Rating System

Lost-MSthApril 28, 2024About 4 min

Each chart (denoted as $\chi$ ) may have its corresponding chart const, roughly representing its difficulty. This is a positive real number, but we conventionally consider it to be a fixed-point number with only one decimal place. For convenience, we will denote its value as $C(\chi)$ .

The server-side database will store ten times its true value, which is an integer. Specifically, if this value is set to a negative value, it is considered that this chart does not participate in potential value calculation, which is an additional feature of this server.

Score and Verification

After playing a certain chart, players can upload a score (denoted as $x$ ) once. At this point, there are some hit counts: Shiny Pure count $x_0$ , total Pure count $x_1$ , Far count $x_2$ , Lost count $x_3$ , then the single play score is:

S(x) = \frac{x_1 + x_2 / 2}{x_1 + x_2 + x_3} \times 10^7 + x_0

Note that there are constraints $x_0 \leqslant x_1$ , $\forall x_i \in \mathbb{Z}^+$ and $\sum_{i=1}^{3} x_i = N(\chi)$ , where $N(\chi)$ is the total note number. Obviously, there is an upper bound $S(x) \leqslant 10^7 + N(\chi)$ on the score, which is called theoretical value.

The server will verify whether the score calculated from the hit count matches the uploaded score and check some constraints.

Play Rating

Based on the player's single score $S(x)$ and the chart const $C(\chi)$ , the single potential value (play rating) can be calculated according to a piecewise linear relationship:

R(x, \chi) = \begin{cases} C(\chi) + 2, \ S(x) \geqslant 10^7 \\ C(\chi) + 1 + \frac{S(x) - 9.8 \times 10^6}{2 \times 10^5}, \ 9.8 \times 10^6 \leqslant S(x) < 10^7 \\ C(\chi) + \frac{S(x) - 9.5 \times 10^6}{3 \times 10^5}, \ L(\chi) \leqslant S(x) < 9.8 \times 10^6 \\ 0, \ S(x) < L(\chi) \end{cases}

Note that a play rating is not allowed to be negative. Then there is a lower score limit $L(\chi) = [95 - 3 C(\chi)] \times 10^5$ that can obtain a non-negative play rating. Obviously, the play rating function $R[S(x), C(\chi)]$ mentioned above is a continuous function of score.

Single Score and Play Rating Calculator

SPURE: PURE: FAR: LOST:
Chart Const:

Score: 0.0

Play Rating: 0 + 0.000 = 0.000

World Ranking Score: (0.00% + 0.00%) × 0 = 0.00000

Single World Ranking Score

Info

All the things in this section come from this video's authors. Please refer to it for more information. We do not guarantee that this formula is completely correct.

Based on the player's single play $x$ and the chart const $C(\chi)$ , the world ranking score for a single play can be calculated:

\begin{aligned} W (x, \chi) &= N C(\chi) [W_{\text{sp}}(x, \chi) + W_{\text{score}}(x, \chi)] , \\ W_{\text{sp}}(x, \chi) &= \max \left[ 0, \min \left(0.095, \frac{x_0}{N(\chi)} - 0.9 \right) \right] , \\ W_{\text{score}}(x, \chi) &= 28.5 \max \left[0, \min \left(0.01, 10^{-7} S(x, \chi) - 0.99 \right) \right] . \end{aligned}

In the formula: $N$ is any positive constant, which will not affect the world ranking, and the specific value is currently unknown; $S(x, \chi)$ is the score for a single play; $N(\chi)$ is the total note number; $x_0$ is the Shiny Pure count of the play $x$ .

It can be seen that the world ranking score is divided into two parts: the Shiny Pure part $W_{\text{sp}}$ and the play's score part $W_{\text{score}}$ . These two parts are both linearly dependent and have upper and lower bounds on truncation, meaning that if they are lower than a certain proportion, they will be zero, and if they are higher than a certain proportion, they will be fully scored. In addition, the maximum of the score part is three times the maximum of the Shiny Pure part.

Sum up the world ranking scores of one user's best plays of FTR difficulty and above to obtain a total world ranking score. The user's world ranking is sorted in descending order based on this total score.

Potential

The total potential of users consists of two parts: the sum of the potential of Best 30 and the sum of the potential of Recent Top 10. After adding the two and dividing by 40, the total potential is obtained, which calculates the average potential value (play rating) for the 40 selected scores.

Best 30

As the name suggests, Best 30 is the best 30 scores, which means the top 30 scores with the highest play rating among all the best scores on different charts.

Recent Top 10

The Recent Top 10 is the top 10 most recent scores and will be selected from the Recent 30. The only selection requirement is that the chart of the 10 scores is different, and the "best" meaning is that under this selection requirement, the sum of the play rating of the 10 scores that can be selected from Recent 30 is the maximum. Obviously, this selection combination must exist and may not be unique, but the sum of the maximum play rating obtained is unique.

Recent 30 Calculation Rules

Recent 30 is nominally the most recent 30 scores, but there are subtle differences in reality. It is just a score combination similar to a queue, basically following the first in, first out principle, with some special rules added. The current rules adopted by the server are as follows:

The queue capacity is 30 scores, with first in, first out, meaning that when new scores are added, the oldest score in the queue will be discarded.
The queue entry and exit operation will try to ensure that the number of different charts is greater than or equal to 10. If the number of different charts including new scores is greater than 10, the oldest score will be discarded normally; Otherwise, 31 new grades will be included in the statistics, and the charts with duplicate grades will be selected, with the oldest score among them discarded.
When the hard mode Track Lost, the score is greater than or equal to $9.8 \times 10^6$ , or the score exceeds the current best score on the server (including the first time), the submission of this new score will protect the total potential of Recent Top 10 from decreasing. The logic is: on the basis of meeting the second rule, filter out the eligible scores in the queue, find the lowest among the scores that are lower than the play rating of the new score, and discard them (if there are multiple lowest scores, choose the oldest one). If an eligible score cannot be found, discard the current new score.