madison he was going to leave Springfield and that he had left his mark on Springfield. Defendant stayed with Madison overnight and awoke at approximately 10:30 a.m. Madison drove defendant to the place he was staying at noon, then drove alone to Miletta’s house. She went inside but did not see Miletta. She returned several times to Miletta’s house but each time she found the house empty. The next morning *396Madison returned to Miletta’s house but he was still not there. Later, the police arrived and she allowed them to search the house. At that time, the police discovered Miletta’s body covered with clothes in the basement.
The police noticed what they believed to be blood on the carpeting, stairway, and kitchen floor. Near the body the police discovered a dented portable propane torch which appeared to have blood smeared on the canister. The police also observed a bedsheet and paper sack covering what appeared to be a blood trail from the | body. When the clothes around the body were removed, the police found the body lying facedown with arms above the head. The police recovered a mop which was behind the kitchen door leading to the basement. The mop had a reddish stain on the sponge and on the handle, and there appeared to be hair on the end of the mop near the sponge. The police also found fingerprints in the reddish stain on the mop handle.
The body had approximately 19 wounds of varying degrees. Dr. Travis Hindman observed two stab wounds in the right shoulder, three wounds to the right of the midline chest, three wounds on the left side at the base of the neck as well as just in front of the left shoulder, a wound along the inside of the lower lip from the left side with damage to a partial denture, a wound over the surface of the base of the thumb joint, a wound at the base of the index finger of the left hand, two wounds to the left side of the back, a wound at the base of the skull on the left side, a wound at the base of the neck, and several wounds on the right side of the back. Hindman stated that some of the injuries were compatible with wounds caused by a knife. Hindman testified that significant force was required to cause the injuries to the lower lip and chest wall, and fracture the skull. He opined the cause of death was hemorrhage due to multiple stab wounds to the body. He testified that the mop and propane tank found at Miletta’s house could have caused several of the wounds observed on the back of the skull.
Madison testified that defendant did not like Miletta and had previously told Madison that he would “fix it” so she didn’t have to go out there anymore. Madison also recalled that on a previous occasion, when she stayed at Miletta’s house, the defendant had discovered her and Miletta sleeping together. While holding a hand sickle, defendant told her that he could have killed both of them. Madison also testified she recalled seeing a knife holder in the kitchen with a full set of six knives. This set was later recovered in the spare bedroom of Miletta’s house with only two knives. She also *397stated that a set of keys recovered at the foot of the stairs by the police belonged to defendant.
On January 8, 1991, the Madison County sheriffs department arrested defendant. Defendant did not admit to the crime but explained that on the night in question he was at a local tavern and eventually went to Madison’s house at 3 a.m. Defendant told the police that on the following day he left Springfield for East St. Louis.
At trial, the court admitted the mop with the bloody fingerprint, which was shown to match a fingerprint of the defendant, and defendant’s green army jacket and shoes, which were both bloodstained. The jury returned guilty verdicts of first degree murder and aggravated battery. At sentencing, the court found in aggravation that the victim was over 60 years of age and was handicapped, and that the crime was exceptionally brutal and heinous. Ill. Rev. Stat. 1989, ch. 38, pars. 1005 — 5—3.2(b)(4)(ii), (b)(4)(iii), (b)(2).
On appeal, defendant initially contends the trial court erred in denying his motion challenging the jury selection. During jury selection, defendant made an oral challenge to the selection process on grounds that no blacks were in the venire thereby precluding defendant, who was black, from receiving a fair and impartial trial. The trial court replied:
“I’m going to allow you to make that motion, but I am going to continue with the jury process. At this time I haven’t seen a written motion. A motion such as that needs to be in writing so that the State can respond, and during the course of the trial I’ll allow you — you’re not waiving that issue, but we’re going to proceed.”
After the close of the State’s evidence, on the fourth day of the jury trial, defendant filed his written motion. The trial court denied the motion as untimely. At the hearing on defendant’s post-trial motion, defendant again challenged the jury selection process. In denying the motion, the trial court stated that “no evidence” had been presented to show any pattern of excluding blacks from the jury.
