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8/13/2014 3:52 P.M. ET

Relaxed, mature Gillaspie finds on-field success

SAN FRANCISCO -- When Conor Gillaspie popped back to his feet after safely sliding in for a triple Tuesday night, he'd accomplished something he never did as a Giant: hit a triple.

Back at AT&T Park for the first time since the Giants traded him to the White Sox in February 2013, Gillaspie the White Sox resembles Gillaspie the Giant in appearance only. San Francisco's former second-round Draft pick hit .205 in his brief 29-game (2008-12) stint with the Giants. Gillaspie entered play Wednesday with a .312 average, the American League's seventh-best mark.

Thanks to Chicago's so-so record and Jose Abreu's monstrous rookie campaign, Gillaspie's breakout season has flown under the radar. He's fine with that and credits the increased on-field success to an improved off-field mindset.

"I was a younger player here, and I had a lot to learn. I made a lot of mistakes that I learned from," Gillaspie said of his time with the Giants. "Moving forward, I can honestly say that this game, while it is my job and it is very important to me, is on the backburner when it comes to my wife and my son.

"There are so many other things that I put before this game now, and I think that's somewhat helped me cope with the failures of this game and made it somewhat easier to do a better job the next day if something doesn't work out."

After an underwhelming first season with the White Sox in 2013 (he hit .245), not much hasn't worked out since for the 27-year-old whose stellar season (his average hasn't dipped below .300 once) doesn't exactly have the organization rushing top prospect and presumptive third baseman of the future Matt Davidson to the Majors.

"He's done great as far as understanding what pitchers are trying to do to him and understanding his own swing," manager Robin Ventura said. "You go through confidence sways of whether or not you belong here, but since Spring Training, he's known that he can be a Major League hitter and a good Major League hitter."

A strong rapport with first-year hitting coach Todd Steverson and an increased familiarity with AL parks and pitchers have helped, but Gillaspie said the perspective he's gained from becoming a husband and father has been the key. It's made baseball a little less important, and he's been quite a bit better for it.

"I wouldn't say I'm old by any means," Gillaspie said, "but I've matured enough to know there are certain things you give light to and there are certain things that need to be pushed aside and forgotten.

"If you put too much stock into a game, eventually you're going to be disappointed enough to where you make stupid mistakes. I try to not get to that point."

Abreu's parents coming to South Side

SAN FRANCISCO -- Jose Abreu's parents watched him play live in America for the first time in Minneapolis at last month's All-Star Game. They'll see him play in person for the White Sox for the first time on the team's six-game homestand that begins Friday against the Blue Jays.

"It's important for anyone to have that kind of support," Abreu said when asked about his parents' move to America two months ago. "It allows you to concentrate on the game and what you're doing a lot better."

The rookie sensation promptly went on a tear after their arrival, as he hit .343 with 16 home runs and 41 RBIs in 50 games in June and July. The uptick in power coincided with his switch in bats. Adam Dunn allowed Abreu to use one of his models. It's the same length and weight that Abreu was previously using, but he preferred Dunn's model.

Lately, though, there has been a power outage, for his standards. In 23 games since the All-Star break, Abreu hit just two home runs. Despite last homering July 29, he entered play Wednesday tied for the Major League lead with 31 on the season.

"That happens; it happened to me in Cuba," Abreu said of the recent power decrease. "There are periods of time where I hit a lot of home runs, and there are times you go cold. They will be back."

Worth noting

• Paul Konerko hasn't played many games in San Francisco (Tuesday was his ninth) in his 16-year career, but he is one of the last remaining Major Leaguers to have played at Candlestick Park. Adrian Beltre, Jason Giambi, LaTroy Hawkins, Joe Nathan, Aramis Ramirez, Alex Rodriguez and Jamey Wright join Konerko on that slim list.

• Bright spots like his Tuesday night heroics have been few and far between this season for Gordon Beckham, but his manager has admired the mindset and work ethic he's maintained while his batting average has plummeted nearly 80 points.

"There are times when he's frustrated, but he doesn't take it to the field," Ventura said before Wednesday's series finale in San Francisco. "Look at last night. Defensively, he doesn't take it with him out there. That's a mature response.

"Anybody struggling, not feeling right, sometimes you see they might miss a pitch here or there because their mind might be wandering, but he hasn't let that happen."

• After having an off-day Monday and another coming Thursday, Ventura bumped Jose Quintana up to start Wednesday's game against the Giants. Scott Carroll was originally slated to start the game, but his turn in the rotation isn't being skipped this time through. Ventura said he'll likely start Sunday against the Orioles.

• All indications are that pitching coach Don Cooper (vertigo) will return to the team Friday, Ventura said.

Ryan Hood is an associate reporter for MLB.com. Follow him on Twitter @ryanhood19. This story was not subject to the approval of Major League Baseball or its clubs.