KANNE, Circuit Judge.

On August 26, 1998, Jeremy Gross shot and killed Christopher Beers while robbing a convenience store in Indianapolis. Gross was convicted of murder and sentenced to life in prison without parole, in accordance with a jury's recommendation. Gross claims that he received ineffective assistance of counsel because his attorney never advised him of his right to testify at the sentencing phase of his trial. The Indiana courts denied Gross post-conviction relief from his sentence, holding that he had suffered no prejudice from his counsel's conduct. Gross filed a petition for a writ of habeas corpus in the district court, which denied his claim because the state courts reasonably applied federal law. We now affirm.

I. BACKGROUND

In the early morning hours on August 26, 1998, Gross and accomplice Joshua Spears entered the Convenient Food Mart in western Indianapolis where Gross was a part-time employee. Gross, who had been smoking marijuana, brandished a gun and fired six rounds, striking the cashier Christopher Beers three times and mortally wounding him. Gross and Spears stole $650 from the store, ripped out the phone lines, grabbed the video recorder, and fled. Gross admitted to the robbery and shooting when he was arrested later that morning.

Gross was charged with murder, felony murder, conspiracy to commit robbery, and robbery. Defense lawyer Robert Hill was appointed to defend Gross. Hill and his team presented an intoxication defense at trial, but their primary focus was on the penalty stage of the proceedings.

Forty-two witnesses testified for the defense during the sentencing phase to tell the story of Gross's childhood. The testimony revealed that Gross and his sister had suffered physical violence, sexually inappropriate interactions, and rampant substance abuse. At one point, Gross's mother Cindy sprayed lighter fluid onto a couch where his father was sleeping and lit it on fire. After his parents divorced, Gross was forced to share his home with a variety of undesirable house guests, including a child molester and a prostitute who slept nude on the couch with assorted men. At times during his childhood, Gross did well in structured environments such as foster care, a youth center, and the Indiana Boys School, but he always returned to his mother's care, where he inevitably reverted to a life of drinking and drugs.

Gross did not testify before the jury. The only time the jury heard him speak was in excerpts from a taped news conference introduced into evidence. The jury convicted Gross and unanimously recommended a sentence of life in prison without parole.

On June 9, 2000, the court conducted a sentencing hearing. The judge employed a two-phase analysis to determine the appropriate sentence. First, he addressed the state's argument that the court should override the jury's recommendation and impose the death penalty. The judge agreed with the jury that the state had proved an aggravating factor — the intent to kill — beyond a reasonable doubt, and that aggravating factors outweighed mitigating factors. Nonetheless, the court declined to impose the death penalty.

The court then proceeded to the second phase and conducted its own analysis to determine whether the sentence should be life without parole or a term of years. The court heard testimony regarding victim impact, and Gross expressed his remorse and apologized to Beers's family. After considering this testimony and the information contained in the presentence investigation report, the court sentenced Gross to life in prison without parole for the murder charge.

Gross filed a Petition for Post Conviction Relief, alleging that his trial counsel was ineffective due to his failure to apprise Gross of his right to testify at the sentencing phase of trial. At a post-conviction relief hearing on March 18, 2005, Hill, Gross's trial counsel, testified to the following:

Q: Did you ever discuss with Jeremy the possibility of testifying at this trial?

A: I don't remember discussing with [sic] Jeremy. I'm sure we did it and I'm sure I just told him it wasn't going to happen.

Q: Do you remember, or would it be your practice to advise him that he had a right to testify at either the guilt phase or the penalty phase?

A: I don't remember whether I did or not here. I'm sure I would have mentioned it, but I would have instructed him that no, it wasn't going to happen.

Q: So if you spoke to him about it, would you characterize it as a real discussion about it or just more of a unilateral decision?

A: It would be more of a kind of a discussion I'd have with my 9-year-old about whether he's going to clean his room, that this is the way it's going to be, that kind of discussion. No, there wasn't a give and take, if that's what you mean.