Section 114 — 3 of the Code of Criminal Procedure of 1963 expressly provides that an objection to the manner in which a jury panel has been selected or drawn “shall be in writing supported by affidavit and shall state facts which show that the jury panel was improperly selected or drawn” and such motion “shall not be heard after a jury has been sworn to hear the cause.” (Ill. Rev. Stat. 1989, ch. 38, pars. 114 — 3(b), (a).) The Illinois Supreme Court has *398held that such an objection is to be made before the jury has been sworn. (People v. Gill (1973), 54 Ill. 2d 357, 363, 297 N.E.2d 135, 139.) If a venire has been improperly chosen, the problem may be remedied by the substitution of a new venire if that is done before the jury is sworn. Accordingly, the trial court properly rejected defendant’s motion as untimely. The trial court did not substantially mislead defendant on this issue. The trial court properly noted the objection had to be in writing, that it would allow a written motion to be filed at a later time, and that defendant was not waiving his right to file a motion by proceeding with the selection of the jury, but the trial court did not indicate how much time defendant had to file the motion. The trial court began to say the motion could be filed during the course of the trial, but stopped itself. It was defendant’s obligation to file the motion within the proper time, even if the trial court was unaware what that time might be when it denied the oral motion.
Even if the motion was timely, however, it was properly dismissed because it failed to establish grounds for relief. (People v. Rodriguez (1989), 187 Ill. App. 3d 484, 489, 543 N.E.2d 324, 327-28 (appellate court may sustain judgment on any ground appearing in record, regardless whether the trial court’s reasoning was incorrect or whether that ground was relied on by the trial court); cf. Geaslen v. Berkson, Gorov & Levin, Ltd. (1993), 155 Ill. 2d 223, 230 (appellate court should not consider theories which might have been refuted if they had been raised in trial court).) Here, defendant’s motion did not allege any facts but simply made conclusory allegations of discrimination in the jury selection process. Defense counsel’s cursory observation of racial composition of the jury pool is insufficient to support a claim of racial discrimination. (People v. Lane (1982), 106 Ill. App. 3d 793, 800, 436 N.E.2d 704, 710.) Defendant must present evidence of the method by which the venire was selected to make a prima facie case of systematic and deliberate exclusion of blacks. (People v. Flowers (1985), 132 Ill. App. 3d 939, 941, 478 N.E.2d 524, 525.) Because defendant’s motion was not in writing accompanied by an affidavit and did not allege sufficient facts, the trial court was under no obligation to hold a hearing on it. People v. Hughes (1977), 46 Ill. App. 3d 490, 501, 360 N.E.2d 1363, 1370; People v. Beacham (1980), 87 Ill. App. 3d 457, 467, 410 N.E.2d 87, 95; People v. Rosa (1982), 111 Ill. App. 3d 384, 389, 444 N.E.2d 233, 237.
Next, defendant claims the trial court erred by admitting, over objection, evidence on blood-frequency probabilities because the sta*399tistical conclusions in the case lacked foundation and adequate reliability. Prior to trial the defense filed a motion to preclude the State from introducing blood-frequency probabilities, on the grounds that the methodology of electrophoresis was scientifically unacceptable and that the State would be unable to lay a foundation and prove its relevancy to this case. The trial court reserved its ruling and later denied the motion at trial. The evidence at issue concerned the testimony of Phil Sallee, a forensic serologist with the Illinois State Police. Sallee testified to blood testing and blood samples, and used the standard ABO-type testing as well as electrophoresis.
Electrophoresis is the movement of suspended particles through fluid under the action of an electromotive force applied to electrodes in contact with the suspension. (Webster’s New Collegiate Dictionary 364 (1976).) Electrophoresis is one of the steps used in DNA testing:
“The third step is the electrophoresis procedure, which involves placing the DNA in a gel and passing a slight electrical current through the gel. This causes the DNA fragments to move, resulting in their being separated by size from small to large on a continuum.” (People v. Lipscomb (1991), 215 Ill. App. 3d 413, 418, 574 N.E.2d 1345, 1348.)
