Additionally, I would say that baseball symbolizes the American Dream.

In American culture, baseball is known as something that is quintessentially American (although it now has significant appeal in Cuba and Japan). Troy's inability to enter professional baseball, despite his talent, is not unlike the inability of black men to enter the middle-class jobs they desired in their migration to northern cities (early in the play, in its exposition, August Wilson narrates those men's disappointment when they confronted the same racism that limited their lives in the South).

For Troy, baseball—like the American Dream—seemed just at the edge of his fingertips. Rose attempts to reason with him, saying that he just came along too early, before Jackie Robinson had entered the Major Leagues. Troy scoffs at this and argues that he had seen plenty of players who were better than Jackie Robinson, and that if you're good "they should let you play." His problem is that no one let him "play," or display his talents and motivations, rather, they simply excluded him for his skin color. This is the same exclusion that extinguished the dreams of other ambitious black people.

While one could interpret Troy's opposition to Cory's football dreams (another segregated sport) as concern, it could also have been jealousy. He resented that his son would receive an opportunity that Troy had merely been shown, but was never allowed to seize.

Baseball is a symbol to Troy of what he was prevented from doing because of racism. Troy has never forgotten his dreams of playing baseball. In his front yard, there is a baseball made out of rags and a baseball bat leaning against a tree. Through Troy was a great hitter and a home run king, he wasn't allowed to play professional baseball. He thinks the same degree of racism will prevent his son, Cory, from playing college football. Troy believes that whites will never let African Americans play sports. Though Rose tries to tell Troy that times have changed, Troy doesn't believe it.

When Cory and Troy have the argument that causes Cory to leave home, Cory strikes at his father with a baseball bat. It's fitting that the bat is what brings them to blows, as the bat and baseball as a whole stand for the bitterness that Troy harbors at never having been able to achieve his dream. It is this bitterness that drives a wedge between him and Cory.

Baseball is an integral part of Wilson's drama.  On one hand, the structure of the play is relevant to baseball.  Troy's life is depicted in nine scenes.  To an extent, this corresponds to how Troy's life unfolds with a beginning, middle, and end similar to baseball games.  I think that the full extent of baseball on Troy's life comes out of Scene Three.  It is at this moment that we see Troy attempt to shut down Cory's hopes of playing football.  Rose brings out that the child's pursuit of his dreams is similar...