In short, each participant has a performance value for each contest that they participated in. The list of performance values is then sorted in non-increasing order and a weighted sum is taken, where bigger weights are assigned to earlier items in the list.

In particular, the rating system has the following characteristics.

• The rating of a user will never decrease. Therefore, it is never optimal to skip a contest as each contest will contribute a non-negative rating delta.
• The performance of a user in a contest does not depend only on the rank, but also on the score, which encourages users to widen the gap between them and the next lower participant and shorten the gap between them and the next higher participant.

Performance Calculation

For a user $u$ and contest $c$, define:

• $\mathrm{score}(u, c)$ as the score of the user. In ICPC-style contests, this is the number of solves; in IOI-style contests, this is the raw score.
• $\mathrm{penalty}(u, c)$ as the penalty of the user. In IOI-style contests, this value is always $0$.
• $\mathrm{rank}(u, c)$ as the rank of the user, which is defined as $1$ plus the number of users with larger score or equal score and smaller penalty.

Additionally, let $U(c)$ be the set of users participating in contest $c$.

Each user is assigned a performance value for each contest, which is a real number in the range $[0, 4\,000]$. The performance value for user $u$ and contest $c$, $\mathrm{perf}(u, c)$, is calculated as

In other words, the best participant will always have a performance of $4\,000$, while the other participants get a fraction of the performance based on their rank and score.

External Participation

If during a contest, a user participates in another training or competition that results in the user unable to join the contest, the user is considered to have an external participation.

Let $P$ be the list of length $n$ of the user's actual performances, sorted in non-increasing order. The $i$-th external participation ($i \ge 1$) is considered to have a performance equal to $P_{i (i + 1) / 2}$ if $i (i + 1) / 2 \le n$, and $0$ otherwise.

Rating Calculation

For a user $u$, let $P^\prime$ be the list of their performances in this season after accounting for external participation, sorted in non-increasing order. Let $k$ be the length of $P^\prime$. The weights of the performances, $W_i \ (1\le i \le k)$, is a capped geometric progression as follows:

In particular, the geometric progression will be capped at $0.01$ starting at the $46$-th greatest performance of the user.

The rating of the user for this season, say $s$, is then calculated as

where $\mathrm{rating}_0(u) = 0$ for all $u$, and $\mathrm{seasonReset}$ is the season reset function defined below.

Seasons and Season Reset

To maintain the relevance of ratings, the contests are split into (roughly annual) seasons. A new season starts just after the new members from JollyBasic get promoted to Jollybee Intermediate. Users that have participated in the previous season will get an additive bonus to their rating. This bonus is calculated as

In other words, a rating of $4\,000$ is equal to an additive bonus of $400$. The higher the rating in the previous season, the harder it gets to increase the bonus.