It's an interesting question which I have also been curious about. My best guess is somewhere during the teens/early twenties was when the single word first started to appear. Spalding's book, America's National Game, was published in 1911. The game is still refered to as base ball in the book. Other Spalding products such as the National League ball still used the two word name on packaging during the Heydler presidency. By the late 20's it seems that the single word was most common. The change probably took years to gain momentum towards one spelling over the other.
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