His selection for the Hall of Fame was disputed

The effort to elect Cartwright to the Baseball Hall of Fame was followed by 20 years of dispute. Baseball historians and sports figures disagreed on whether Alexander Cartwright qualified as one of the game's founders even though he had died decades previously. For instance, the Mills Commission recognized Abner Doubleday as baseball's creator.

The discussion was reignited by a newspaper item that was found in 2004. The report showed that the regulations ascribed to their club were ones they had brought over from their time with the Gotham Club, according to Knickerbocker co-founder William R. Wheaton. Baseball in the Garden of Eden: The Secret History of the Early Game, written by John Thorn, might be viewed as an expose to the origins of baseball. The author of the book explains why and how early baseball greats like Cartwright could not have been eligible for the Hall of Fame.

Regardless of the controversy's origins, Alexander Cartwright was advocated for inclusion by a lot of baseball fans and sports analysts. Alexander Cartwright's entry into the exclusive group of baseball greats in 1938 is a noteworthy fact.