at least partially motivated by his membership in his family and his family’s political opinion. See Yueqing Zhang v. Gonzales, 426 F.3d 540, 545 (2d Cir.2005). However, because of the vagueness of Spa-hi’s testimony regarding the motivations of his child persecutors, the record would not compel any reasonable adjudicator to find, contrary to the agency, that Spahi was persecuted on account of a protected ground. See 8 U.S.C. § 1252(b)(4)(B); cf. Jin Shui Qiu v. Ashcroft, 329 F.3d 140, 151 (2d Cir.2003) (discussing that credible testimony may be too vague to establish refugee status), overruled in part on other grounds by Shi Liang Lin v. U.S. Dep’t of Justice, 494 F.3d 296, 304-05 (2d Cir.2007); I.N.S. v. Elias-Zacarias, 502 U.S. 478, 481, n. 1, 112 S.Ct. 812, 117 L.Ed.2d 38 (1992) (<HOLDING>). The BIA reasonably concluded that Spa-hi had
holding that the fact that the appellate court might reasonably have concluded that a different sentence was appropriate is insufficient to justify reversal holding that a petitioner must show  that the outcome of his appeal would have been different had counsel raised the issue recognizing that the mere plausibility of a different outcome is not sufficient to justify reversal holding that a plain error that is fatal to a conviction is sufficient to warrant reversal holding that the outcome of the case could have been different if the trial court had imposed the appropriate burden