> Generally speaking the "rating structure" is a lattice where you can, for any two players A and B, tell whether A is a better player than B or the other way around.

Not really. You tend to have cycles, where person A can beat person B who beats person C who beats person A.

There's a guy who was even with the guys playing Go who were 2 or 3 stones weaker than me that would tend to beat me because of some of the unorthodox things he did. (Eventually I strengthened my game against these things).

Considering ratings to be a total ordering is a useful approximation.

> Is the point really predicting outcomes?

Others have pointed out how there is a psychological aspect of rating systems, and no developer wants to constantly field complaints. That said, I believe the answer is yes. A rating system derives meaningfulness from its predictive power. In other words, people want to know how good they actually are compared to one another.

I think that for most game players, outside of the top-N group who just want to be at the head of the list, rankings are largely a mechanism to facilitate playing good games, where good is generally defined as close games where both players feel like they could have won.

There's an interesting question about how you rate players who use fundamentally different strategies. For instance in RTS games, should you match boom vs blitz players of otherwise equivalent elo? Or should you instead (try to) construct a classifier to determine which type of player someone is, and then have a rank against each other type of player and match them according to that rank?

As long as you let players play several games vs each other it's fine. If you met this cannon rushing guy already you'll know what to expect.

That's why people use barcode names (llll1l1l1l1l111l) in starcraft :)