
625 F.3d 410 (2010)
UNITED STATES of America, Plaintiff-Appellee,
v.
Prince P. BECK and Corey J. Thomas, Defendants-Appellants.
Nos. 09-2337, 09-2438.
United States Court of Appeals, Seventh Circuit.
Argued March 31, 2010.
Decided November 5, 2010.
*412 Elizabeth Altman, Attorney (argued), Office of the United States Attorney, Madison, WI, for Plaintiff-Appellee.
Reed Cornia, Attorney (argued), Cornia Law, LLC, Madison, WI, for Defendant-Appellant Prince P. Beck in No. 09-2337.
Robert T. Ruth, Attorney (argued), Madison, WI, for Defendant-Appellant Corey J. Thomas in No. 09-2438.
Before MANION and WILLIAMS, Circuit Judges, and DARRAH, District Judge[*].
MANION, Circuit Judge.
Prince P. Beck and Corey J. Thomas were convicted of several crimes involving a bank robbery in Madison, Wisconsin. During the trial, their attorneys sought to cross-examine a key witness about his potential bias. The judge, however, blocked this line of questioning. On appeal, the defendants primarily challenge this ruling. Although the limits placed on the cross-examination violated their Sixth Amendment rights, the error was harmless beyond a reasonable doubt and we affirm.


