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Several aspects of the AtCoder rating system are briefly described in "rating.pdf" in the dropbox linked as "AtCoder's Rating System" on their front page. The most important thing to note is that the displayed user ratings are less than the internal weighted-performance-average used for calculation purposes, according to the following formulas: $$$ \text{displayed rating} = \text{performance average} - f(\text{number of rated contests}) $$$ $$$ f(n) = \frac{F(n) - F(\infty)}{F(1) - F(\infty)} \times 1200 $$$ $$$ F(n) = \frac{\sqrt{\sum_{i=1}^n 0.81^n}}{\sum_{i=1}^n 0.9^n} $$$Note that $$$ f(10) \approx 157 $$$ and even $$$ f(30) \approx 15 $$$, so this really ought to be accounted for explicitly unless you limit consideration to only accounts with quite a lot of rated rounds. Codeforces started using a similar system last year, but it has $$$f(n) = 0$$$ for all $$$n \geq 6$$$, so no such correction should be necessary. AtCoder also applies some monotonic transformation to ensure that all displayed ratings are positive, but I don't have any knowledge of what transformation that is, exactly. |
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