This time, though, Grant was making a ceremonial first pitch before the Tribe played the Boston Red Sox on April 14. At 72, he's unlikely to be blowing a fastball past anybody. He's fine with that. He seems to have not a single regret about his playing days being behind him.
How could he?
Grant, who debuted April 17, 1958, had a Major League career that any ballplayer would be pleased with. He's pleased with it anyway, and he remembered a goodly portion of it.
He clung to fond memories, too, of his first start: a 3-2 victory over the Kansas City Athletics in front of 2,755 fans in cavernous Municipal Stadium.
"I wasn't nervous," said Grant, relaxed inside a conference room at Progressive Field. "I know it wasn't like just pitching a game, 'cause you had to do well. People expected for you to do well."
To him, "people" meant black fans. They had embraced him the way they had Larry Doby, Satchel Paige and Luke Easter before him.
"Even before the game, people were saying: 'Do it for us. Make us feel good,'" Grant said.
They had already done that for Grant. From the time he first stepped into town, he found arms opened for him.
He needed a place to stay, and a prominent businessman opened his home. He needed a place to eat, and one of the most popular restaurants on the East Side opened its tables. He needed a hair cut, and people pointed him to black barbershops that would cater to his style.
"People knew you weren't making a lot of money," he said, smiling.
Yet as he looked back on '58, Grant reminded himself that the world then wasn't as open to a black man as it is in 2008. The vestiges of racism remained entrenched in too many aspects of American life, and the world of baseball, more than a decade after Jackie Robinson and Doby had integrated it, still had barriers that needed broken.
For a rookie like Grant, it helped to enter the game with Doby still on the Indians roster. Doby was a roommate, a friend and a mentor. He taught Mudcat how to survive in the big leagues.
"I mean, he was 'Mr. It,'" Grant said of Doby. "I mean, he'd gone through some things. So it wasn't the same then as it is now."
He pointed to a ballgame in Baltimore, a city not known for welcoming black ballplayers. Doby, a center fielder, told Grant to take his time about walking off the mound after each inning. He wanted to meet Mudcat before he reached the dugout.
Doby told him: "We can walk in together in case there's a threat or in case somebody runs on the field."
No such incidents happened to Grant or to any other black ballplayer who put on a Major League uniform. The rampant fears that followed integration to the big leagues never led to physical attacks.
Baseball fans showed quickly they would cheer on their team, no matter what color the player in uniform happened to be. That's how Grant remembered the times.
"You had a job to do," he said. "You had to prove a point also: that I deserved to be here; I deserved to get my chance in Major League Baseball."
Grant, who retired in 1971, proved that point and more. He did belong in the big leagues; he did deserve his opportunity, which he earned on merit.
Fifty years after his debut, he appreciated that fact a lot more. He's back where that career began -- in Cleveland, at the ballpark, among baseball fans. He's on the mound again, even if this pitch merely serves a ceremonial purpose.
Cheers came along with it.
"It's a wonderful thing," said Grant, the smile returning. "And to throw out the first pitch for the anniversary 50 years ago, how can you not enjoy coming back to Cleveland?"
Justice B. Hill is a senior writer for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.