*413 I.
Beck and Thomas were charged with multiple crimes stemming from two separate bank robberies. The first robbery was on May 9, 2008. That morning, someone called a Bank Mutual branch in Madison, Wisconsin wanting to know when it opened. By itself the phone call wasn't suspicious, but moments later the bank was robbed by three masked men. At that point the call naturally became suspicious, and it was traced to Beck's phone. A review of the bank's surveillance video showed that Thomas had been in the bank the day before the robbery. And after searching the getaway car, the police found palm prints of Thomas and finger-prints of Jarrell Murray.
After the robbery, Murray took his share and went gambling with several others, two of whom have a prominent role in this case: Lamar Liggons and Michael Simmons. These last two were close friends. Simmons is paralyzed from the waist down and confined to a wheelchair; Liggons served as his nurse, helping him in and out of cars and with his personal needs. In the Spring of 2008, the two of them traveled from their homes in Chicago to Texas, where they picked up a van Simmons's uncle gave Simmons. They stayed there for two weeks and before they left, that same uncle gave Simmons three thousand dollars.
From there, the two went to Memphis and stayed with another of Simmons's relatives. They stayed a couple of weeks there, and during that time Simmons used some of the money his uncle gave him to purchase two guns: a .45-caliber pistol and a Tech 9. Before leaving Memphis, Simmons, Liggons, and several family members posed for pictures brandishing the guns. After leaving Memphis, the two of them took the guns back to Chicago, and with the rest of the money Simmons's uncle gave him, they went gambling with Murray.
According to Liggons, on this trip the gamblers included himself, Simmons, Murray, a woman named Trina, and a man named George. During the trip, Simmons either spent or gambled away all the money his uncle gave him. At some point during the gambling, Murray had bragged that he and Beck were "takedown kings in Wisconsin," i.e., that they successfully robbed both drug dealers and banks. Having lost all of his money, Simmons was interested in this line of work. So, shortly after leaving the casino, Beck, Murray, Simmons, Liggons, and George met up in Chicago and discussed their opportunities. Although Beck and Simmons were old friends, until this meeting Liggons and Beck had never met.
A day or so later, while still in Chicago, Murray, Beck, Simmons, and Liggons met for a second time. At this second meeting, Simmons showed off his new guns, and Beck proposed using Simmons's van as a getaway car for future robberies. Simmons agreed to let them use his van; he then lent Beck the Tech 9, and they split up after agreeing to meet up later that week in Madison to rob a bank.
Early in the morning on May 19, Liggons and Simmons drove to Madison with Alicia, Liggons's girlfriend, and stayed at her mother's house. Later that morning, Simmons and Liggons met up with Thomas, Murray, Beck, a man named Mook, and another man that neither Liggons nor Simmons could identify. The seven of them spent the afternoon driving around scouting banks to rob. They eventually found one and were ready to rob it that day, but Simmons became nervous. He thought that their reconnaissance was too suspicious, and that their vehicle had been marked by bank employees. After Simmons called it off, they dropped off Mook *414 and the unidentified man at the bus station.
The following day, May 20, Murray called Simmons and told him they were going to rob a bank early the next morning. The five of them, Liggons, Simmons, Murray, Thomas, and Beck, met up later that evening at Julia Bell's houseBell was Beck's girlfriend. They spent the night smoking marijuana and slept in her basement. They all woke up early the next morning and dressed, gathered the guns Simmons bought in Memphis and some other tools of the trade, consumed more drugs, and left to rob the bank. On the way, Thomas realized that in their haste they had forgotten gloves, so they stopped off at a Dollar Store and picked up some common kitchen gloves. After that detour, they reached the bank, conducted some brief surveillance, and parked the van.
At this point things started to unravel, quickly. Simmons, who, again, is confined to a wheelchair, decided he wanted to helpbeyond letting the others use his van as the getaway car. He had a plan: he would go in and pretend to open an account, and the others "could put the money on his lap and wheel him out." Despite the fact that this plan was not well-received by the others, Simmons insisted. At some point, he put an end to the discussion, grabbed a gun, and wheeled himself into the bank where, true to his plan, he asked about opening a checking account. The others entered soon after, brandishing guns and demanding access to the safe. As they were collecting the money, Simmons wheeled himself toward the exit but couldn't open the door. Eventually after the others escaped with the money, Simmons managed to get outside, only to discover that they had left without him.
Under the circumstances, Simmons did the best he could and went around the neighborhood trying to blend in. Naturally some of the bank employees had grown suspicious of Simmons's behavior both during and after the robbery, and they shared these suspicions with the police. The police found Simmons down the block, and after his story fell apart, they arrested him for obstruction of justice.
