Here's why:
* Baseball's focus on the ball: In baseball, the objective is to hit the ball and run to a base. The batter needs to keep their eye on the ball throughout its trajectory to be successful.
* Early uses: The earliest documented uses of the phrase in print appear in the late 19th and early 20th centuries, around the same time baseball was becoming increasingly popular in the US. These early uses often referred to the sport directly.
* Metaphorical extension: Over time, the idiom took on a broader metaphorical meaning, extending beyond the literal act of playing baseball. It came to signify the need to stay focused, alert, and attentive to the task at hand, whatever it may be.
So, while the exact origin of the idiom is difficult to pinpoint, its connection to baseball seems undeniable. The imagery of the batter focused on the ball perfectly captures the idea of staying attentive and focused on the task at hand, regardless of the activity.