Hill later clarified that it would have been his practice to let Gross know that he had the right to testify. However, he stated that he would have "[told] him it's not going to happen" because, in his view, it is a "huge mistake" for defendants to testify in death penalty trials.

Gross's petition for post-conviction relief from his murder sentence was denied. The post-conviction court based its decision in part on an erroneous conclusion that Gross had in fact testified at the sentencing phase of his trial. Notwithstanding this error, the Indiana Court of Appeals affirmed on July 18, 2006. It acknowledged the post-conviction court's faulty finding, but held that Gross had suffered no prejudice because he had presented no evidence that he ever desired to testify during the penalty phase of his trial.

On April 30, 2007, Gross filed a pro se petition for a writ of habeas corpus in the Southern District of Indiana. He claimed once again that Hill was constitutionally ineffective for failing to discuss with him the option of testifying at the penalty phase of trial. The district court denied Gross's petition, holding that the Indiana Court of Appeals took the constitutional standard seriously and did not apply it unreasonably to the facts of the case. Gross now appeals.

II. ANALYSIS

To be entitled to federal habeas relief from a state court judgment, a petitioner must show that he is being held in violation of the Constitution or laws of the United States. 28 U.S.C. § 2254(a); Virsnieks v. Smith, 521 F.3d 707, 721 (7th Cir. 2008). Where an alleged violation was adjudicated on the merits in state court, federal courts may grant relief only if the state determination was contrary to, or an unreasonable application of, clearly established federal law, or based on an unreasonable determination of the facts. 28 U.S.C. § 2254(d); Arredondo v. Huibregtse, 542 F.3d 1155, 1167-68 (7th Cir. 2008). We review the district court's denial of Gross's petition de novo and its factual determinations for clear error. Williams v. Bartow, 481 F.3d 492, 497 (7th Cir. 2007).

Gross claims that he received ineffective assistance of counsel in violation of the Sixth Amendment. To prevail on this claim, Gross must show that (1) his counsel's performance was deficient; and (2) this deficient performance prejudiced him. Strickland v. Washington, 466 U.S. 668, 687, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984); Osagiede v. United States, 543 F.3d 399, 408 (7th Cir. 2008). The Indiana Court of Appeals denied Gross's claim because he presented no evidence that he ever desired to testify at trial and thus suffered no prejudice from his counsel's conduct. It did not address whether Hill's conduct was deficient. Because we agree that Gross has failed to meet his burden to show the prejudice required under Strickland, we confine our review to this prong as well.

To demonstrate that he suffered prejudice, Gross must establish that there is a reasonable probability that the result of the proceeding would have been different but for counsel's deficient performance. Strickland, 466 US. at 694, 104 S.Ct. 2052. Gross does not need to show that it was more likely than not that Hill's conduct altered the outcome of the case. Julian v. Bartley, 495 F.3d 487, 498 (7th Cir. 2007). Instead, this court has defined a "reasonable probability" as a "better than negligible" chance. Id.; United States ex rel. Hampton v. Leibach, 347 F.3d 219, 246 (7th Cir. 2003).

The determination of the Indiana Court of Appeals that Gross failed to demonstrate prejudice was not based on an unreasonable application of federal law or determination of the facts. The only evidence Gross cites to support this claim is Hill's testimony at the hearing. Hill did not remember any specific conversation with Gross regarding his right to testify, and he merely speculated as to what his typical practice would be. In fact, Hill stated that his usual practice would have been to inform a defendant that he had a right to testify, but that he would have instructed him not to. He did not, at any time during his testimony, indicate that Gross had actually expressed a desire to testify or that he had prohibited him from doing so. In fact, he referred to Gross as an "easy client" who followed his recommendations.

