Scoring and Judgment¶

The scoring system and judgment system in Bemuse focuses on both accuracy and combo.

Judgment¶

When hitting the note, the accuracy of your button press will be judged according to this table:

Name Maximum Offset (ms) Accuracy Score
METICULOUS! 20 100%
PRECISE! 50 80%
GOOD! 100 50%
OFFBEAT! 200 0%
MISSED! 0%

Source code reference

Scoring¶

The player’s score is calculated from this formula:

$\begin{split}\text{score} &= 500000 \times \text{accuracy} + 55555 \times \text{combo bonus} \\[10pt] \text{accuracy} &= \frac{ \sum\text{accuracy score} }{\sum\text{total combos}} \\[10pt] \text{combo bonus} &= \frac{ \sum_{c \in \text{combos}}{\text{combo level}(c)} }{\sum_{i = 1}^{\text{total combos}}{\text{combo level}(i)}} \\[10pt] \text{combo level}(c) &= \begin{cases} 0 & c = 0 \\ 1 & 1 \leq c \leq 22 \\ 2 & 23 \leq c \leq 50 \\ 3 & 51 \leq c \leq 91 \\ 4 & 92 \leq c \leq 160 \\ 6 & 161 \leq c \end{cases}\end{split}$

Here’s how the combo level formula comes from. Let’s assume, for simplicity, a player with 99% hit rate, regardless of difficulty. The probability that the player will attain $$c$$ combos is $$0.99^c$$.

Now we have 6 combo levels. The probability that the player will attain that level gradually decreases. Therefore, the minimum combo is $$\left\lceil\log_{0.99} p\right\rceil$$.

Combo Level Max. Probability Min. Combo
1 100% 1
2 80% 23
3 60% 51
4 40% 92
5 20% 161

Source code reference