What's the meaning of the phrase 'Ballpark figure'?
A ballpark figure is an estimate, within a reasonable range of accuracy.
What's the origin of the phrase 'Ballpark figure'?
The ballpark being referred to is a baseball stadium - commonly called a ballpark in the USA.
I'll have to make it clear at the outset that, being English, I know as much about baseball as most Americans know about cricket, that is, pretty much nothing. Nevertheless, as no real understanding of the game is needed to explain the phrase, I'll press on.
Before we get to 'ballpark figure' we need first to look at the slightly earlier expression 'in the same ballpark'. Baseball grounds are large so if two things are 'not in the same ballpark' they are a long way distant from each other.
An early use of 'in the same ballpark' is in The Ontario newspaper The Windsor Star, February 1942:
The only way Lem [Franklin] will get into the same ballpark with Joe [Louis] will be to buy his ticket at the box-office.
The related term 'in the right ballpark' is also found first in the 1940s.
The term 'ballpark figure' came into being soon afterwards. An early example of that is in the Maryland newspaper The Morning Herald, May 1944:
Sen. Jim Sasser said in a speech that total U.S. aid for the current year is about $250 million. He said "a ballpark figure" is that his proposal would halt $150 million to $180 million.
Add please Americans, don't pick me up on the minutiae of baseball field placings - not unless you can tell me where Silly Mid-off stands on a cricket pitch.