ELO ranking

[vila]

How do they count ELO score?

[sorryimlikethis]

After a game is finished if you hover over your new ELO it will show (mostly) the calculations of how it got there.

Basically you are assigned a % chance of winning a game based on your and your opponents' ELOs. Same ELO and it's a 50/50 chance, if your ELO is higher you are expected to win more etc. Your ELO reward is based on your winning chances. If you have a 60% chance to win you get 0.4 ELO for example.

This is then multiplied by a "K Factor", an arbitrary number to make it look pretty. In your first 21 games this number is high because BGA is trying to place you at your correct level faster. Beat someone in your 3rd game for example, your 0.4 gain is multiplied by K Factor 60 to make 24 ELO.
From your 22nd game onwards your K Factor will be 20, so your 0.4 gain will typically be 8 ELO.

When you're playing a game like Catan with more than 2 players you are assumed to have beaten everyone you place above and lose to everyone you place below. On top of this there is a slight discount for beating or losing to multiple people at once. You have a 60% chance to beat opponent A and a 60% chance to beat opponent B. You get (0.4 + 0.4) x 20 = 16 multiplied by 0.75 to get 12 ELO total. The higher the player count the more this discount will be, it's designed to limit volatility with huge player count games.