Meanwhile, the others sped off to Julia Bell's house. In the van, they took off their masks, gloves, and shirts and threw them out the windows. Then at some point during the drive, Beck exited the van with the money and the guns, while the others continued to Bell's house. There, they changed clothes and emptied the van. But in the excitement they forgot the bag of kitchen gloves they had bought on the way to the bankLiggons's and Thomas's fingerprints were on the bag. They also left the pictures Liggons and Simmons had taken in Memphis showing off the guns. Once they finished, Thomas and Liggons got a different car and went looking for Simmons. But by this time, the bank was surrounded by police and Simmons had been arrested, so they returned to Bell's house.
While Liggons and Thomas were looking for Simmons, Beck and Murray counted the money. Beck eventually called Thomas and let him know the take: they had stolen over $130,000. Inexplicably, however, Liggons decided to leave Madison with Alicia before getting his cut.
As Liggons was leaving Madison, Simmons sat in jail hoping someone would post his bail. Initially, he called George with whom he had been gambling earlier. When George didn't answer, he called Beck. The two of them talked in an obvious and easily discernible code, the gist of which was that Simmons swore he had not talked to the police and told Beck to bail *415 him out. Over the next couple of days, they spoke several times. Two aspects of these conversations are important. First, Beck made many statements implying his own connection with the robbery. Second, they repeatedly referenced George, another man named "Big Bro", and a street gang named "B.O.S."at trial Simmons defined it as the "Brothers of the Struggle."
At first Simmons's bail was set at $300. But soon it was raised to $250,000. No one came forward with bail money, and after some time in jail, Simmons decided to cooperate and gave a statement implicating Beck, Thomas, Murray, and Liggons. Much later and shortly before trial, Liggons was arrested. After he was given Simmons's statement, he too decided to cooperate. While Murray was also arrested and pleaded guilty, he did not cooperate with the government.
At trial Liggons testified first. His testimony was straightforward and the defense's cross-examination was relatively harmless. He unremarkably testified that he was not in a gang and he did not have any friends in common with Simmons. Simmons testified next, and he gave the same basic details about the robbery as Liggons. The difference was that in Simmons's version, Mook and the unidentified man were missing. Simmons assured the prosecutor that they were not with the group that went scouting banks on the 19th and they were not dropped off at a bus station that day. Simmons also testified that both he and Liggons were part of the Gangster Disciples and had many mutual friends.
During Simmons's cross-examination, the defense began by questioning him about points in Liggons's testimony and then asked some preliminary questions about the phone calls between Simmons and Beck, specifically inquiring about "Big Bro." After several objections concerning Simmons and his gang activity, the attorneys went sidebar. There, the defense attorneys explained for the first time the theory of the defense: Simmons was protecting higher-ups in the Gangster Disciples by framing the defendants who were innocent, lower or non-members of the gang. They argued that Simmons and Liggons were covering up for others: namely, "Big Bro", George, Mook, and the unidentified man, all of whose appearances and place in the story are hard to reconcile between the testimonies. And it was critical to their defense that they be allowed to confront Simmons about his gang membership because it provided a motive for him to lie and frame the defendants.
After hearing the arguments, the judge sustained the government's objection and would not allow the defense to question Simmons concerning his gang membership or ask whether he was protecting gang members who were the real robbers. At the next recess, the defense made an offer of proof articulating what it wanted to ask Simmons, including that he was a lower-level gang member, that the real robbers (not Thomas and Beck) were above him, that he would be exposed to danger if he testified against higher-level gang members, and that he expected protection and financial assistance in prison from the other gang members.
Although the bulk of the evidence concerning the May 21 robbery came from Liggons and Simmons, the government also produced several pieces of evidence that tied Beck and Thomas to the robbery. The bag of kitchen gloves that were used in the robbery were found in the van, with Liggons's and Thomas's fingerprints on them. In the days after the robbery, both Thomas and Beck purchased cars; Thomas purchased his with hundred-dollar bills. Bell testified that the night before the *416 robbery, five men may have spent the night at her place. In addition, the government produced transcripts of Beck's conversations with Simmons, who was calling from jail. These transcripts were rife with incriminating statements that showed Beck's familiarity with the robbery and the other robbers, allusions to the money being divided and the gun Liggons took with him into the bank, and many other statements that showed Beck's consciousness of guilt. Ultimately, the jury acquitted Beck and Thomas of the May 9 robbery but convicted them of three charges stemming from the May 21 robbery.

