*860 Ricardo Sanchez seeks review of an order of the Board of Immigration Appeals denying his motion to reopen its prior decision denying him discretionary cancellation of removal. See 8 U.S.C. § 1229b(1). Because Sanchez's petition presents questions of law, we have jurisdiction to review the Board's order and, for the reasons that follow, we grant his petition and remand to the Board for further proceedings.

I.

Sanchez, aged 44, is a native and citizen of Mexico who has lived in the United States without documentation for more than 25 years. He is married to another Mexican citizen and national (also undocumented) who lives here in the United States with him; together, they have three U.S.-citizen children aged nine, seven, and two and one-half years. Their youngest child has experienced developmental delays in his motor skills and has been prescribed therapy to address those delays.

Sanchez has been arrested and convicted for driving under the influence on four separate occasions between 1997 and 2013. In December 2013, after receiving a one-year suspended sentence for the last of his convictions, Sanchez was apprehended by immigration officials and served with a notice to appear in a removal proceeding for being in the country illegally. See 8 U.S.C. § 1182 (a)(6)(A)(i).

Sanchez subsequently admitted the facts set forth in the notice to appear and conceded his removability; but he applied for cancellation of removal on the basis of the extraordinary hardship that he believed his removal would cause to his two children (at that time his youngest had not yet been born). An immigration judge conducted a hearing on the merits of his application at which Sanchez was the sole witness. Sanchez was represented by counsel at the hearing.

In an oral decision, the immigration judge denied Sanchez's application for cancellation of removal and ordered him removed to Mexico. A.R. 368, 369-81. The judge found in the first instance that Sanchez lacked the "good moral character" that is a prerequisite to cancellation of removal, see 8 U.S.C. § 1229b(b)(1)(B), in view of, inter alia , Sanchez's multiple DUI convictions as well as his decision to ignore court orders to appear and respond to two of the DUI charges, which resulted in multi-year delays in resolving those cases. (Sanchez testified that he failed to appear out of fear he would be deported.). A.R. 376-78. The judge also found, in the alternative, that Sanchez had "simply failed to put a case forward" for the notion that his removal from the country would impose an "exceptional and extremely unusual hardship" upon his children. A.R. 379; see § 1229b(b)(1)(D). Sanchez had presented no testimony regarding his sons, including any medical or educational needs they might have, nor was it even clear whether his family would accompany him to Mexico in the event of his removal. A.R. 379-80. Finally, and also in the alternative, the judge concluded that even if Sanchez qualified for cancellation of removal, he did not merit that discretionary relief. The judge identified as positive factors the presence of Sanchez's spouse and children in the United States and the financial support he provided to his family members in Mexico. Sanchez had a history of steady employment and had testified that he paid taxes, but the judge pointed out that there was nothing in the record to show that he had ever filed an income tax return. On balance, the judge found that the factors supporting Sanchez's request for cancellation were insufficient to outweigh his history of disregarding traffic and safety laws, as *861 evidenced by his multiple DUI convictions. A.R. 379-80.

Sanchez, represented by new counsel, unsuccessfully appealed the adverse decision to the Board. Sanchez argued both that the Immigration Judge erred on the merits of his application for cancellation of removal and that his previous attorney had been ineffective in preparing him to testify and in presenting his application. The Board declined to reach the ineffectiveness claim, noting that Sanchez had not submitted the evidentiary materials that Matter of Lozada , 19 I. & N. Dec. 637 (B.I.A. 1988), overruling vacated by Matter of Compean , 25 I. & N. Dec. 1 (B.I.A. 2009), requires for such a claim. A.R. 186. 1 As to the merits of the claim for cancellation of removal, the Board concluded that Sanchez had not shown that his removal would result in exceptional and extremely unusual hardship to his qualifying family members. A.R. 185-86. In view of that holding, the Board found it unnecessary to consider whether Sanchez had the requisite good moral character to qualify for cancellation of removal. A.R. 186.

