This tale is about the importance of family, an element of life surpassing even Peavy's intensely competitive spirit when he takes the mound for the White Sox. It's about kids' unconditional love of their parents, helping to erase even the worst nights on the job for Peavy.
"I can recall a game where I went out there and didn't have a good game, pitched three or four innings, gave up five or six runs, lost the game, and only struck one out," Peavy said. "I got in bed that night, just bumming, but I had my two little boys crawling all over the top of me, running all over me.
"[Peavy's middle son] Wyatt said, 'Daddy, you did so good tonight. I saw you strike that guy out,'" said Peavy, with a smile. "That just melts you right there. He truly was so proud I was out there and struck that guy out."
Family support for the White Sox hurler stands as multi-generational.
He has three sons -- Jacob, Wyatt, and Judson -- who love to come to the ballpark and watch their dad with admiration. Peavy's father, Danny, and his grandfather, Sonny, also enjoy seeing Jake knock down the opposition, just as they did when Peavy was working his way to the Majors.
All of the Peavy men will be together in honor of Father's Day, allowing Peavy to reflect on the blessings he has.
"Just a good family time and experience, with all of them being at the games, and living and dying with the White Sox," Peavy said. "For me to sit back and see it all happening because of what I do for a living, it's really something special. It's a cool experience on both ends: to be a dad, and then to see my dad and granddad be a part, and so excited about what you do for a living, and be such a huge fan."
Missing out on that family time, especially being together with his sons -- ages 8, 6, and 2 -- played a major role in Peavy using his no-trade veto toward the White Sox first overtures to acquire him on May 21 of last season. Playing in Chicago, and having his family in the San Diego area, was just too much distance for the hurler.
Baseball is ultimately a business, at the core of a game. When Peavy realized he no longer fit in San Diego, he had to figure out how to balance what seemed to be a better chance to win in the Midwest with staying connected to his family two time zones away.
"Wanting to stay there had everything to do with wanting to be a dad, and wanting to be around my kids as much as possible," Peavy explained. "There is a big reason why I was so hesitant to make the move to Chicago. I was living in San Diego, and it means when your kids are in school, seeing them every time when you go home from the road.
"Being here, it's a big sacrifice not being able to see them on the weekends. It takes a lot out of the kids to travel just for the weekends back and forth. Being a father is the biggest joy in my life. There's nothing in this world that can make me feel like those three little boys can.
"There are so many blessings in this life and the life I'm able to give them. Hopefully, on the back side of things, we get to catch up on a lot of lost time. Obviously, a lot of people don't see the sacrifice at times we have to make, especially when you don't live in the city where you play."
In order to combat that absence, Peavy goes home every chance he gets during the season. He might not be able to see all the baseball games played by his two older sons, but he makes some, and gets to practices as well.
"Down the road, they certainly will understand there was nothing I can do. It's not like I voluntarily want to miss anything. It's part of the sacrifice we make," Peavy said. "It's part of the give and take. This is a wonderful life we get to live, but there are some sacrifices that are made when you live the lifestyle we have to live.
"My biggest thing is I love keeping my two lives separate. I give everything I got to the White Sox, and then when I leave here -- win, lose, or draw, good, bad, or ugly -- and go home, and be with those boys, there's nothing else in the world that matters.
"When you walk in, and those boys run up to you, and give you a hug, and want to play, and want to watch Discovery Channel, and fall asleep on you, it's a great release from the daily grind we live in, and the baseball world."
For the Father's Day weekend, the life of Peavy, White Sox pitcher, and Peavy, devoted father, son, and grandson, will come together. But that's not to say Peavy hasn't already used the principles of each responsibility to help him make both areas better.
"You have to have patience in everything you do," Peavy said. "We live in such a world that you want things to happen. Think of being a dad: You want to see your kids do the right things, or behave in the right way, but it takes patience when you discipline them. You need to have patience with your kids.
"Same things apply with baseball a lot of times. You want things to happen now, but you gotta understand it's always a work in progress. That's certainly something that is comparable."
Scott Merkin is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.