I was just looking through a 1962 edition of the Encyclopaedia Brittanica (don't ask why I have it hanging around) for an "older" point of view on baseball, and it goes through this whole commission appointed by (who else) National league presidents and players in 1908 to prove that baseball was "a distinctly American sport [that] had no connection with rounders or any other foreign game".

However, it then goes through disproving the report and starts off with "A Little Pretty Pocket-Book" as the oldest known reference to something very much like today's baseball, then spends pages talking about various other games with similar rules between then and the 1839 so-called "invention" by Doubleday.

Football (or any game where each of two teams try to kick, carry or force a round or oval ball through a goal or across a goal line defended by the opposite team) go back to ancient Rome. And the ball was typically an inflated animal organ. Nothing new under the sun there. :-)