[highd]

Regarding this and previous discussions on this topic on HN, it seems to me that one of the primary motivating factors when constructing a new ranking system should be the possibility of cyclical dominance a la rock/paper/scissors, which we should expect to see in many modern complex games. If one wanted to solve that problem, I think it would require some form of multidimensional ranking. Then one would have added flexibility so you could accurate predict winners from the scoring with some function f(x_1,x_2) even in cyclical cases. This would be less interpret-able, but it would have a fair shot at actually modelling/predicting/depicting the dominance relationships between players.

[morelandjs]

I agree this is a critical feature that Elo ratings omit. Elo ratings are transitive, i.e. if I know the probability that A beats B and the probability that B beats C, then I know the probability that A beats C. It's almost certainly the case that non-linear "rock-paper-scissors" effects exist in professional sports.

The tricky bit is trying to estimate these effects with a finite number of samples or observations. Elo thrives on limited data.