
588 F.3d 1142 (2009)
Jerry MAHAFFEY, Petitioner-Appellant,
v.
Anthony RAMOS, Respondent-Appellee.
No. 08-3916.
United States Court of Appeals, Seventh Circuit.
Argued December 2, 2009.
Decided December 21, 2009.
*1143 Alan M. Freedman, Attorney (argued), Evanston, IL, for Petitioner-Appellant.
Erin O'Connell, Office of the Attorney General (argued), Chicago, IL, for Respondent-Appellee.
Before BAUER, KANNE and TINDER, Circuit Judges.
BAUER, Circuit Judge.
Jerry Mahaffey burglarized a home in which he murdered one person, raped and murdered another, and attempted to murder a third. In seeking relief from his life sentence, he contests not that he is actually innocent of these crimes, but that he deserves a new trial because the prosecution improperly used peremptory challenges to exclude members of his race from the jury. But the state court found that the prosecutor's use of peremptory challenges was motivated by legitimate, race-neutral concerns. As this finding was not clearly unreasonable, we affirm the district court's denial of Mahaffey's habeas petition.

I. BACKGROUND
In 1983, Mahaffey burglarized a home in which he murdered Dean Pueschel, raped and murdered Jo Ellen Pueschel, and attempted to murder, by beating and stabbing, their eleven-year-old son Richard. The evidence of Mahaffey's guilt of these crimes is overwhelming, including Richard's identification of Mahaffey, Mahaffey's confession, and that property taken from the Pueschel home was found in Mahaffey's home. Indeed, Mahaffey's attorney admitted at oral argument that the State of Illinois "can prove its case" even now, almost three decades later, were we to order a new trial. But Mahaffey seeks relief not because he is actually innocent of the crimes, but because he claims the prosecution violated the Fourteenth Amendment by excluding blacks from the jury on account of their race.
Mahaffey is black, the victims were white, and the jury that convicted Mahaffey was all white except for one Asian-American. While Mahaffey's direct appeal *1144 to the Illinois Supreme Court was pending, the United States Supreme Court decided Batson v. Kentucky, 476 U.S. 79, 106 S.Ct. 1712, 90 L.Ed.2d 69 (1986), which held that a defendant may rely solely on evidence at his own trial to establish that a prosecutor's use of peremptory challenges on the basis of race denied him equal protection, and Griffith v. Kentucky, 479 U.S. 314, 107 S.Ct. 708, 93 L.Ed.2d 649 (1987), which held that Batson applied retroactively. So the Illinois Supreme Court directed the trial court to conduct a Batson hearing to determine whether the prosecution had violated the Fourteenth Amendment in employing its peremptory challenges. After conducting that hearing, the state trial judge concluded that Mahaffey had failed to establish a prima facie case of discrimination under Batson. The Illinois Supreme Court affirmed, and in 1995 Mahaffey petitioned the federal district court for a writ of habeas corpus, which the district court declined to issue. We reversed, finding that Mahaffey indeed established his prima facie case, and ordered the district court to grant the writ unless the state trial court held a new hearing on Mahaffey's Batson claim, this time requiring the prosecution to come forward with race-neutral explanations for each of the challenged strikes. Mahaffey v. Page, 162 F.3d 481 (7th Cir.1998), rev'g 151 F.3d 671 (7th Cir.1998). The trial court held a new hearing in which it received the prosecution's testimony and heard oral argument, and concluded that in light of the proffered justifications, Mahaffey still failed to establish his burden of proving purposeful discrimination. The Illinois Appellate Court affirmed and the Illinois Supreme Court denied leave to appeal on December 1, 2005.
On November 21, 2006, Mahaffey filed in the federal district court a "motion to reinstate" the 1995 habeas petition's Batson claim, which the district court promptly granted. On February 19, 2008, Mahaffey filed a "memorandum" in support of his Batson claim. The district court then dismissed Mahaffey's habeas petition as untimely, construing the memorandum, not the motion to reinstate, as his new substantive habeas petition. It then granted a certificate of appealability as to the timeliness of Mahaffey's habeas petition and the merits of his Batson claim.

