Abstract: Bemuse introduces an easier set of timegates, determined from statistical data of past 60000 games played on Bemuse, which will be applied to charts with level 1~5. Charts at level 6+ are not affected by this change.


Bemuse has very strict timegates. More strict than LR2’s EASY judge (which most BMS uses):

Judgment Bemuse LR2
Meticulous / PGreat 20ms 21ms
Precise / Great 50ms 60ms
Good / Good 100ms 120ms
Offbeat / Bad 200ms 200ms

However, this makes this game very unfriendly for beginners.

Analyzing the impact of the problem

I analyzed the data of about 60,000 games played on Bemuse.

Assuming that beginners play level-1 songs (7,000 games), here is the distribution of the given grades:

Grade Minimum Score Percentage
F 0 35%
D 300000 15%
C 350000 18%
B 400000 19%
A 450000 10%
S 500000 3%

68% of all the level-1 games ended with bad grades (F, D, C). Getting bad grades all the time is quite demotivating for new players.

First proposal

First, I put a proposal to add beginners timegates with the following thresholds:

Judgment Normal Beginner
Meticulous 20ms 50ms
Precise 50ms 100ms
Good 100ms 160ms
Offbeat 200ms 200ms

The beginner timegates would be applied on level-1 and level-2 songs.

I chose to adjust the timegates over other options because:

  • I don’t want to introduce options (e.g. adding a beginner mode) as that would complicate the game and the scoreboard.

  • I don’t want to adjust the grading threshold as that would make the grading scheme inconsistent. I prefer to be able to say “If you get more than 450,000 you get an A” regardless of levels or settings.

Therefore, I decided to inflate the score for beginner charts, so that they get good grades easier, while retaining the rest of the game mechanics.


I received several initial feedback from people in the BMS Chat Discord group:

  • People would have hard time adapting to normal timegates when it is suddenly 2.5x smaller.

  • Changing the timegates at level-3 seems too sudden. A more gradual transition may be better.

  • Some people are not sure whether forcing an easier timegates on easier charts is a good idea or not.


  • It will be very easy to get a full perfect score (555555). The scoreboard will be filled with the same scores if the meticulous timegate is too wide.

Several ideas are suggested:

  • Gradual increase in difficulty. As level increases, make the timegates stricter.

  • Separate beginner mode.

  • Binary judging (e.g. only Meticulous and Offbeat/Missed).

The plan forward

I decided to implement gradual increase in difficulty up to level 5, so that it does not affect any players playing level 6 and above.

I decided not to implement a separate mode due to the reasons listed in the previous section. Also, I decided not to do binary judging as that would result in many people ending up getting the same score (I try to avoid that).

So, I decided to implement 5 sets of timegates:

  • Beginner timegates for songs at level 1 and 2.
  • Level3 timegates for songs at level 3.
  • Level4 timegates for songs at level 4.
  • Level5 timegates for songs at level 5.
  • Normal timegates for songs at level 6+.

But what numbers should I use for these sets of timegates?

Let’s understand the behavior of players more.

Segmenting the users

I obtained the table of scores at the 1st, 2nd and 3rd quartile for each level.

Note: Level 0 is the tutorial.

Level Q1 Q2 Q3 Average n(Games)
0 104686 154259 268021 198136 2765
1 252622 346444 414653 327137 7336
2 322991 381918 426359 366219 2560
3 324557 381131 427655 368571 4374
4 320880 385333 438184 371018 4677
5 329700 388028 436259 375340 5827
6 341833 397973 443670 385106 5423
7 354577 411894 452297 392514 5189
8 377016 421752 456300 408947 4247
9 377461 429192 466141 415859 5267
10 379397 431703 469782 416676 5373
11 400372 443042 474009 428015 2611
12 399461 437981 469937 422399 3610

Then I decided 5 personas:

  • Beginners: Level-1 games that scored between Q1~Q2 (252622~346444).
  • Level3: Level-3 games that scored between Q1~Q2 (324557~371131).
  • Level4: Level-4 games that scored between Q1~Q2 (320880~385333).
  • Level5: Level-5 games that scored between Q1~Q2 (329700~388028).
  • Normal: Level-8 games that scored between Q1~Q3 (377016~456300).

