(Update 01/12/2022: As pointed out by Amasugi, maimai でらっくす's ranking doesn't have the E-F ranks anymore, instead replaced by BB and BBB. I've updated the table below to reflect that!)

(Update 26/02/2024: Updated a few things because I know more about the game now!)

I have been playing maimai でらっくす for a couple of months a while now, and personally, I am very intrigued by the internal workings of the game. After working on Tachi's maimai でらっくす implementation, I started learning about the game's internal rating system. This post will focus on exactly that, from the very bottom up.

What is this "Rating" you're talking about?

Let's start by understanding "rating". In maimai でらっくす, for every difficulty of a song (hereby referred to as "chart") played, there will be an integer rating associated to it, depending on multiple factors. Each account will have a total rating, usually used as a metric to gauge progress and skill level. This total rating number can only increase, not decrease, as higher scored and harder charts gets played on that account. For each total rating range, there will be also a colored plate representing that range. In the community, it is referred to as below:

Color	Total rating range
White	0-999
Blue	1000-1999
Green	2000-3999
Yellow	4000-6999
Red	7000-9999
Purple	10000-11999
Bronze	12000-12999
Silver	13000-13999
Gold	14000-14499
Platinum	14500-14999
Rainbow	15000+

So, how is this "rating" calculated?

We can start with the easier one out of everything: total rating. An account's total rating is made up of two parts, New Charts' ratings, and Old Charts' ratings. These ratings only accomodate for the best records on that account, and will not change if you achieve a downscore on the same chart.

New Charts

• New Charts are charts that are added in the latest title version (i.e. Universe, Universe Plus, etc.)
• The top 15 ratings are listed here.

Old Charts

• Old Charts are charts that are added in previous title versions.
• The top 35 ratings are listed here.

The formula for total rating is given below:

$$\text{Total Rating} = S_N + S_B$$

• $S_N$ is the sum of all Ratings in New Charts.
• $S_B$ is the sum of all Ratings in Old Charts.

With that out of the way, we can now get into how each chart's rating is calculated. Chart ratings are calculated with the formula given below:

$$\text{Chart Rating} = \lfloor\text{Chart Constant} \times \text{Score} \times \text{Rank Multiplier}\rfloor$$

This formula shows that there are three relevant quantities when it comes to calculating the Chart Rating. Each of the sections below will proceed to explain each of them.

Chart Constant

In the game, each chart is assigned an integer difficulty level, ranging from 1-15. Between level 7-15, there are also intermediate levels, with a plus added to them to better distinguish charts' difficulties (e.g. 7+, 8+, 9+, etc.).

If you looked at this, you would assume that all charts of the same difficulty level are actually of the same difficulty. This is a false assumption, as internally, each chart is assigned a decimal level for them. Given a difficulty level $X$, its internal level will range between $X.0$ to $X.6$, while $X+$ will range from $X.7$ to $X.9$.

These values are usually derived from the rating changes observed when finishing a chart ingame, using the above formula, but finding for $\text{Chart Constant}$. For those who has access to the game files, this is also defined in the chart's XML file as well.

Score

This is just the score you obtained, converted to a decimal. So, for example, 100% will have a value of 1, and 101% will have a value of 1.01. With maimai でらっくす's system, score will always have a maximum value of 101%, whereas maimai FiNALE scores will have a maximum value depending on the amount of BREAK notes found in the chart.

This writeup will not go deep into how scores in both games are calculated, as it is not the focus of what we are discussing.

Another thing to note is all scores above 100.5% will be treated as 100.5%, so the rating algorithm essentially caps out at 100.5% if you are aiming to maximize rating for your scores.

Rank Multiplier

For maimai でらっくす, SEGA has opted for a rank-based multiplier, instead of a more linear multiplier like in CHUNITHM. This means your rating will increase with each rank, while small score increments will usually not result in a rating increase.

Rank	Multiplier
SSS+	22.4
SSS	21.6
SS+	21.1
SS	20.8
S+	20.3
S	20
AAA	16.8
AA	15.2
A	13.6
BBB	12
BB	11.2
B	9.6
C	8
D	5

Conclusions

With all three main parts of the formula and the total rating explained, I feel like this is enough for a wrap-up. For now, this should be everything that is needed to understand and work with maimai でらっくす's rating system.