Origin of "ballpark estimate" to mean a very rough estimate?

I'm wondering where the term "ballpark estimate" comes from? Sometimes "ballpark" is said stand-alone to mean a rough estimate, as in "these numbers are a ballpark". I understand it must come from baseball or some other sport. Does it refer to the idea that a batter might point in the direction he'll hit the ball? Or is it something that relates to a rough guess at the attendance that day? What part of the ballpark or sports does one use a rough estimate?

Etymonline has this interesting bit:

ballpark "baseball stadium," 1899, from (base) ball + park (n.). Figurative sense of "acceptable range of approximation" first recorded 1960, originally referring to area within which a spacecraft was expected to return to earth; the reference is to broad but reasonably predictable dimensions.

But I'll bet there's more to the story. . .

Edit #1:

Looks like the first figurative use of the phrase is from Kenneth Patchen's 1945 Memiors of a Shy Pornographer. In a discussion of the merits of various great artists, two characters have this dialogue:

The earliest use of the phrase I can find in the context of facts and figures is from 1950 (check) in Volume 5 of Petroleum Processing:

Edit #2:

There's several phrases involving ballpark that have similar usage trajectories. Ballpark figure and ballpark estimate mean approximate or rough. It seems these are derived from the earlier phrase in the ballpark to mean within a particular range or area. Additionally, in the same ballpark has come to mean within the same scope or range.

Edit #3:

To get back to the Etymonline entry, I found an interesting article from a 1976 issue of American Speech by Willis Russell and Mary Gray Porter that claims the theory of the figurative use of ballpark originating in 1960 has to do with an actual satellite recovery area in the Pacific Ocean near Hawaii called the "ballpark." The article includes several early 60s references to this location. The authors conclude, however, given new evidence of earlier figurative uses of the phrase, that the U.S. space program was not the origin of ballpark as approximate.

(Submitting this as an answer based on a suggestion in comments to Callithumpian's answer.)

I've always assumed (without any real support) that it's the difference between "within the ballpark" (this ball is in play) and "out of the ballpark" (it's a goner). To be "in the ballpark" means it's within a range that you can deal with. I think. :-)

I think it comes from the crowd in the ballpark, which is always a rough estimate for the commentators etc.

One school of thought over the saying's origin is that it lies in baseball and refers to the way in which stadium announcers would give an estimated attendance figure for the game.

http://www.blurtit.com/q179020.html