Electrophoresis of a blood sample causes the different enzymes present in the blood to separate into their protein components. “ ‘After separation, the enzymes and their protein components can be identified and, in this way, the blood can be classified more specifically than is possible by traditional A, B, O blood grouping.’ ” (People v. Partee (1987), 157 Ill. App. 3d 231, 261, 511 N.E.2d 1165, 1184-85, quoting Robinson v. State (1981), 47 Md. App. 558, 574, 425 A.2d 211, 220.) Electrophoresis is generally accepted in the relevant scientific community and is therefore reliable as evidence. (People v. Byler (1989), 133 Ill. 2d 173, 215, 549 N.E.2d 268, 287, citing Partee, 157 Ill. App. 3d at 261, 511 N.E.2d at 1185.) This is not to say that mistakes cannot be made, only that a defendant challenging electrophoresis testimony is not entitled to a hearing pursuant to Frye v. United States (D.C. Cir. 1923), 293 E 1013, but must seek to persuade the jury by cross-examination of prosecution witnesses and presentation of defendant’s own witnesses. People v. Thomas (1990), 137 Ill. 2d 500, 517-18, 561 N.E.2d 57, 63-64, cert. denied (1991), 498 U.S. 1127, 112 L. Ed. 2d 1196, 111 S. Ct. 1092.
The absence of a certain characteristic in the victim’s blood which is present in the sample to be identified (or vice versa) is *400conclusive proof that the sample does not contain the victim’s blood. The presence of a characteristic both in the victim’s blood and in the sample to be identified does not conclusively establish that the sample contains the victim’s blood, because other individuals could have the same characteristic in their blood. In this latter situation the most that can be said is that the presence of the characteristic makes the fact that the sample contains the victim’s blood more or less probable in accordance with the frequency with which the characteristic occurs in the population at large. (For example, type A blood occurs in approximately 40% of the population.) As modern science identified additional categories of blood types, however, it became possible to establish that the chances of the sampled blood belonging to anyone other than the victim are remote. If a certain characteristic is found in only one-tenth of the population, another is found in only one-fiftieth of the population, and a third is found in only one-seventy-fifth of the population, the chances of the blood containing all three characteristics belonging to anyone other than the victim are only 1 in 37,500 (10 multiplied by 50 multiplied by 75). This is sometimes referred to as the “product rule.” People v. Miles (1991), 217 Ill. App. 3d 393, 404, 577 N.E.2d 477, 484-85.
It may be argued that use of the product rule in the present case was improper. The product rule has been explained as follows: “the probability of the joint occurrence of a number of mutually independent events is equal to the product of the individual probabilities that each of the events will occur.” (Emphasis in original.) (People v. Collins (1968), 68 Cal. 2d 319, 325, 438 P.2d 33, 36, 66 Cal. Rptr. 497, 500.) For the product rule to have been properly applied here each of the different blood characteristics found in one particular blood sample must have been mutually independent of each other blood characteristic. If the chances are 1 in 20 that factor X will be present, and 1 in 10 that factor Y will be present, the chances that both X and Y will be present are not 1 in 200 if Y is usually found where X is found. Additionally, the testimony regarding statistical probabilities (e.g., the combination of blood types on the mop handle occurs one time in every 218 Caucasians) indicated the likelihood of the occurrence of blood with certain characteristics in the Caucasian population of the United States. It may have been more useful to know the likelihood of the occurrence of those blood characteristics in Sangamon County, or among the victim’s acquaintances. However, the process of generating probability statistics is an integral part of the DNA identification process and such statistics have previously been held admissible. (Miles, 217 Ill. App. *4013d at 405, 577 N.E.2d at 485.) Again it was up to defendant, through cross-examination of prosecution’s witnesses and presentation of his own witnesses, to persuade the jury there were concerns regarding the product rule and statistical probabilities. It was not the State’s obligation to prove that the product rule is generally accepted in the scientific community. That has already been done.
In this case defendant argues there must be something wrong with expert testimony that the blood on the mop handle occurs one time in every 218 Caucasians, the blood on defendant’s shoe occurs one time in every 549,000 Caucasians, and the blood on defendant’s jacket occurs once in every 123,000 Caucasians, when, according to the theory of the prosecution, all three samples came from the same individual, the victim. The explanation appears to be that the expert could not determine all categories of blood type for each sample taken from the three items. The expert was testing for nine different categories of blood type, but on the mop, for example, was able to determine only four. Even though Sallee was not able to get every category of blood type for every sample and even though the figures differed between the mop, shoes, and jacket, the trial court was not required to exclude the statistical analysis. These circumstances would only go to the weight or reliability of the evidence, not its admissibility. The differences between the number of blood types found would simply be considered by the jury in determining whether the expert’s conclusion was correct. Sallee concluded that the stain on the mop, the stain on the shoe, and both stains on the jacket “could have come from John Miletta and did not come from Keith Stanley.”
