As a black boy in the Deep South in the 1920s, he'd listen to baseball games on the radio. He was 8 or 9 years old at the time -- old enough to read and write, he says. But he never heard announcers mention a black player.
Moore asked his parents why.
"They told me baseball was segregated; whites and blacks didn't play together," Moore says. "I know that we didn't go to school together. I was born in Atlanta, Ga., and they had blacks in one place and whites in another."
That was just life in America in the first half of the last century. Color was a great divider, a rigid barrier that had the force of the law propping it up.
"I never thought of playing with the white boys," Moore says.
So any dreams Moore, now 91, might have had about playing baseball for a living didn't include wearing a Major League uniform.
"My ambition was to play with one of those Negro League teams -- when I was young, coming up," he says.
He had no other choices. Yet the lack of choices didn't squash Moore's ambition. He always played baseball as a boy the way white boys did: with broomsticks, tennis balls and everything else, Moore says.
And like the white boys on the other side of Atlanta or elsewhere, Moore became good at the game. By the time he reached 17, he'd caught the eye of scouts with the Atlanta Black Crackers, a Negro Leagues franchise.
His career as a professional took roots there.
From 1936 to 1940, he earned a reputation as one of the game's premier first basemen. Moore played on three All-Star teams and three second-half championship teams. He was selected to the 1938 Southern News Services All-American Negro League Baseball Team.
Yet he had to wonder what a more open society might have done for him. No one should ask whether Moore had regrets about what racism did to him. He has no regrets -- not a one.
He never looked at the Negro Leagues as second-class baseball. Nor did he ever experience second-class treatment from the people who came to see him, for they saw greats of the game: Satchel Paige, Oscar Charleston, Ray Dandridge, Buck Leonard and Buck O'Neil. Those fans celebrated the game.
"We were really crazy about baseball," says Moore, whose playing career was cut short by World War II. "On Sundays, we used to play, and it even looked like the pastor cut church service early so the people could come to the game. They'd come to the baseball game all dressed up; they'd leave church to come to the baseball game."
The sport didn't bring Moore big paychecks. But he didn't take a vow of poverty to play the sport either. What it did more than anything was expose Moore to a world outside the South.
They met interesting people along the way; they saw America from north and south; and they built great friendships.
"Those girls were liking them ballplayers," says Moore, smiling. "We met a lot of them girls on the road, you know."
It was a great time to be young and a ballplayer, despite the color issues.
For as a ballplayer, Moore became a figure in the growth of the game, although his star never shined as brightly as some of his black contemporaries.
As he lives in the twilight of his life, he's got reason to appreciate the legacy he and others from the Negro Leagues have left for baseball. Nowadays, so many of those men aren't alive, so their stories survive through the Red Moores of the world.
They still have plenty to tell.
Moore and 29 others who can trace their baseball lineage to the days of segregation did plenty of storytelling here Thursday. They shared their stories on a day that Major League Baseball used to welcome these Negro Leaguers into its family.
As part of a ceremonial draft, each team picked one player from "black baseball."
Moore went to the Braves, a team he follows from his home in Atlanta.
"I'm so elated to live to be a part of this," Moore says. "I just can't express in words; I can't use the big words -- the elephant words -- that I would like to use to express how I feel.
"I mean, this is one of the greatest things that ever happened to me."
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.