II. DISCUSSION

A. Timeliness of Habeas Petition
We review the district court's denial of Mahaffey's habeas petition as barred by the statute of limitations de novo. Lo v. Endicott, 506 F.3d 572, 574 (7th Cir. 2007). Congress mandates that a one-year statute of limitations shall apply to "an application for a writ of habeas corpus." 28 U.S.C. § 2244(d)(1). Mahaffey's habeas petition filed in 1995 challenging the state trial court's first Batson hearing does not satisfy the statute of limitations, because we treat the state trial court's subsequent Batson hearing as a "new holding" requiring a "new petition." Coulter v. McCann, 484 F.3d 459, 466 (7th Cir.2007). At issue then is what constitutes Mahaffey's new petition: (1) his motion to reinstate, or (2) his memorandum in support of his Batson claim. If the motion to reinstate, then we may consider the merits of his petition because it was filed within the limitations period, running from February 23, 2006, ninety days after Mahaffey's new state-court judgment became final. 28 U.S.C. § 2244(d)(1)(A). If the memorandum, then we are barred from considering the merits because it was filed almost one year late.
The motion to reinstate, not the memorandum, constituted the habeas petition and so it was not time barred. Habeas petitions must state the relief requested, specify the ground for relief, and state *1145 the facts supporting the ground for relief. See Rule 2(c) of the Rules Governing § 2254 Cases. Mahaffey's motion to reinstate stated the relief requested, where it said "Petitioner ... requests that this Court ... grant the petition pursuant to 28 U.S.C. § 2254." Mot. to Reinstate at 1. It also specified the ground for relief, where it said "the State's use of peremptory challenges to exclude blacks from the jury violated petitioner's right to equal protection of law as guaranteed by the Fourteenth Amendment to the United States Constitution." Id. The remaining issue is whether the motion "state[d] the facts supporting" his Fourteenth Amendment challenge as required by Habeas Rule 2(c), i.e., whether it provided sufficient factual support to challenge the second Batson hearing's holding that the prosecutor's race-neutral explanations for striking particular jurors are credible.
We did not address this issue of habeas petition pleading standards in Coulter, 484 F.3d at 466, the only case we are aware of in any circuit to review a second Batson hearing that had been remanded to state court, thus initiating a second habeas petition. Here, we find that Mahaffey's motion pleaded sufficient facts to draw enough of a connection between his right to equal protection and the trial court's alleged racially motivated use of peremptory challenges to render his claim cognizable on habeas review. Mahaffey's motion pleaded, incorporating from the 1995 petition, that out of twenty black members on the seventy-seven person venire panel for Mahaffey's trial, none served, and that, although thirteen were excused for cause, seven were peremptorily struck by the prosecution. These numbers describing the prosecution's use of peremptories, as "remarkable" as those in Miller-El v. Dretke, 545 U.S. 231, 240-41, 125 S.Ct. 2317, 162 L.Ed.2d 196 (2005), constitute at least some evidence for disbelieving the state's race-neutral justifications. Id. And although Mahaffey's motion lacks mention of the state's race-neutral justifications, it does cite and exhibit a case discussing them, People v. Mahaffey, No. 1-03-2409, 2005 WL 6249262 (Ill.App.Ct. Aug. 1, 2005). While these bare facts may have been insufficient to render Mahaffey's petition meritorious, they enabled it to be cognizable. See Holiday v. Johnston, 313 U.S. 342, 350, 61 S.Ct. 1015, 85 L.Ed. 1392 (1941) (finding that pleadings in habeas petitions "ought not be scrutinized with technical nicety"); Kafo v. United States, 467 F.3d 1063, 1068 (7th Cir.2006) (holding that habeas petitions must, for a federal court to address them, "provide some evidence beyond conclusory and speculative allegations") (emphasis in original); Perruquet v. Briley, 390 F.3d 505, 512-13 (7th Cir.2004) (explaining the difference between cognizability and sufficiency of a habeas petition); Lloyd v. Van Natta, 296 F.3d 630, 633 (7th Cir.2002) (noting that habeas petitions "need not be pleaded with particularity") (citation omitted). Therefore, Mahaffey's motion to reinstate constituted his substantive habeas petition.
Given when Mahaffey filed his new habeas petition in the form of his motion to reinstate, we hold that the district court erred when it denied Mahaffey's petition for failure to meet the statute of limitations. So we need not reach Mahaffey's alternative argument that the district court should have equitably tolled the statute of limitations in his favor.

