Hm, you’re right; guess I was thinking in terms of how this would apply to Go, where it’d be as simple as counting territory.
Still, just to spitball: one “obvious” approach, at least in our modern world where technology is an inextricable part of the game, would be to ask a chess-computer: “given that both players play optimally from now on, what would be the likelihood of each player winning from this starting board position?” The situations where this answer is hard/impossible to calculate (i.e. estimations close to the beginning of a match) are exactly the situations where the ELO contribution should be minuscule anyway, because the match didn’t contribute much to tightening the confidence interval of the skill gap between the players.
Of course, players don’t play optimally. I suspect that, given GPT-3 and the like, we’ll soon be able to train chess-computers to mimic specific players’ play-styles and seeming limits of knowledge (insofar as those are subsets of the chess-computer’s own capabilities, that it’s constraining its play to.) At that point, we might actually be able to ask the more interesting question: “given these two player-models and this board position, in what percentage of evolutions from this position does player-model A win?”
Interestingly, you could ask that question with the board position being the initial one, and thus end up with automatically-computed betting odds based on the players’ last-known skill (which would be strictly better than ELO as a prediction on how well an individual pair of players would do when facing off; and therefore could, in theory, be used as a replacement for ELO in determining who “should” be playing whom. You’d need an HPC cluster to generate that ladder, but it’d be theoretically possible, and that’s interesting.)