I've read that cricket was the main summer sport in the US until the Civil War, unsurprising when you consider where many of the immigrants came from. Lacrosse could stake a claim, of course, and probably could be said to be the more indigenous game - any Canadians / Native Americans out there?
Of course, the soldiers suffered from a lack of cricket pitches (ok not their main cause of suffering) and used their bats (wider cricket-style ones by then, not curved ones) to play the more two-dimensional English game known as rounders. [Joke alert / Irony Warning Scheme has proved ineffective] Now in Jane Austen's baseball and indeed in modern rounders, baseball, softball etc the ball doesn't need a pitch to pitch on and so in the 1860s soldiers could pitch up and play on any rough piece of ground.
Are you with me?
Comments welcomed: there are similarities - innings (singular and plural) but also inning (singular) in AmE; 22 yards / 66 feet pitch but only 20 yards / 60 feet approximately from batter to pitcher / bowler; cricket / baseball caps / helmets; hard ball (roughly same size & weight); umpires (?); the Art of Fielding (not the novelist) etc. Special language of both sports?