B. Merits of Batson Claim
At this point we could remand Mahaffey's case to the district court. But instead we proceed with the merits here, because they were fully briefed by both parties and we are equally positioned with the district court to evaluate Mahaffey's Batson claim based solely on the state record. See Cone v. Bell, ___ U.S. ___, *1146 129 S.Ct. 1769, 1792, 173 L.Ed.2d 701 (2009) (Alito, J., concurring in part and dissenting in part).
We do not consider denying Mahaffey's petition on the ground that the prosecution's claimed errors were harmless i.e., that any juror, black or white, would have convicted Mahaffey by attending to the overwhelming horrific evidence against himbecause the State of Illinois failed to pursue this argument. Although the State noted that "it is unlikely in the extreme that race played a role in [Mahaffey's] conviction," Respondent-Appellee's Br. at 54, it devoted only one paragraph to the harmless-error argument and cited, against a significant amount of contrary authority, no potentially helpful authority. Perfunctory, undeveloped arguments without discussion or citation to pertinent legal authority are waived. United States v. Haynes, 582 F.3d 686, 704 (7th Cir.2009); United States v. Hook, 471 F.3d 766, 775 (7th Cir.2006).
So we are left to determine whether the Illinois trial court's determination that the prosecution's race-neutral explanations were true was "an unreasonable determination of the facts in light of the evidence presented in the State court proceeding." Miller-El, 545 U.S. at 240, 125 S.Ct. 2317 (quoting 28 U.S.C. § 2254(d)(2)). We presume the Illinois court's factual findings to be sound unless Mahaffey rebuts the "presumption of correctness by clear and convincing evidence." 28 U.S.C. § 2254(e)(1). Under this deferential standard of review, we will not reverse the state trial court's decision "simply because we would have decided the case differently, ... and instead will reverse only if, after reviewing the evidence, we are left with a definite and firm conviction that a mistake has been committed." United States v. Stephens, 514 F.3d 703, 712 (7th Cir.2008) (citations omitted). Accordingly, "there is no basis for reversal on appeal unless the reason given is completely outlandish or there is other evidence which demonstrates its falsity." Tinner v. United Ins. Co. of Am., 308 F.3d 697, 703 (7th Cir.2002) (citation omitted).
As we discussed above, the numbers describing the prosecution's use of peremptories are remarkable. However, while happenstance may be "unlikely to produce this disparity," Miller-El, 545 U.S. at 241, 125 S.Ct. 2317, more than "bare statistics" is required to prove purposeful discrimination. Id. at 241-66, 125 S.Ct. 2317. Accordingly, Mahaffey argues additionally that local prosecutors had a historic policy of systematically excluding blacks from juries. He explains that the Illinois Appellate Court recognized, in 1983, "an open secret that prosecutors in Chicago and elsewhere have been using their peremptory challenges to systematically eliminate all Blacks, or all but token Blacks, from juries in criminal cases where the defendants are Black." People v. Gilliard, 112 Ill.App.3d 799, 68 Ill.Dec. 440, 445 N.E.2d 1293, 1299 (1983). But Mahaffey's jury selection occurred in 1985, almost two years later. That it occurred before Batson may be of some import. Nevertheless, Mahaffey bears the burden of persuasion, which "never shifts," United States v. Jones, 224 F.3d 621, 624 (7th Cir.2000), to identify a specific Illinois policy that was in place when his jury was selected, such as the discriminatory manual entitled "Jury Selection in a Criminal Case," available to the prosecutor in Miller-El, 545 U.S. at 264, 125 S.Ct. 2317. Mahaffey identifies no such specifics contemporaneous with his case. Without more, he must show that the prosecution's proffered race-neutral justifications were pretextual, in order to meet his burden of persuasion on clear-error review.
