For the most part, Cox's belief has proven to be correct. But as Jones' struggles have continued to mount this year, there's even more reason to believe that he'll enter the free-agent market coming off a season in which he didn't even compile a .260 batting average.
Over the past four seasons, Jones has averaged 579 at-bats/season. Assuming that's the total he registers this year, Jones would need to hit .305 (98-for-321) the rest of the season just to finish at the .260 mark.
"It's just one of those years," Jones said. "You don't want it to go that way, but I guess it just goes that way. You just have to put it behind you, keep playing and help your team any way you can."
While Jones' offseason conditioning program has allowed him to continue proving why he's earned nine consecutive Gold Glove Awards, the weight loss he experienced hasn't exactly brought consistency to his game. The .205 batting average he carried into Tuesday night's game against the Red Sox was the lowest mark among National League regulars.
Philadelphia's Pat Burrell had compiled the NL's second-lowest mark with a .211 batting average. But he, at least, has constructed a .383 on-base percentage, much more impressive than the .303 mark tallied by Jones.
Jones, who is hitting just .175 since May 1 and .139 in June, has spent countless hours working on his swing in the batting cage. But at the same time, he's said in the past that he's a pull hitter, and with that mentality, he has proven to be susceptible to swing and miss far too many pitches.
"Your body is going follow your brain," Chipper Jones said. "If your brain is thinking left-field seats, that's where your body is going to go. Until he gets to the point where he gets his brain driving the ball through the center-field wall, he's going to struggle."
Andruw believes he has allowed his struggles to affect him mentally. All of the benefits of the extra batting practice he's taken in an attempt to physically fix his mechanics have been erased when he's gone to the plate and allowed himself to think about what needs to be fixed.
"Sometimes when you work on mechanical stuff too much in the cage, you start thinking too much when you go into the game, instead of just going out there and playing the game," Andruw Jones said.
Jones said the fact that he'll be entering the free-agent market at the end of this season hasn't proven to have a negative effect.
"That's just part of baseball, it's a business," Andruw said. "I really don't think about it. I just worry about getting our team into first place and back into the playoffs."
Chipping along: Through the first 24 at-bats he recorded since coming off the disabled list last week, Chipper Jones was hitting .500. The fact that just one of the 12 hits he'd recorded went for extra bases wasn't surprising to the veteran third baseman, who missed nearly a month after bruising both of his hands during a May 11 fall at PNC Park.
"I told you all my thumbs weren't really going to allow me to drive balls and to hit balls out of the park," Chipper said. "I'm doing what I can. Trust me, I'm not going up there trying to hit singles. At times, I'm trying to serve a ball or what not. Early in the count, I'm trying to juice balls."
Chipper Jones suffered a scare during the eighth inning of Monday night's game, when he made a diving grab of a sharp Julio Lugo grounder. The impact caused his right hand to sting for about 30 seconds. But he was fine to bat the next half-inning and wasn't feeling any ill effects on Tuesday.
Braves bits: Peter Moylan, who hasn't allowed a run in his past 7 1/3 innings, has limited opponents to a .194 batting average, the best mark among NL rookie pitchers. ... There are still tickets available to purchase for Wednesday night's series finale against the Red Sox. ... Since watching Jarrod Saltalamacchia play first base for two games last week, Scott Thorman has started to show signs that he wants his everyday role back. Entering Tuesday, Thorman had six hits, including two doubles and two homers, in his previous 11 at-bats.
Coming up: The Braves will conclude their three-game Interleague series against the Red Sox on Wednesday night at 7:35 ET. They'll send Buddy Carlyle (1-1, 4.44 ERA) to the mound to oppose Julian Tavarez (4-4, 4.97).
Mark Bowman is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.