# 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.