Royals players view the term as a compliment about their skills, as in "He's a player!" but few know the origin of Kuntz's "Player!"
"I was with Houston, my second or third year coaching," Kuntz recalled. "All the players would address me as 'Coach' because they were young guys and I was an instructor, and they grew up calling all their coaches 'Coach.'
"Now, I would tell them, 'Hey, my name is Rusty. Call me Rusty.' But every spring, players kept calling me 'Coach.' They didn't get it. So after a while, I would just start calling them 'Player.' If you're going to call me 'Coach', I'll call you 'Player.' And then over the years, that just evolved into calling everyone 'Player.'"
Royals players love it, and they often playfully mock Kuntz, who doesn't mind a bit. That is the type of relationship Kuntz has with the team.
Kuntz, a fan favorite whom manager Ned Yost calls the coaching staff's "media darling," can be tough, too. He doesn't tolerate tardiness from his players or lack of effort. And he lets them know it.
"They know my heart is good," Kuntz said. "But they know my bite can be kind of hard, too."
Still, Kuntz, 61, knows the game has changed, and players today don't adapt well to scolding, not the way his generation of ballplayers once did.
And that was one of the first lessons Kuntz learned as a coach.
"I came up in a different time," Kuntz said. "When you did something wrong, you got your [butt] chewed. If you were one minute late for a meeting, even if you had the perfect excuse, it didn't matter. Times have changed.
"So anyway, I had this kid back when I was coaching with Houston in 1986 who was just busting his butt the first couple of days, really impressive, flying all over the place. Then the third day, he was a little slower. By the fourth day, he was just dogging it. I went up to him and started yelling, 'What the hell is going on here? What are you doing?' I just lit into him, really lit into him.
"He starts crying. Just alligator tears. So I yell some more, 'What are you crying for? There's no crying here. What the hell is wrong with you?' He's crying so hard he can't catch his breath. Just sobbing. Well, he finally catches his breath enough and says, 'My mom just died and I don't have any money to go home for her funeral.'
"Well, I'm speechless. I nearly fell over. I didn't know what to do. I gave him a hug. I reached down for my little wallet and gave him some money to get home. Then I told myself, 'This never happens to me again.'"
And Kuntz said it never has. His players appreciate it.
"He's got everyone's respect," outfielder Lorenzo Cain said. "We know how hard he works, too."
Indeed, a typical day for Kuntz here in the desert starts at 5 a.m. He hustles to the ballpark by 5:30 a.m.
"And then it's all about planning," Kuntz said. "You're planning the day's schedule, the practice sessions, what fields everyone is on, what players need extra work, you pore over video, you eat while you're walking, you throw some BP maybe, you do more planning, hit outfield. You take video home with you so you can plan some more.
"It used to be that a coach's day was done when the players were done. But the game has evolved beyond that."
Before the Spring Training games start, Kuntz is lucky to get back to his condo by 4 p.m.
"I don't think I've seen 7 p.m. here," he said. "When the sun goes down, I'm ready for bed."
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During the season, Kuntz will arrive at the ballpark around noon for a 7 p.m. game and get home after midnight.
Squeezed into a 162-game schedule are 12 off-days, half of which are mostly consumed with travel. Of the six home days off, four are used for charity events.
Kuntz can't count the number of anniversaries and family birthdays he has missed over the years. That is why he has coveted a roving instructor job the past two seasons. But Yost and general manager Dayton Moore keep persuading him to come back to the coaching staff for another season.
"He's just too valuable for what we do," Yost said.
Kuntz just shrugs his shoulders.
"Hey, it's the life we chose," he said.