Sanchez filed a motion asking the Board to both reconsider and reopen its decision, but the Board again denied him relief. Sanchez endeavored to correct the Lozada problem with his ineffectiveness claim by attempting to fill in the gaps in his supporting materials. He further argued that it was his prior counsel's ineffectiveness that prevented him from presenting evidence that would establish his good moral character and demonstrate the extraordinary hardship his removal would pose to his children. The Board rejected Sanchez's request to reconsider its finding that his ineffectiveness claim failed in the first instance to satisfy Lozada , noting that at the time of its prior decision, Sanchez in fact had not complied with Lozada . A.R. 3. As for the motion to reopen, the Board acknowledged Sanchez's belated effort to comply with Lozada . A.R. 4. But as to the merits of the ineffectiveness claim, the Board concluded that Sanchez had not shown that he was prejudiced by any ineffectiveness on the part of his prior counsel. The Board noted that its prior order had focused on the lack of proof that Sanchez's removal would impose the requisite degree of hardship on his children, so the Board confined its analysis of prejudice to that one aspect of Sanchez's request for cancellation of removal. A.R. 4. And as to that component, the Board indicated it was not convinced that the evidence Sanchez faulted his attorney for failing to present "would likely have altered the outcome of [Sanchez's] case with regard to the hardship that would accrue to his children" in the event of his removal. A.R. 4.

Sanchez then filed his petition to review the Board's decision.

II.

Sanchez presses two arguments in his challenge to the Board's decision denying his motion to reopen: (1) that the Board assessed his ineffective-assistance-of-counsel claim using the wrong legal standard as to the prejudice component of that claim; and (2) the Board engaged in such a cursory analysis of his ineffectiveness claim, devoid of reason and essentially ignoring *862 the evidence he presented in support of that claim, that its decision amounts to an abuse of discretion. 2 Because we agree with Sanchez as to the first of these arguments, we need not reach the second.

Before turning to the merits of Sanchez's appeal, however, we must pause to consider our jurisdiction. As a general matter, whether to grant Sanchez cancellation of removal is a discretionary decision that is beyond our jurisdiction to review. E.g. , Perez-Fuentes v. Lynch , 842 F.3d 506 , 510 (7th Cir. 2016) ; see 8 U.S.C. § 1252 (a)(2)(B)(i). And where we lack the power to review the Board's underlying order denying an alien this sort of discretionary relief, we ordinarily lack the authority to review the denial of a request to reconsider or reopen that order. See Cruz-Mayaho v. Holder , 698 F.3d 574 , 576 (7th Cir. 2012) (citing Martinez-Maldonado v. Gonzales , 437 F.3d 679 , 683 (7th Cir. 2006) ); but see Calma v. Holder , 663 F.3d 868 , 873-78 (7th Cir. 2011) (judicial review of procedural ruling ancillary to Board's denial of underlying claim for discretionary relief is foreclosed only when rationale for procedural ruling establishes petitioner's inability to prevail on underlying claim). 3 Nevertheless, we do have authority to resolve any constitutional or other legal issues presented by the Board's handling of the motion to reopen. § 1252(a)(2)(D). The government agrees that the issues raised by Sanchez's petition present legal questions that fall within our jurisdiction. See Jezierski v. Mukasey , 543 F.3d 886 , 888 (7th Cir. 2008) (cognizable errors of law include Board's use of incorrect legal standard); Iglesias v. Mukasey , 540 F.3d 528 , 530-31 (7th Cir. 2008) (petitioner's contention that Board "completely ignored the evidence he presented, as demonstrated by the lack of reasoned analysis in its decision," constituted reviewable question of law). We may therefore turn to the merits of Sanchez's first argument.