It is well established that expert testimony is admissible where the expert has knowledge or experience not common to a layman which renders his opinion an aid to the jury in making its determination regarding the facts in issue. (People v. Jordan (1984), 103 Ill. 2d 192, 208, 469 N.E.2d 569, 576.) Evidence is relevant, and admissible, where it fairly tends to prove the offense charged or where it has any tendency to make the existence of any fact that is of consequence to the determination of the cause more or less probable. (Eyler, 133 Ill. 2d at 217, 549 N.E.2d at 288.) The admissibility of evidence is left to the wide discretion of the trial court and its determination will not be reversed on appeal absent an abuse of that discretion. (Eyler, 133 Ill. 2d at 211-12, 549 N.E.2d at 285.) An abuse of discretion may be found where the trial court’s decision is arbitrary, fanciful, unreasonable, or where no reasonable person could take the view adopted by the trial court. (People v. Illgen *402(1991), 145 Ill. 2d 353, 364, 583 N.E.2d 515, 519.) The testimony here tended to show that the blood found on the mop, jacket, and shoe likely came from the victim and did not come from defendant. We cannot say the trial court abused its discretion by admitting the expert testimony.
Additionally, we note the evidence showed defendant had a motive for the murder as the victim had discovered that defendant forged some of his checks. Defendant’s fingerprints were found in dried blood on the mop used to strike the victim’s head. Defendant had threatened to kill the victim prior to the murder and admitted to Madison that he left his mark on Springfield before leaving town the day after the murder. Accordingly, even if the frequency calculations should have been excluded, the error was harmless since the evidence of defendant’s guilt was overwhelming. People v. Redman (1985), 135 Ill. App. 3d 534, 541, 481 N.E.2d 1272, 1277.
Defendant also argues the conviction for aggravated battery should be vacated as an included offense of first degree murder. In determining whether an offense is an included offense of another, the courts often look to the statutory definition of each offense, or to the manner in which the offenses are charged. (People v. Mays (1982), 91 Ill. 2d 251, 255, 437 N.E.2d 633, 635.) Here defendant was charged with four counts of murder as well as one count of aggravated battery. While sufficient proof was presented to support all four charges of murder, defendant could only be convicted of one count. (People v. Mack (1984), 105 Ill. 2d 103, 136-37, 473 N.E.2d 880, 898.) The intentional murder charge constituted the most serious offense and defendant’s murder conviction and sentence must be deemed based on that count. People v. Johnson (1992), 149 Ill. 2d 118, 157, 594 N.E.2d 253, 272; Mack, 105 Ill. 2d at 137, 473 N.E.2d at 898.
People v. King (1977), 66 Ill. 2d 551, 566, 363 N.E.2d 838, 844, held that (1) where several offenses are based on a single act, only the conviction for the most serious offense is permitted; (2) where several offenses are based on related multiple acts, only the conviction for the most serious offense is permitted, if some of the offenses are lesser included offenses; and (3) where several offenses are based on related multiple acts, but none are lesser included offenses, then multiple convictions and concurrent sentences are permitted. This case involved two offenses, aggravated battery and murder, which were based on related multiple acts. Under King, the conviction for aggravated battery would be prohibited if it was a lesser included offense of murder.
Included offense means an offense which is established by proof of the same or less than all of the facts or a less culpable mental *403state (or both), than that required to establish the commission of the offense charged. (Ill. Rev. Stat. 1989, ch. 38, par. 2 — 9(a).) The information charged that defendant “without lawful justification and with intent to kill *** stabbed [John F. Miletta] with a knife.” The aggravated battery charge alleged that defendant “without legal justification intentionally caused great bodily harm to [John F. Miletta], in that he stabbed [John F. Miletta] with a knife.” As charged here, aggravated battery is a lesser included offense of murder. (People v. Lyons (1974), 26 Ill. App. 3d 193, 198, 324 N.E.2d 677, 680-81.) Accordingly, we vacate the conviction and sentence for aggravated battery.