Indeed, Mahaffey devotes most of the merits portions of his briefs in arguing *1147 that the prosecution's explanations are pretextual for four of the black jurors it dismissed (Mahaffey has abandoned any claims regarding the remaining three): Angela Mack, Nathaniel Howard, Bea Marshburn, and Catherine Taylor. The prosecutor offered the following race-neutral explanations for dismissing these four jurors: (1) Mack worked for a police department; (2) Howard would suffer hardship because he cared for his invalid mother-in-law, including lifting her from bed "like a baby"; (3) Marshburn had a background in psychology; and (4) Taylor had poor communication skills. These race-neutral reasons are unquestionably valid. See Purkett v. Elem, 514 U.S. 765, 769, 115 S.Ct. 1769, 131 L.Ed.2d 834 (1995) (finding the growing of long, unkempt hair a valid nondiscriminatory reason for dismissing a juror). So for Mahaffey to prove purposeful discrimination, he would need to show that the reasons were pretextual. Id. He seeks to show pretext first by showing disparate treatment, i.e., that the prosecution failed to peremptorily dismiss white jurors similarly situated to the four black jurors. See, e.g., Miller-El, 545 U.S. at 248, 125 S.Ct. 2317 (finding pretext where the prosecution dismissed black juror, but not white jurors, who were ambivalent on imposing the death penalty). But Mahaffey fails on this score because he cannot show that any serving white juror was similarly situated to the four jurors whose dismissals he challenges. Specifically, he claims that one white juror was related to police department employees, not an actual police department employee like Mack, who would have developed personal preconceptions about how police reports should look. Mahaffey claims that another white juror shopped and shoveled snow for his elderly parents, not that he would suffer hardship from jury service comparable with Howard, who cared for an invalid. He claims that another white juror taught and coached special needs children, not had a background in psychology like Marshburn. Finally, he claims that other white jurors were similarly situated to Taylor, because they did not subscribe to periodicals. But the prosecution was entitled to credit additional factors beyond Taylor's non-subscription to periodicals, such as Taylor's monosyllabic responses to questions and the prosecutor's "instincts," Batson, 476 U.S. at 106, 106 S.Ct. 1712 (Marshall, J., concurring), and "experienced hunches and educated guesses," J.E.B. v. Alabama ex re. T.B., 511 U.S. 127, 148, 114 S.Ct. 1419, 128 L.Ed.2d 89 (1994) (O'Connor, J., concurring), in finding that Taylor lacked communications skills.
Nor does Mahaffey show pretext by showing that other explanations by the prosecution were inconsistent. Specifically, the prosecution said it also excluded Taylor because she equivocated about the weight she would give police testimony, about whether she would follow the court's instructions, and about whether she would set aside what she previously knew about the case. But the prosecution gave all its proffered reasons when required to do so at the second Batson hearing, and gave these reasons second, after emphasizing the primacy of Taylor's lack of communication skills. 8 Supplement to R. on Appeal at 13-15. Nothing in the record suggests that these explanations were pretextual, as opposed to "secondary reasons" as the State of Illinois contends. Respondent-Appellee's Br. at 49; cf. Miller-El, 545 U.S. at 246, 125 S.Ct. 2317.
The prosecution also added secondarily that it excluded Taylor because "she had a preconceived notion that under certain circumstances certain crimes should be punished by the death penalty," and excluded Mack because she stated that "the defendant should prove his own innocence." Id. at 15, 22. Mahaffey finds these reasons *1148 "obviously pretextual," Reply Br. at 20, 22, because "a prosecutor would clearly desire to have a person with these views on the jury." Mahaffey's Br. at 36; see also id. at 31. But this argument assumes that prosecutors in general do not want fair trialsa proposition we do not accept. Indeed, the prosecution explained that it wanted jurors who would "follow the law." 8 Supplement to R. on Appeal at 15, 22. Anyway, we find this reason not so clearly "improbable" as to discredit the Illinois trial court's determination that this or the other more primary race-neutral justifications offered by the prosecutor were credible. Miller-El v. Cockrell, 537 U.S. 322, 339, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003).
Finally, Mahaffey urges that the prosecution's explanations changed over time, and that the prosecutor's opening statement and closing argument took advantage of the racial sensitivity of the case and the racial composition of the jury. We find no support for these arguments in the record.
For the reasons discussed above, we hold that the Illinois Court did not clearly err in finding that Mahaffey failed to meet his burden of proving purposeful discrimination.

III. CONCLUSION
Mahaffey's petition for a writ of habeas corpus was timely but unmeritorious. We therefore AFFIRM the district court's denial of the writ.
