Re:Elo sucks – better multiplayer rating systems for smaller...
by Someone on Tuesday July 21, 2020 @06:36PM
(#23911715)
“player skill is assumed to be normally distributed”
I would think player skill level (at best; there easily can be cases where P typically beats Q, Q beats R and R beats P) is an ordinal (https://en.wikipedia.org/wiki/Ordinal_data), so one can’t say “player P is twice as good as player Q”, “player P is as much better than player Q as player R is better than player S”, and certainly can’t prove or disprove whether skill is being normally distributed. It is customary to assume that, though.
Also, if one assigns numbers to skill levels, those can be normally distributed. It probably is possible to design an ELO-like system that, given enough games, guarantees that the set of skill level numbers of all players approaches being normally distributed.
I would think player skill level (at best; there easily can be cases where P typically beats Q, Q beats R and R beats P) is an ordinal (https://en.wikipedia.org/wiki/Ordinal_data), so one can’t say “player P is twice as good as player Q”, “player P is as much better than player Q as player R is better than player S”, and certainly can’t prove or disprove whether skill is being normally distributed. It is customary to assume that, though.
Also, if one assigns numbers to skill levels, those can be normally distributed. It probably is possible to design an ELO-like system that, given enough games, guarantees that the set of skill level numbers of all players approaches being normally distributed.