He might not be the only name they mention. He might not be the first. But they almost always get around to him at some point. And then they'll tell a story.
Maybe it's something they heard. Maybe it's something they saw for themselves.
For instance, take Braves general manager Frank Wren. Back when Wren was Dave Dombrowski's assistant general manager with the Marlins, he became intrigued by how Leyland interacted with his players.
"Craig Counsell was probably the 25th guy on our roster," Wren said. "And I'm sure there are managers who might not give a guy fighting to hang on the time of day."
Leyland did just the opposite.
"Almost every day during stretching, Jim would walk through the group making small talk, having a few laughs, that kind of stuff," Wren said.
"He would usually mention Craig Counsell," Wren said. "He would bring up his name in some context. Tell a joke. Tell a story. I didn't understand it at first. But the more I watched, the more I got what he was doing."
Leyland was letting his players know that he knew all their names and that every player, from the biggest star to the 25th guy, was important to the club.
Wren noticed something else Leyland would do almost daily. During batting practice, he would make a point of approaching almost every player for two or three minutes of small talk.
Those chats weren't usually about baseball. Just small talk -- how's the family, how are the kids, how's your mom? Again, there was something else at play.
Leyland was making himself available to his players, letting them know he cared about them, hoping they understood that he was available if they needed him.
To understand why Jim Leyland was one of the best Major League managers that ever lived, begin here: Leyland knew strategy and Leyland knew talent, but beyond all of that, Leyland knew people.
During 22 seasons with the Pirates, Marlins, Rockies and Tigers, no manager ever did a better job building bridges to his players, gaining their trust and getting them to bust their tails for him.
In the wake of Leyland's departure from the Tigers, it might be difficult to find a single player who would say a bad word about him. They knew he was a very basic man. What you see is what you get. Leyland never played games. Leyland never used the media to send a message.
He expected his players to play hard and to put the team first. If they did those things, they never had a problem with their skipper. From Barry Bonds and Gary Sheffield to Todd Helton and Prince Fielder, Leyland looked players in the eye and told them exactly how he felt.
He inherently understood the culture of a clubhouse, how parts of leadership must be handled by players. He saw his job as organizing, listening, evaluating, running games, managing the bullpen and putting his guys in position to succeed.
Leyland was no soft touch. He could be harumph, gruff. But when he felt things had to be said, he said them behind closed doors. Players respected him for that, too. He never changed much, either. He formed his core beliefs during all those years in the Minor Leagues. Didn't change all that much.
Leyland was about the most loyal friend you could have. Somewhere along the way, he got to know Don Zimmer. For the last 20 or so years, they've spoken by telephone virtually every single day. Last summer, Leyland invited Zim to be part of his American League All-Star coaching staff.
Zimmer declined, saying his health would not allow it. Then a couple of days later, Zimmer excitedly told Leyland that National League manager Bruce Bochy had asked him to be on his staff. And he'd accepted.
There was silence on the phone as Zimmer allowed Leyland to think, "What the heck is going on? Is this guy messing with me, or has he lost his mind?"
Zimmer cackles as he tells the story and how he finally told Leyland that Bochy had issued no such invitation.
Leyland's closest friend in baseball, Tony La Russa -- the guy who hired him for his Major League staff in Chicago -- has a simple nickname for his buddy.
During their frequent telephone conversations, La Russa would see Leyland's phone number pop up on his cell phone and answer, "Hey, it's Sparky Murtaugh."
That nickname combined the names of Sparky Anderson and Danny Murtaugh, the two best managers the Tigers and Pirates ever had.
In La Russa's mind, Leyland was as good as there has ever been, a man with such a deep knowledge of the game, and of players and strategy, that he deserved to be mentioned in the same breath as any manager ever.
Leyland was loyal to his coaches, too, stood by them, defended them, looked out for them. They understood that he could be gruff, that he could be funny, but that he expected every single drill, every single bullpen session to be done with a purpose.
There are fans in Detroit and other places who will tell you that Leyland could have done better with his lineups or his game strategy or any of that stuff.
Here's what they're failing to understand. At a time when almost every front office has data that can help managers with defensive alignments, pitching matchups and the like, Leyland brought a unique gift to the table.
Leyland understood players. He understood their insecurities and their drive. He could size up a player and figure out what that guy needed from a manager.
Leyland's personality played well in a season that begins in February and ends in October. He was very basic in what he wanted. He was very basic in the things that set him off.
Players knew Leyland always had their backs, and that if he told them something, they knew it was the unvarnished truth.
Oh there were days he could be cranky. Lord, could he. But in those 22 seasons, he became as respected and as admired as virtually any manager who ever lived. He has countless friends, from those who played for him to those that worked with him and almost everyone in between.
Leyland has been a large presence in baseball these last two decades. He's an emotional man, a passionate man, and he has more friends and admirers than he can count. As legacies go, it's hard to get better than that.