This allows me to take a closer look at each persona.

The accuracy data

Along with each game’s score, Bemuse also collects the accuracy data, which is a histogram of note offsets.


Note offsets generally follows a normal distribution curve. So, by looking at the S.D. (standard deviation) number we could approximate the accuracy. We assume that the mean is 0ms.

First, start with the S.D. value itself:

$$ \sigma = 17.1\text{ms} $$

Calculate the probability that a note would receive a certain judgment, according to the Normal judge:

P[Meticulous] & = 2(\Phi(0) - \Phi(-\frac{20\text{ms}}{\sigma})) = 75.8\% \\
P[Precise] & = 2(\Phi(-\frac{20\text{ms}}{\sigma}) - \Phi(-\frac{50\text{ms}}{\sigma})) = 23.9\% \\
P[Good] & = 2(\Phi(-\frac{50\text{ms}}{\sigma}) - \Phi(-\frac{100\text{ms}}{\sigma})) = 0.3\%

Combine those probabilities to obtain the expected accuracy:

E[Accuracy] & = P[Meticulous] + (0.8) P[Precise] + (0.5) P[Good] \\
& = 95.1\%

Which is quite close to the actual accuracy score reported by the game, 95.07%.

Therefore, the S.D. represents how precise the player is able to hit those notes, independent of the timegates used. The lower the S.D., the more precise.

Data of each persona

Next, we look at each persona, and find out:

  • The average S.D. (used to approximate the timegates-independent accuracy).
  • The average combo bonus score (used to determine expected final score).

Here is the resulting data:

Persona: Normal Level5 Level4 Level3 Beginner
E[S.D.] 38ms 50ms 52ms 52ms 64ms
E[Combo bonus] 21340 14752 15009 14800 19912

Then we calculate the grade a persona would get under the Normal judge:

Persona: Normal Level5 Level4 Level3 Beginner
P[Meticulous] 40.1% 31.1% 29.9% 29.9% 24.5%
P[Precise] 41.0% 37.2% 36.4% 36.4% 32.0%
P[Good] 18.0% 27.2% 28.2% 28.2% 31.6%
E[Accuracy] 82.0% 74.4% 73.2% 73.2% 66.0%
E[Score] 431112 386685 380897 380768 349705
E[Grade] B C C C D

Devising a new judgment scheme

Next, I devised a judgment scheme with the following constraints:

  1. For each persona, the expected grade should be B. Expected final score should be 400000~450000.

  2. It should still be impractical for experts to get a perfect score on beginner songs. The probably of obtaining a perfect score by an expert should stay below 1%.

For this, we need another persona: the Expert persona, which represents the games that scored over 540000. About 100 games were found, so this persona represents the top 0.16% of all the games. This persona have a S.D. value of 12 ms average.

For beginner songs, we calculate the chance of getting a perfect score by calculating the probability in which this persona would get 100 consecutive Meticulous judgments, $P[Meticulous]^{100}$.

For $P[Meticulous]^{100}$ to stay below 1%, the Meticulous timegate should be no more than 24ms.

With this constraints, it’s time to tweak the knobs!


I played around with different numbers until I came up with this judgment scheme:

Judgment Normal Level5 Level4 Level3 Beginner
Meticulous 20ms 21ms 22ms 23ms 24ms
Precise 50ms 60ms 70ms 80ms 100ms
Good 100ms 120ms 140ms 160ms 180ms
Offbeat 200ms 200ms 200ms 200ms 200ms
E[Score] 431112 408684 419273 429940 430191
E[Grade] B B B B B

These sets of timegates will hopefully make Bemuse easier for beginners, while retaining the difficulty in the most part.

Sign up for free and join this conversation.
Sign Up
If you already have a Qiita account log in.