Sanchez asked the Board to reopen its prior ruling denying him cancellation of removal on the ground that the attorney who represented him before the Immigration Judge deprived him of the effective assistance of counsel. Although Sanchez did not have a Sixth Amendment right to effective representation by counsel in the removal proceeding, he did have a Fifth Amendment due process right to a fair hearing; and if his counsel's asserted errors resulted in a proceeding that was so unfair as to have precluded Sanchez from reasonably presenting his case, then he was deprived of due process. See Zambrano-Reyes v. Holder , 725 F.3d 744 , 750 (7th Cir. 2013) ; Lozada , 19 I. & N. Dec. at 638 . The ineffectiveness claim required Sanchez to both identify the errors that prevented him from presenting his case in favor of cancellation of removal and to show that he was prejudiced. See , e.g. , Mojsilovic v. I.N.S. , 156 F.3d 743 , 749 (7th Cir. 1998). The prejudice prong requires a showing *863 that counsel's errors "actually had the potential for affecting the outcome of the proceedings." El-Gazawy v. Holder , 690 F.3d 852 , 860 (7th Cir. 2012) (quoting Rapheal v. Mukasey , 533 F.3d 521 , 533 (7th Cir. 2008) ).

Without reaching the question of whether Sanchez's former counsel was, in fact, ineffective, the Board concluded that Sanchez had failed to show that he was prejudiced by any shortcomings in his attorney's performance. Again, in the Board's words, it was "not persuaded that the evidence offered in support of [Sanchez's] ineffective assistance of counsel claim would have likely altered the outcome of this case with regard to the hardship that would accrue to his children." A.R. 4.

The Board's language indicates that it applied the wrong standard in evaluating the prejudice component. As Sanchez rightly puts it, the standard as the Board articulated it is one of probability, when the correct standard as we have articulated is one of possibility. The difference between the two is material. The Board's "would likely have altered the outcome" language suggests that it was requiring Sanchez to show it was more likely than not ( i.e. , a probability of more than 50 percent) that the outcome of the removal proceeding would have been favorable to Sanchez but for his counsel's alleged missteps. But in actuality, Sanchez needed only to establish that he would have had a reasonable chance of prevailing had his counsel provided him with competent representation. See Strickland v. Washington , 466 U.S. 668 , 693-94, 104 S.Ct. 2052 , 2068, 80 L.Ed.2d 674 (1984) (rejecting notion that criminal defendant alleging ineffective assistance of counsel must show that the result of the trial more likely than not would have been different but for his counsel's errors, noting that ineffectiveness claim calls into question fairness and reliability of underlying proceeding, and thus requires defendant to show only a reasonable probability that result of proceeding might have been different); Miller v. Anderson , 255 F.3d 455 , 459-60 (7th Cir. 2001) (so long as habeas petitioner had non-negligible chance of acquittal but for trial counsel's ineffectiveness, he was entitled to relief even if likelihood of acquittal was less than 50 percent) (collecting cases), j. modified in part in other respects , 268 F.3d 485 (7th Cir. 2001) ; El-Gazawy , 690 F.3d at 860 (alien must show that "he could have succeeded on the merits" but for his counsel's ineffectiveness).

The government points to certain language from some of our own attorney-ineffectiveness and other due process cases which could be read as being consistent with the language that the Board used here and which, to the government's mind, suggests that the two different formulations of the standard are interchangeable. For the most part, however, these cases accurately recognize that the prejudice standard for due process claims connotes the possibility rather than the probability of a different result. See , e.g. , Silais v. Sessions , 855 F.3d 736 , 745 (7th Cir. 2017), cert. denied , --- U.S. ----, 138 S.Ct. 976 , 200 L.Ed.2d 246 (2018) (in order to establish prejudice resulting from due process violation, petitioner must "produce some concrete evidence indicating that the violation of a procedural protection actually had the potential for affecting the outcome of ... deportation proceedings") (emphasis added) (quoting Shahandeh-Pey v. I.N.S. , 831 F.2d 1384 , 1389 (7th Cir. 1987) ); Bathula v. Holder , 723 F.3d 889 , 903 n.34 (7th Cir. 2013) ("To succeed on an ineffective assistance claim the petitioners must demonstrate not only that counsel's performance was deficient, but that they ' could have succeeded on the merits' of their claims but for counsel's defective performance")