II.
On appeal, Beck and Thomas argue two points of error from the trial. The first concerns the May 9 robbery and the government calling, over Beck's objection, his probation officer to testify that he gave her the same phone number as the one used to call the bank the morning of the robbery. Although Beck was acquitted of this charge, he argues that the error tainted the whole trial for him. We review the judge's decision to allow testimony for an abuse of discretion. United States v. Harris, 587 F.3d 861, 867 (7th Cir.2009).
Second, the defendants argue that the limits the district court placed on their cross-examination of Simmons violated their Sixth Amendment Confrontation Clause rights. Sixth Amendment challenges require a two-step review. As an initial matter, we must determine whether the questions concern peripheral matters in the trial or whether they touch on the core values of the Confrontation Clause. United States v. Smith, 454 F.3d 707, 714 (7th Cir.2006). If the questions only concern peripheral matters, we review the judge's ruling for an abuse of discretion, but if the questions implicate the Confrontation Clause, then we review the ruling de novo. Id. And if we find there was an error in the judge's ruling, then we must determine whether or not it was harmless. Id. at 715.

III.
Against Beck, the evidence concerning the first robbery centered on the use of his phone to call the bank minutes before the robbery. The phone at issue was not registered to Beck but to Ms. Kayla King. She testified that while she owned the phone, Beck was the primary user. The government then called Erin Graf, Beck's probation officer, to testify that she used that same number to reach Beck. The defense objected to Graf testifying and over its objection, the judge allowed her to testify and tell the jury that she was a probation officer.
We review the district court's admission of this testimony over the defendant's objection for an abuse of discretion. Harris, 587 F.3d at 867. The Rules of Evidence carefully govern the admission of a defendant's prior convictions. E.g., Fed.R.Evid. 404, 609. This ensures that he is not convicted on anything but the evidence produced at trial. United States v. Johnson, 27 F.3d 1186, 1193 (6th Cir.1994). And we have repeatedly cautioned courts to consider carefully the introduction of previous convictions. See, e.g., United States v. Taylor, 522 F.3d 731, 732-33 (7th Cir.2008).
Here, while there was not an explicit statement that Beck was previously convicted of a crime, most jurors would likely understand that a person on probation has previously been convicted of a crime. And although the probation officer only stated that she was a probation officer and not Beck's probation officer, the distinction does not address the concern courts have with such evidence. No matter how thinly *417 the government would slice the semantic distinctions between "his probation officer" and "a probation officer" on appeal, the obvious inference at trial was that she was Beck's probation officer and that he had been previously convicted of a crime.
While evidence of Beck's probation could be admitted to establish his identity, under Rule 404(b), the judge still has to weigh its appropriateness under Rule 403. Taylor, 522 F.3d at 732-33. Here, the probative value of the testimony was minimal given Ms. King's cumulative testimony tying Beck to the phone. And what little probative value there was in having the probation officer testify was substantially outweighed by the danger of unfair prejudice that comes with the jury learning the defendant is a convicted felon. Therefore, we find that the district court erred in allowing the probation officer to testify. Further, even if it was necessary to have the probation officer testify that Beck used that phone, the court should not have allowed her to identify herself as a probation officer.
When a district court errs, as it did in this case, by admitting evidence at trial we review it under the harmless error standard. Taylor, 522 F.3d at 735. The probation officer's testimony concerned the first robbery and Beck was acquitted of that charge. Thus, we must analyze whether the prejudice from that testimony affected Beck's rights regarding the second robbery. We address that analysis later in the opinion.

IV.
Both defendants raise the second point of error that centers on the limits the district judge placed on the cross-examination of Simmons. While trial courts enjoy wide discretion to impose reasonable limits on cross-examination, when, for example, the questioning is confusing, repetitive or irrelevant, defendants have the right to cross-examine witnesses and expose "a witness' motivation in testifying." Davis v. Alaska, 415 U.S. 308, 316, 94 S.Ct. 1105, 39 L.Ed.2d 347 (1974); U.S. Const. amend. VI; Delaware v. Van Arsdall, 475 U.S. 673, 679, 106 S.Ct. 1431, 89 L.Ed.2d 674 (1986). And the exposure of these motivations lies at the "core" of the confrontation right. Davis, 415 U.S. at 316, 94 S.Ct. 1105; see also United States v. Presbitero, 569 F.3d 691, 703 (7th Cir.2009) ("Cross examining a witness to establish bias implicates a core value of the Sixth Amendment's Confrontation Clause."). This encompasses everything from a witness's personal preferences to his self-interest. United States v. Abel, 469 U.S. 45, 52, 105 S.Ct. 465, 83 L.Ed.2d 450 (1984). We have consistently noted that such evidence is always relevant, and "parties should be granted reasonable latitude in cross-examining target witnesses." United States v. Manske, 186 F.3d 770, 777 (7th Cir.1999); United States v. Thompson, 359 F.3d 470, 479 (7th Cir.2004).

A.
As an initial matter, we review the limits a judge places on cross-examination to determine if they touch on peripheral matters or strike at the core of the Sixth Amendment. If they involve the defendant's constitutional rights, we review the judge's ruling de novo; otherwise our review is for an abuse of discretion. Smith, 454 F.3d at 714. This inquiry hinges on whether, with the limits placed on the cross-examination, the jury has sufficient information to make an appraisal of the witness's bias.[1]Davis, 415 U.S. at 316, 94 *418 S.Ct. 1105. If so, the limits drawn along those lines only touch on peripheral matters: "it is of peripheral concern how much opportunity defense counsel gets to hammer that point down to the jury." United States v. Sasson, 62 F.3d 874, 882 (7th Cir.1995). But when the defense is kept from exposing the witness's bias, then the Constitution is implicated. Id. at 883.
With this line of questioning, the defense was trying to establish Simmons's motive to lie: Simmons claimed to be a gang member possibly in league with other gang members to rob this bank, and his allegiance to the gang, his fear of retribution from the gang, and his anticipation of future benefits from the gang motivated him to frame the defendants. By cutting off that line of questioning, the judge kept the defendants from attempting to expose Simmons's bias. It also kept them from developing for the jury a plausible reason for why Simmons and Liggons would frame them. Without this basis for why Simmons and Liggons would lie, the jury would be left with the mere fact that their stories did not match in several particulars. Mere inconsistencies do not suggest they would frame the defendants. There must be a reason. The defendants insist that the limitations the judge placed on the cross-examination kept the jury from accurately assessing Simmons as a witness, and this kept the defendants from developing their theory of the defense, all of which strikes at the core of the Sixth Amendment. Abel, 469 U.S. at 48-49, 105 S.Ct. 465; Davis, 415 U.S. at 317, 94 S.Ct. 1105; see also United States v. Vega Molina, 407 F.3d 511, 523 (1st Cir.2005) (reversing when defense was kept from inquiring into his "framing defense"). Thus, we review the trial court's evidentiary rulings de novo. Smith, 454 F.3d at 713.

