Mr. Carhart, who lives on Staten Island with his wife, Anna, and their two children, said his goal was to create a link between the generations of the game’s greatest stars.

“I’ll never get into the Hall of Fame for my curveball or hitting prowess, so this is my only chance,” he said.

Jon Shestakofsky, a spokesman for the Hall of Fame, said Mr. Carhart’s project “illustrates the seemingly limitless scope of baseball fandom.”

“The Hall Ball’s journey serves as a glowing example of the power and pull of baseball, and the respect and reverence associated with the game’s all-time greats,” Mr. Shestakofsky said, though he would not say if the hall would consider Mr. Carhart’s submission.

“He’s trying to make a human connection with the living and a spiritual connection with those who’ve moved on,” said John Thorn, the official historian for Major League Baseball. He added that when it came to 19th-century baseball history, Mr. Carhart was “about as nerdy as they come, which is high praise from me.”

Mr. Carhart said the project grew out of his love for baseball and genealogy and was born during a family visit to Cooperstown, N.Y., which is home to the Hall of Fame, in 2010. His wife found a baseball in a creek next to Doubleday Field, which is part of the hall’s complex, and it eventually became the Hall Ball.