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Anderson was rested for England's three-wicket win at Headingley but returned to their side on his home ground this week, taking the new ball from the James Anderson End. He bowled tightly throughout the drawn Test, returning match figures of 1 for 81 in 37 overs, but his only wicket came when Pat Cummins chipped the first ball of the second day to cover-point.
Across the series, Anderson has taken four wickets in three matches at 76.75 apiece, and he has still not finished an Ashes Test on the winning side since 2015. Heading into the fifth Test at The Oval next week, during which he turns 41, Anderson will face competition for his place from both Ollie Robinson and Josh Tongue.
"We all agreed that James Anderson deserved to have that sentimental pick because he's a legend of the game, but it may have cost England," Vaughan told the BBC's Ashes Daily podcast. "Josh Tongue is a young quick who has created impact in that one game that he has played, and I know the Australians don't like facing him.
"Jimmy, in the three Test matches that he's played in this series, has just had no impact at all. I don't remember him getting a key wicket at any stage and that's very unlike Jimmy Anderson.
"We pick on Jonny [Bairstow] because he's dropped a few chances but we've got to be honest: Jimmy Anderson has played three games and has had no impact at all in this series, and it might just be that for The Oval, he might not be in England's best XI."
Vaughan said that Anderson lacked "that zip that he used to get" during the Manchester Test. "Chris Woakes has almost showed us what can be done with the Dukes ball when you've got that zip because he's been going over the top with the seam and it's just been doing enough," Vaughan said.
"It's been wobble seam and a bit more action off the surface at a similar pace. It's not like Chris has been bowling three or four mph quicker than Jimmy. For whatever reason, Jimmy's not been getting that kiss off the surface that we've seen for many, many years."
At this stage, Anderson has given few hints about his future as an England player, but there is a long break until their next Test series against India in January-February 2024. With home series against Sri Lanka and West Indies next summer, there is a case that England should look to refresh their side after this Ashes series.
"I just think Jimmy will make his own decision," Vaughan added. "I can't imagine he's going to be the type who is going to say 'this is my last Test and I'm going to retire at the end of it'. I don't think he'll let anybody know. I think he wants to carry on playing.
"He loves playing cricket, he loves bowling, he loves being out in the battle, he loves the dressing room. I think he'll find it very, very difficult to leave the game as a player. He's played on for such a long period of time, he clearly is absolutely in love with playing the game and his body is pretty good.
"Robert Key [England's managing director] will deal with that very professionally. I don't think he's the kind of guy who will go up to Jimmy and say, 'Oh, by the way, you're not going to get another contract.' I think if Jimmy Anderson wants to carry on, England will work a way that [will allow him to] carry on."