B.
At trial, the government gave three reasons for barring the defense's line of questioning: first, defense counsel lacked a good-faith basis for the inquiry; second, it was improper Rule 404(b) evidence; and three, it was irrelevant. In sustaining the government's objection, the judge did not state the basis for her ruling. She could have found all three reasons persuasive, so we will examine each of them as a possible basis for sustaining the government's objection.
The first reason given was that the defense did not have a good-faith basis to ask these questions. No attorney may ask a question if he doesn't have a good-faith basis to ask it; that is, attorneys cannot take a shot-in-the-dark approach to their questions. Taylor, 522 F.3d at 736. But an attorney does not need definitive proof to have a good-faith basis, just "[a] well reasoned suspicion that a circumstance is true." United States v. Sampol, 636 F.2d 621, 658 (D.C.Cir.1980). At sidebar the defense articulated several facts and corresponding inferences that provided a good-faith basis for this line of questioning, including inconsistencies in the testimony; allusions to "Big Bro" and "George" in the recorded calls; and common knowledge that gangs operate with a hierarchy. See United States v. White, 582 F.3d 787, 794-95 (7th Cir.2009) (noting the typical hierarchy inherent in street gangs). These facts and the corresponding inferences provided what is arguably a good-faith basis for the defense counsel to probe Simmons's gang membership as it *419 relates to him covering up for the real robbers, including his motive for doing so. Furthermore, cross-examination into a witness's potential bias must be permitted "even though [defense counsel] cannot state to the court what facts a reasonable cross-examination might develop." Clark v. O'Leary, 852 F.2d 999, 1007 (7th Cir. 1988) (quoting Alford v. United States, 282 U.S. 687, 692, 51 S.Ct. 218, 75 L.Ed. 624 (1931)). At that point, counsel proceeds at his own peril.
The second reason given was that the line of questioning was eliciting improper Rule 404(b) evidence. It was not. That rule bars "[e]vidence of other crimes, wrongs, or acts ... to prove the character of a person in order to show action in conformity therewith." Fed.R.Evid. 404(b). Questions about Simmons's bias as it relates to his gang allegiance and anticipated benefits for testifying falsely do not implicate Rule 404(b)'s prohibition. Here, the questions were not aimed at showing that because Simmons is a gang member, he lies generally and he was doing so here. Instead, it was offered to show why he was lying: that he was covering up for the real robbers (perhaps Mook, George, the unidentified man, or Big Bro) who were higher-ranking gang members. Because the cross-examination questions sought to show Simmons's bias and not his bad character in general, they did not implicate Rule 404(b). See Young v. Rabideau, 821 F.2d 373, 378-79 & n. 3 (7th Cir.1987). Further, the danger inherent in such questions is correctly resolved under a Rule 403 analysis. Harris, 587 F.3d at 867; United States v. Cooper, 591 F.3d 582, 589 (7th Cir.2010). In this case, the questions were relevant, sufficiently probative to explore possible bias, and the issue of unfair prejudice was minimal, at least at the point where the court cut off the questioning. United States v. Seals, 419 F.3d 600, 606 (7th Cir.2005).
The third reason given was that the questions were irrelevant. To the contrary, the questions were clearly probative of Simmons's bias. And as we have noted before: "[b]ias is always relevant, and parties should be granted reasonable latitude in cross-examining target witnesses." Manske, 186 F.3d at 777.
At the stage when the court cut off these questions, the defense arguably had a good-faith basis to continue the questions at issue; they were not improper under Rule 404(b); and they were relevant. Therefore, the judge erred when she prevented the defense from questioning Simmons about his potential bias. But that does not automatically entitle the defendants to a new trial; rather, the error is subject to a harmless error analysis. Van Arsdall, 475 U.S. at 684, 106 S.Ct. 1431.

