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The game will be held July 14 at Great American Ball Park, the home of the Reds, and will be televised by FOX.
"With Donnie growing up a Reds fan and Bryan being there, it's an honor for them," Bochy said.
While Hinch, whose surprising Astros are in first place in the AL West, makes his All-Star Game coaching debut, it'll be the second time for McClendon, who was on Dusty Baker's NL staff at the 2003 All-Star Game in Chicago.
Mattingly served on Joe Torre's All-Star Game staff in 2004 in Houston, while Price will be making his All-Star Game coaching debut at his home ballpark.
"I'm excited about it," Price said. "You know, I've never been to an All-Star Game, it's going to be great to be around Bruce and his staff while we're playing in Cincinnati. It's going to be a great experience. It's an honor to have this opportunity, for sure."
Both Bochy and Yost are bringing their respective teams' coaching staffs, as well.
Bochy's staff from San Francisco -- assistant coach Shawon Dunston, bullpen coach Mark Gardner, first-base coach Bill Hayes, third-base coach Roberto Kelly, batting coach Hensley Meulens, pitching coach Dave Righetti and bench coach Ron Wotus -- will join him in Cincinnati, while Yost will bring his Royals coaching staff consisting of pitching coach Dave Eiland, catching coach Pedro Grifol, bullpen coach Doug Henry, third-base coach Mike Jirschele, first-base coach Rusty Kuntz, hitting coach Dale Sveum and bench coach Don Wakamatsu.
The trainers for the AL squad will be Adam Nevala (head athletic trainer of the Angels) and Paul Harker (assistant athletic trainer of the Rays), and the NL trainers will be Reds head athletic trainer Paul Lessard and Rockies assistant trainer Scott Gehret.
On Tuesday, July 14, watch the 2015 All-Star Game live on FOX, and during the game visit MLB.com to submit your choice for the Ted Williams Most Valuable Player Award presented by Chevrolet via the 2015 MLB All-Star Game MVP Vote.
MLB.com will provide extensive online coverage of All-Star Week festivities.
The 86th All-Star Game will be televised nationally by FOX, in Canada by Rogers Sportsnet and RDS, and worldwide by partners in more than 200 countries via MLB International's independent feed. ESPN Radio and ESPN Radio Deportes will provide national radio coverage of the All-Star Game. MLB Network and SiriusXM will also provide comprehensive All-Star Week coverage. For more information, please visit allstargame.com.