You may want to take a look at
http://forum.shuffleit.nl/index.php?topic=1679.0The general information is correct, I'm not sure if you still actually start with level 20. The third post in that thread goes into the mathematical details.
Generally, the system considers the "base rating" it assumes you have (μ), and the "uncertainty" it has about that "base rating" (φ). Your base rating starts at 0 (averge) and the uncertainty at 2. The uncertainty will rapidly go down when you play more games. Basically it models that the rating system can be alot more sure about your rating when you play 10 games a day than when you play 1 game every 10 days. I rarely play and my uncertainty is 0.3561. If I don't play, the uncertainty will slowly go up, if I play, it will go down.
Now the "intermediate rating" is calculated as (μ - 2φ). That means it tries to be conservative, it is always lower than your base rating (your uncertainty is always greater than 0). The more unsure the system is about your rating, the lower the intermediate rating will be. My base rating is 0.5165, so even though that is half a point above average, my intermediate rating is 0.5165 - 2*0.3561 = -0.1957, which is below 0.
Now, nobody wants their rating to be negative, and people don't want to deal with 4 figures after the decimal point, so the level that you get shown in the game is
50 + 7.5 * "intermediate rating".
For me that gives 48.53, which the game shows as 49.
You can find those values I mentioned here also in the game in the ratings tab.
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Topic: What is the starting rank on Dominion.games? (Read 1557 times)