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Fundamentally these equations simply distribute players across a scale from 0 to 10. Rank (reverse order of elimination) or score is used to assign the distribution. Virtually the same equation designed for Stars!, also works well with the Civilization board game.
if Game is Stars! OR Score == 0 thenGameRating = (10 / NumPlayers) * (NumPlayers - Rank + 1)
else
GameRating = (Score * 10) / HiScore
A player's overall rating is the average of their game ratings for each game they've played. Once a player has more than 6 recorded games, the 3 most recent games continue to account for half of the rating, while all previous games share the other half. Once a player has more than 10 recorded games, the oldest games are ignored so that the rating only considers the 10 most recent recorded ratings.
Ex: (Avg(Game 2-8) + Avg(Game 9-11)) / 2