# Ranklist, scores and difficulties

## Your score

Your score is simply the sum of difficulties of your solved problems. Solving the same problem twice does not give any extra points. Note that Kattis' difficulty estimates vary over time, and that this can cause your score to go up or down without you doing anything.

Scores are only updated every few minutes — your score and rank will not increase instantaneously after you have solved a problem, you have to wait a short while.

If you have set your account to be anonymous, you will not be shown in ranklists, and your score will not contribute to the combined score of your country or university. Your user profile will show a tentative rank which is the rank you would get if you turned off anonymous mode (assuming no anonymous users with a higher score than you do the same).

## Combined scores

The combined score for a group of people (e.g., all users from a given country or university) is computed as a weighted average of the scores of the individual users, with geometrically decreasing weights (higher weights given to the larger scores). Suppose the group contains $n$ people, and that their scores, ordered in non-increasing order, are $s_0 \ge s_1 \ge \ldots \ge s_{n-1}$ Then the combined score for this group of people is calculated as \[S = \frac{1}{f} \sum_{i=0}^{n-1} \left(1-\frac{1}{f}\right)^i \cdot s_i,\] where the parameter $f$ gives a trade-off between the contribution from having a few high scores and the contribution from having many users. In Kattis, the value of this parameter is chosen to be $f = 5$.

For example, if the group consists of a single user, the score for the group is 20% of the score of that user. If the group consists of a very large number of users, about 90% of the score is contributed by the 10 highest scores.

Adding a new user with a non-zero score to a group always increases the combined score of the group.

## Problem difficulty

Kattis has problems of varying difficulty. She estimates the difficulty for different problems by using a variant of the Elo rating system. Broadly speaking, problems which are solved by many people using few submissions get low difficulty scores, and problems which are often attempted but rarely solved get high difficulty scores. Problems with very few submissions tend to get medium difficulty scores, since Kattis does not have enough data about their difficulty.

The difficulty estimation process also assigns an Elo-style rating to you as a user. This rating increases when you solve problems, like your regular score, but is also affected by your submission accuracy. We use your rating to choose which problems to suggest for you to solve. If your rating is higher, the problems we suggest to you in each category (trivial, easy, medium, hard) will have higher difficulty values.