Can the total number of possible wins/draws/losses be calculated? http://s13.postimg.org/miyhhh113/chess_finite_graph.png

I'm trying to imagine the finite graph of all positions in chess. Due to the sheer number of possible positions, it is impossible with current technology to build an exhaustive database. Such a database would require more than 100 zetabytes of storage.

But even if we can't store the positions exhaustively, would it be possible to count winning lines for each side? That is, can the number of arrows going to Draw, to Black Won, and to White Won be determined mathematically? And if so, would White have more winning arrows than Black?
Theoretically, we don't know, because we can't calculate it yet. Chess is not solved as an universal and general problem and we don't know that if two gods play chess in an infinite manner, which color wins or maybe it's just a draw.

Statistically, you can gather data from chess databases in websites, tournaments and computer tools to have an estimation. For example see this online databases.