As the Indiana Court of Appeals noted, Gross had every opportunity to explain at his post-conviction hearing that Hill never informed him of his right to testify and that he would have testified had he been so informed. He failed to do so. Gross made such an argument in briefs to the Indiana Court of Appeals and this court, but arguments are not evidence. In fact, Gross declined to testify at the hearing altogether, and he never presented any actual evidence that he was not advised of this right to begin with. The only evidence was Hill's speculation. It was therefore entirely reasonable for the state court to find that Gross had failed to demonstrate prejudice as required under Strickland.

Gross relies heavily on Underwood v. Clark, 939 F.2d 473 (7th Cir. 1991), for his argument that his testimony was unnecessary to establish prejudice. In Underwood, we rejected a rule requiring that the defendant protest his lawyer's actions during the trial. Id. at 476. In so doing, we noted that "the defendant might well feel too intimidated to speak out of turn." Id. We held that to later maintain an action for ineffective assistance of counsel, "[t]he defendant need not protest [at trial] and the judge need not question him." Id. Thus, Underwood established a principle that a lack of evidence at trial demonstrating that a defendant was prohibited from testifying is not fatal to his claim. See id.

But the situation we discussed in Underwood is not before us. The Indiana Court of Appeals did not inquire as to whether Gross had expressed a desire to testify at trial; it simply reviewed the record from the post-conviction relief hearing. Considering that Gross had already brought a claim against his trial attorney for ineffective assistance of counsel, the concern that he would be "too intimidated to speak out of turn" does not apply to the hearing. Nothing in Underwood changes the fact that Gross was required to present the post-conviction court with some evidence that he would have liked to testify or that he was prohibited from doing so.

In fact, we rejected the defendant's ineffective assistance of counsel claim in Underwood because he had not produced sufficient evidence to establish that he was prevented from testifying. See id. at 475-76. We held that "the defendant must produce something more than a bare, unsubstantiated, thoroughly self-serving, and none too plausible statement that his lawyer . . . forbade him to take the stand." Id. at 476. We suggested that an affidavit from the defendant's lawyer might suffice. Gross now argues that Hill's testimony is adequate evidence because it establishes that he either failed to inform Gross of his right or forbade him from testifying. But this misconstrues Hill's testimony. Hill merely speculated as to what course of action he would take if, hypothetically, a defendant in a death penalty trial expressed the desire to testify. This is certainly not sufficient to render the decision of the Indiana Court of Appeals unreasonable in light of the facts.

Moreover, even if Gross had proved that he would have testified if properly advised, we are not persuaded that there is a better than negligible chance his testimony would have resulted in a different outcome. At the time Gross was sentenced, the judge was not bound to follow the jury's sentencing recommendation. Ind. Code § 35-50-2-9(e) (2000). To impose a sentence of life in prison, the jury was required to find that the state proved an aggravating circumstance and that the aggravating circumstance outweighed the mitigating factors, id. § 35-50-2-9(k), but the court made the final sentencing determination after taking the same factors into account, id. § 35-50-2-9(e).

The aggravating factor in this case was the intentional killing of Christopher Beers. Considering the vast amount of mitigating evidence the defense offered on Gross's behalf, we do not believe that there is a "better than negligible" chance that Gross's expression of remorse would have been sufficient to convince the jury that an intentional murder did not outweigh the mitigating factors. Once the jury made this finding, the judge was free to disregard its recommendation and impose a term of years. Instead, the judge concluded that life in prison was warranted after conducting a careful analysis considering the evidence presented at trial, victim impact statements, and Gross's expression of remorse at the sentencing hearing. We do not find a "better than negligible" chance that the result would have been different had Gross testified before the jury, rather than the judge alone.

III. CONCLUSINO

The decision of the Indiana Court of Appeals that Gross did not suffer prejudice as required by Strickland was not unreasonable in light of federal law or the facts in the record. Gross has not demonstrated that he would have testified at trial, nor has he convinced us that his testimony could have altered his sentence. The judgment of the district court is AFFIRMED.