*864 (emphasis added) (quoting El-Gazawy , 690 F.3d at 860 ). Isolated use of language akin to "would have altered the outcome" or "likely would have altered the outcome" can be found in these cases, but when evaluated in context, these references do not suggest that "would have" or "likely would have" mean the same as "could have" or "might have," or that the Board's phrasing of the standard in this case is a correct articulation. As we read these cases, our use of "would have altered" rather than "might have altered" simply signaled our confidence that the due process violations alleged in those cases made no difference at all to the result. To take one example, in Bathula , the petitioners faulted their attorney for not presenting their daughter's testimony in support of their requests for asylum or withholding of deportation. But those requests had failed for want of proof of a nexus between the acts of alleged persecution and the petitioners' putative social groups; and nothing in the prospective testimony of the petitioners' daughter would have cured that defect in the petitioners' case. Thus, as the petitioners were forced to acknowledge, "the daughter's testimony could not alter the nexus finding and therefore would not have affected the asylum and withholding decisions." Id. at 905 (emphasis added).

By contrast, taking the Board's order in this case at face value, we cannot be confident it applied the correct prejudice standard in a manner consistent with our precedents. Although the Board cited (and parenthetically quoted from) Bathula for the proper standard, in the one and only sentence of the Board's order actually analyzing prejudice, the Board's own words held Sanchez to the higher burden of showing that his attorney's alleged ineffectiveness "would likely have altered the outcome" of the case. A.R. 4. That is an incorrect formulation of the prejudice standard, and neither Bathula nor any other precedent from this court genuinely supports that formulation. The Board's language suggests that it did not appreciate the difference between requiring proof of a possibility rather than the probability of a different outcome. Indeed, the Board used essentially the same language when it separately evaluated Sanchez's new-evidence claim, as to which Sanchez indeed bore the "heavy burden" of showing that the evidence in question would likely have produced a different result. See A.R. 4, citing Matter of Coelho , 20 I. & N. Dec. 464 , 472 (B.I.A. 1992) ; see also , e.g. , De Soon Lin v. U.S. Att'y Gen. , 602 F. App'x 789 , 792 (11th Cir. 2015) (non-precedential decision); Perez v. Holder , 740 F.3d 57 , 62 (1st Cir. 2014) ; Young Sun Shin v. Mukasey , 547 F.3d 1019 , 1025 (9th Cir. 2008) ; and see generally Strickland v. Washington , supra , 466 U.S. at 694 , 104 S.Ct. at 2068 (distinguishing proper standard for ineffectiveness claim from standard for new-evidence claim). Had the Board, in evaluating the ineffectiveness claim, said more about that claim that was consistent with the correct possibility standard, then perhaps we could overlook the error in its articulation of the standard. Cf. Floyd v. Hanks , 364 F.3d 847 , 852-53 (7th Cir. 2004) (habeas corpus relief not warranted where although state court improperly referenced "reliability" in its assessment of prejudice, its actual analysis of counsel's conduct properly focused on potential effect counsel's actions had on outcome of trial); Carter v. Duncan , 819 F.3d 931 , 944-45 (7th Cir. 2016) (same). But that is not the case.

As it is the Board that has the authority to decide whether to reopen its prior decision on the question of cancellation of removal, the appropriate remedy for the error is to remand this matter to the Board for reconsideration in light of the correct prejudice standard.

*865 In view of our decision to remand, we need not address Sanchez's second argument as to the Board's failure to address his evidence and articulate a rationale for its conclusion that Sanchez had not established prejudice resulting from his attorney's performance. We have every confidence that the Board will rectify any such shortcoming when it re-evaluates Sanchez's ineffectiveness claim applying the correct standard as to prejudice.

III.

For all of the foregoing reasons, the petition for review is GRANTED, and the case is REMANDED to the Board for further proceedings consistent with this opinion.