C.
Under the harmless error analysis, our inquiry is twofold. We first "assum[e] that the damaging potential of the cross-examination [was] fully realized." Van Arsdall, 475 U.S. at 684, 106 S.Ct. 1431; accord Smith, 454 F.3d at 715; Cotto v. Herbert, 331 F.3d 217, 256 (2d Cir.2003). Then, we look to whether "the error was harmless beyond a reasonable doubt." Van Arsdall, 475 U.S. at 684, 106 S.Ct. 1431. Meaning: is it "clear beyond a reasonable doubt that a rational jury would have found the defendant guilty absent the error?" Neder v. United States, 527 U.S. 1, 18, 119 S.Ct. 1827, 144 L.Ed.2d 35 (1999). To determine this, we look at a host of factors including the "importance of the witness's testimony in the prosecution's case, whether the testimony was cumulative, the presence or absence of corroborating or contradictory evidence and the overall *420 strength of the prosecution's case." Smith, 454 F.3d at 715.

i.
Here, given how hostile a witness Simmons was, it is likely that had the judge allowed the questioning to proceed, it would have backfired on counsel.[2] But for the sake of our analysis here "we assume that the damaging potential of the cross-examination was fully realized." Van Arsdall, 475 U.S. at 684, 106 S.Ct. 1431. It is unlikely that counsel expected Simmons to break down on the stand and admit that his perjury was part of an elaborate scheme to frame the defendants. Only Perry Mason enjoyed such moments.
Rather, the questioning was aimed at developing a tenable story through Simmons that would lead the jury to believe or have reasonable doubts about whether he and Liggons were framing the defendants. Although this story was unlikely, the thrust of it would explain for the jury why the two witnesses would frame the defendants: to cover up for higher-up gang members who actually robbed the bank in return for continued benefits from the gang, including protection and monetary support. At the same time, it would provide a plausible basis for why there were several inconsistencies between the two testimonies: they were framing Beck and Thomas. If this unlikely scenario had been effectively presented on cross-examination, the government's case could have been undermined. See United States v. Cavender, 228 F.3d 792, 799 (7th Cir.2000) (evidence that the key government witness was lying would make the case fall apart).

ii.
The next question is, of course, whether Liggons's credibility is also affected by what we assume is the effect of Simmons's cross-examination. The two are closely linked through both their roles in the robbery and their shared history. That is the situation that confronted the Supreme Court in Olden v. Kentucky, 488 U.S. 227, 109 S.Ct. 480, 102 L.Ed.2d 513 (1988). There, the testimony that was affected by a Confrontation Clause violation was corroborated by someone who would also be affected by the questions the defense counsel hoped to ask. Id. at 233, 109 S.Ct. 480. In cases like Olden the reliability of both witnesses is affected by the limitations placed on the cross-examination. Thus, under Van Arsdall we would presume that both defendants' testimony would be undermined.
*421 But that is not the situation here. Two things keep us from finding that Liggons's credibility would also be affected. First, on cross-examination Liggons maintained the same critical story as Simmons. With the exception of references to Mook and the unidentified man, the discrepancies between the two were insignificant and the normal consequence of two people recounting many details about the same story a year later. Second, Liggons testified before Simmons. Yet, the defense did not go into this line of questioning during Liggons's testimony. If the entire defense hung on this argument, then it would naturally have come across in the questioning of both cooperating witnesses. But there was nothing until the sidebar that pointed to this theory of the defense. Whether this silence was a tactical decision doesn't matter: the disbelief assumed in Simmons's testimony does not spread to Liggons without at least some suggestion that he too was framing the defendants. The defendants have not pointed to anything Liggons said or did indicating that persons other than he and Simmons robbed the bank.[3]

