Hello,

This is an interesting topic. I also have analyzed the ELO ratings in our website for quite a long time.

It has come to me to find our the formula to calculate our ELO as following:

New_ELO = Old_ELO + K*( Result - 1/(1+10^((Opp_ELO-Old_ELO)/800)))

Where:

New_ELO = your new ELO after the game

Old_ELO = your old ELO before the game

Opp_ELO = your opponent's ELO

Result = 0 if you lost, Result = 1 if you win

K = K-factor, which will be discussed below

So, basically, the difference between this formula and the popular formula you can find in the internet is the number 400 (such as in FIDE chess ELO calculator) is replaced by 800.

I also do believe that our website has some cap for the ratings you can gain/lose in a game, to avoid extreme cases (e.g: a 2000-player lost to a 1000-player will not lose too much ratings as in the formula).

The problem you see is because the K-factor is not fixed in our website. It is depending on the number of games you have played before (i.e K-factor changed as you are more experienced with the game).

For lost cities, I guess you have played 300+ games (or even more?), hence the K-factor is set at the minimum value, i.e 23 (or somewhere near that). But for new games like Cartographer, while you have played less than 50 games, the K-factor is very high (somewhere from 80 downto 28?, it will eventually reduce to 23 at some points when you play an enough number of games).

That's why in new games like Cartographer, your rating jumps quite fast after a single game, unlike in the games that you have played for long time such as lost cities.

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All of the above is just my observation and reasoning. I do make an excel file to calculate and keep track of my ratings to guess the value of K-factor used in each game, but it is rather messy because of the number rounding problem, and somehow lost and draw at early messed up my formular (?!). Hope that someone can give a full detail about how the value of K-factor is applied.