To be in the ballpark in the figurative sense of "within an acceptable range of approximation" is first recorded 1954, originally in the jargon of atomic weapons scientists, perhaps referring to the area within which a missile was expected to return to earth; the idea is broad but reasonably predictable dimensions. Hence ballpark (adj.) "approximate" (1967), of figures, etc.
The result, according to the author's estimate, is a stockpile equivalent to one billion tons of TNT. Assuming this estimate is "in the ball park," clearly there is valid reason for urging candor on the part of our government. [Ralph E. Lapp, "Atomic Candor," in Bulletin of the Atomic Scientists, October 1954]