Nausicaa and her attendants play with a ball in the Odyssey, which must date from about 3000 years ago.

When I read myths of centaurs I can't help but think they were a metaphoric description of these early horseman tribes, also as the origins of wisdom from the east.

Agreed. They must be a depiction R1a P-I-E tribes who conquered the natives as they spread east (India) and west (Europe).

Compare Anacharsis/Solon.

A ball has to one of the top 10 human inventions of all time along with speech, wheals, wall and garment.

The handegg even greater though, at least in the US.

human invention? heard of rocks?

Rocks are fine for throwing at targets, which behavior certainly dates back much further, but you can't play polo with them. (I found TFA's blithe dismissal of the polo mallets found at the same cemetery unconvincing.)

Would anyone be surprised if we found out that hunter - gatherers played some kind of ball games?

Thinking of https://news.ycombinator.com/item?id=23667506 , I wouldn't be surprised if the "mis-thrown" ball covertly targeted near a group of attractive women wasn't already old in the mesolithic.

They built big monuments, had big rituals. I guess it'd be cool to learn that they had ball games, but I don't think it would be shocking.

Small leather things just don't last as long as big stone things. I wouldn't be surprised if the oldest known ball coming from the lower Nile has less to do with area of use and more to do with desert climate.

    Two vast and trunkless legs of stone
    Stand in the desert ...