alt Hacker NewsThis is an important point. Thank you.
Games like backgammon (that have betting and the doubling cube to continue), Go (which is calculated in stones), and bridge (again having points) have more natural intermediate scoring systems than chess.
In my opinion the "winner takes all" aspect of chess is similar to what makes analyzing voting systems difficult. In a non game context: Aspnes, Beigel, Furst, and Rudich had some amazing work on how all or nothing calculation really changes things: https://www.cs.yale.edu/homes/aspnes/papers/stoc91voting.pdf .
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Go is also winner take all. It's psychologically satisfying to have a big win, in the same way that it's psychologically satisfying to achieve a brilliant checkmate, but in any ordinary game or tournament (outside of certain gambling setups), a win by 1/2 point is the same as a win by 20+ points.
For a while I really dug in to multiple player (and teams-of-players) ELO calculations. I got into an argument with my friend about whether second place was any better than last place... specifically in poker, but applicable to multiple games (imagine chinese checkers [race to finish], or carcassonne/ticket-to-ride [semi-hidden scoring until the end]).
His POV was that "if you don't win, you lose" and my POV was "second place is better than last place". His response was: "if I play poker to get first place it's wildly different than playing for second or third place [and I may end up in last place wildly more often due to risk % or bad beats]"
I've been more used to "climbing" type performance games (ie: last place => mid-field => second place => first place) and in my gut I wanted my ELO to reflect that (top-half players are better than bottom-half players), however his very valid point was that different games have different payout matrices (eg: poker is often "top-3 payout", and first may be 10x second or third).
I think in my mind I've settled on EV-payout for multiplayer games should match the "game payout", and that maybe my gut is telling me the difference between "Casual ELO" (aka: top-half > bottom-half), and "Competitive ELO" (aka: only the winner gets paid).