iii.
Assuming the full extent of the cross-examination was realized and Simmons's testimony was not believable, we must look at the remaining evidence and determine whether "it [is] clear beyond a reasonable doubt that a rational jury would have found the defendant guilty absent the error." Neder, 527 U.S. at 18, 119 S.Ct. 1827. The government "bears the burden of showing that a violation of the Confrontation Clause was harmless beyond a reasonable doubt." United States v. Castelan, 219 F.3d 690, 696 (7th Cir. 2000); United States v. Williams, 559 F.3d 607, 611 (7th Cir.2009). And it is focused on what remaining evidence at trial convinces us beyond a reasonable doubt that a rational jury would have found the defendants guilty. Castelan, 219 F.3d at 696; United States v. McGowan, 590 F.3d 446, 456 n. 1 (7th Cir.2009) (looking to "the strength of the remaining evidence against the defendants" (emphasis in the original)). It is not for the government to show that Simmons was otherwise believable, but that with the residual evidence in this case a reasonable jury would still convict. Chapman v. California, 386 U.S. 18, 24, 87 S.Ct. 824, 17 L.Ed.2d 705 (1967).
Here, the government has met its burden. Liggons's testimony was duplicative of Simmons's and the other physical evidence establishes that Beck and Thomas were the robbers. This evidence included the prison calls between Beck and Simmons; Thomas's prints found on the bag of kitchen gloves in the getaway vehicle; the photos in the car of Liggons and Simmons with the guns in that same getaway vehicle; and the testimony of Beck's girlfriend that five men stayed at her house the night before the robbery. Coupled with the testimony of Liggons, this is strong evidence of guilt. United States v. Jackson, 540 F.3d 578, 593 (7th Cir.2008) (finding harmless error where the evidence of guilt "was overwhelming"); Lanier v. United States, 220 F.3d 833, 839 (7th Cir. 2000). The strength of this evidence also convinces us that the unfair prejudice that attached to Beck from having his probation officer testify was harmless.

V.
Beck also appeals his sentence; he argues that the district court failed to address his argument that his career offender *422 status overstated his criminal history. The judge acknowledged Beck's argument and stated she was not persuaded. There is no basis to suggest that she did not properly calculate his guideline range. Further, Beck's guideline range was 360 months to life, and he received a sentence of 324 months. Given the nature of his offense and his status as a career offender, there is nothing unreasonable about his sentence.

VI.
While we find that the district court erred by allowing Beck's probation officer to testify that she was a probation officer and by not allowing the defense attorneys to further question Simmons about his potential bias, we are confident beyond a reasonable doubt that the error was harmless. Further, there was no error in Beck's sentencing or the sentence imposed. Accordingly, the judgments of the district court are AFFIRMED.
NOTES
[*]  Hon. John W. Darrah, District Judge for the Northern District of Illinois, is sitting by designation.
[1]  In this context, we break from the dictionary and use the terms "motive to lie" or "motive to testify" synonymously with the term "bias." United States v. Salem, 578 F.3d 682, 686 (7th Cir.2009); see also United States v. Abel, 469 U.S. 45, 52, 105 S.Ct. 465, 83 L.Ed.2d 450 (1984) ("Bias may be induced by a witness' like, dislike, or fear of a party, or by the witness' self-interest."). We use them all in reference to why Simmons might testify falsely.
[2]  While we label this limitation on cross-examination as error, albeit harmless, the judge may have foreseen problems that neither party raised and the judge did not recite. Simmons was not a friendly witness and was not submissive on the stand. He had already testified about any benefits he was receiving from the government in exchange for his testimony. Prodding questions about his false testimony in exchange for benefits he would receive from the gang during his time in prison, coupled with questions about George, Mook, and Big Bro (questions Beck's attorney purposely avoided), could have caused Simmons to react and point out that Beck and Thomas had absolutely no incentive to sit in court quietly and take the rap for a higher-ranking gang member. The obvious inference is that no one, not even a loyal gang member, is going to sit still and expose themselves to 25 years in prison for a crime they didn't commit. In addition to scuttling the theory of defense, probable demands for a mistrial or a severance of defendants could have quickly infected the trial procedure.

We recognize the reality and demands of a trial like this. Yet perhaps given a few more minutes at sidebar, or more discussion out of the presence of the jury, to reflect on this line of questioning would have disclosed the possible problems that could arise. Such a record on review could have enabled us to avoid the analysis of why the curtailed questioning was harmless error.
[3]  At trial, in fact, the defense took the position that Liggons had no first-hand personal knowledge of the robbery. That fact is belied by the physical evidence placing him there.