Next, defendant argues that defense counsel’s failure to present mitigating evidence at sentencing constituted ineffective assistance of counsel. At sentencing, defense counsel did not offer evidence in mitigation and the trial court subsequently imposed a sentence of 95 years' imprisonment. Defendant contends the presentence investigation report suggested important information regarding defendant’s family. According to the presentence report, defendant stated he was “very close to his mother,” but that “he grew up afraid of his father, due to physical abuse inflicted upon him by his father.” Defendant maintains that the two compelling sources of potential mitigating evidence defense counsel should have investigated were that defendant was abused as a child and that defendant retained a close relationship with his mother and his siblings.
Sentencing is a critical stage in the criminal proceeding at which defendant is entitled to effective assistance of counsel. (People v. Reyes (1981), 102 Ill. App. 3d 820, 837, 429 N.E.2d 1277, 1291.) To establish a sixth amendment violation of the right to effective assistance of counsel, defense counsel’s actions must “[fall] below an objective standard of reasonableness.” (Strickland v. Washington (1984), 466 U.S. 668, 688, 80 L. Ed. 2d 674, 693, 104 S. Ct. 2052, 2064.) Here, defendant must show (1) his counsel’s performance at the sentencing hearing fell below an objective standard of reasonableness under prevailing professional norms; and (2) the deficient performance so prejudiced the defense as to deny the defendant a fair sentencing hearing. (People v. Perez (1992), 148 Ill. 2d 168, 186, 592 N.E.2d 984, 992-93, citing People v. Franklin (1990), 135 Ill. 2d 78, 116-17, 552 N.E.2d 743, 761.) To establish the deficiency of counsel’s performance, defendant must overcome the strong presumption that his counsel’s representation fell within the range of reasonable professional assistance. (Strickland, 466 U.S. at 689, 80 L. Ed. 2d at 694, 104 S. Ct. at 2065.) Defendant is only entitled to competent representation and not perfect or successful representation. (People v. Hillenbrand (1988), 121 Ill. 2d 537, 548, 521 *404N.E.2d 900, 904.) Failure to present mitigating evidence at sentencing does not in itself constitute ineffective assistance of counsel. (Perez, 148 Ill. 2d at 186, 592 N.E.2d at 993; People v. Steidl (1991), 142 Ill. 2d 204, 248, 568 N.E.2d 837, 856, cert. denied (1991), 502 U.S. 853, 116 L. Ed. 2d 125, 112 S. Ct. 161.) On review, this court should defer to the trial counsel’s decision unless there is proof that he failed to present mitigating evidence due to his failure to properly investigate and prepare the defense. (Steidl, 142 Ill. 2d at 249, 568 N.E.2d at 856.) “Mitigating evidence can be double-edged, and trial counsel may feel that the risks in presenting potentially mitigating evidence are too high.” Steidl, 142 Ill. 2d at 249, 568 N.E.2d at 856.
Here, there is nothing in the record indicating trial counsel failed to properly investigate potential mitigating evidence. The situation is not comparable to Perez, cited by defendant, where a post-conviction evidentiary hearing was held regarding defense counsel’s performance and the existence of potential mitigating evidence. (See People v. Williams (1991), 147 Ill. 2d 173, 258, 588 N.E.2d 983, 1018.) Given the record in this case, we can only presume defense counsel made a strategic choice not to present any evidence in mitigation. (Steidl, 142 Ill. 2d at 249, 568 N.E.2d at 856.) At sentencing, the trial court noted several aggravating factors, including that the victim was handicapped, the victim was over the age of 60, and the murder was particularly brutal. Given the overwhelming aggravating evidence, there is no reasonable probability that the omitted evidence would have changed the conclusion that the aggravating circumstances outweighed the mitigating circumstances. (People v. Eddmonds (1991), 143 Ill. 2d 501, 535, 578 N.E.2d 952, 967.) Accordingly, even if counsel’s performance was somehow deficient, there was no indication defendant would have received a different punishment had defense counsel presented mitigating evidence.
Accordingly, defendant’s conviction and sentence for murder is affirmed, and the conviction and sentence for aggravated battery is vacated.
Affirmed in part; vacated in part.
STEIGMANN, P.J., and GREEN, J., concur.