in the modern sense of a game of ball for teams of nine, 1845, American English, from base (n.) + ball (n.1). Earlier references, such as in Jane Austen's "Northanger Abbey," refer to the game of rounders, of which baseball is a more elaborate variety. The modern game was legendarily invented 1839 by Abner Doubleday in Cooperstown, N.Y. Base was used for "start or finish line of a race" from 1690s; and the sense of "safe spot" found in modern children's game of tag can be traced to 15c. (the use in reference to the bags in modern baseball is from 1868). Baseball as "ball with which the game of baseball is played" is by 1885.
The expression second guess originated in big league baseball. In baseball, a man making a play has time only for one thought on that particular play. He must make up his mind in a flash how he is going to make the play. ... The expression came into the common speech because it so patly describes us fellows who sit back and analyze a wrong play after it has been made. [Damon Runyon, "The Brighter Side," Nov. 18, 1938]
The record of the phrase, at least in newspapers, seems to support the baseball origin. Second-guesser (1913) was baseball slang for "fan who loudly questions decisions by players, managers, etc.," and from about 1899 guesser or baseball guesser had been used in sports-writing for "fan who speculates and opines on the upcoming games or season."
Quisser is the new Texas league umpire. Guesser would be a better name for the majority of those who are now employed by president Allen. [El Paso Herald, June 14, 1911]
"one who catches," in any sense, mid-14c., agent noun from catch (v.). Baseball sense is from 1867.