In a motion seeking to vacate a conviction for a breach of supervised release, what is the burden of making out plain error?

Samuel having failed to raise this argument below, we review only for plain error. "Plain error review requires a defendant to demonstrate that (1) there was error, (2) the error was plain, (3) the error prejudicially affected his substantial rights, and (4) the error seriously affected the fairness, integrity or public reputation of judicial proceedings." United States v. Cook, 722 F.3d 477, 481 (2d Cir. 2013) (internal quotation marks omitted). A defendant who seeks to vacate his conviction following a guilty plea cannot show an effect on his substantial rights unless he "demonstrate[s] that there is a reasonable probability that, but for the error, he would not have entered the plea." Id. (internal quotation marks omitted). We see no reason why, in this closely related context, Samuel should not be put to the same burden. To make out plain error, he must show that, but for any error below, he would not have admitted to the supervised-release violation.