Potential

Potential is a mechanic added in version 1.1.0. It acts as a value representing the player's skill level when playing online. It does not affect gameplay in any way, with the exception of unlocking World Mode's map 2-3 (see Singularity § Challenge). Playing songs while online will affect this value, displayed on the icon of your partner at the top of the screen.

Ranks

There are eight different icons for your Potential rating, seven of them representing distinct potential ranges. There is also a special icon for those who have "Show Potential" disabled under Settings. The following table includes a rough description of each icon.

Icon	Potential	Description
	0.00~3.49	The starting rank.
	3.50~6.99	This rank encompasses people playing mainly on Present difficulty.
	7.00~9.99	Purple-ranked players are probably starting to break into more difficult Future charts.
	10.00~10.99	Those in this rank have probably cleared all level 9 charts and a few level 9+ charts. At the higher end, they've cleared most, if not all, of the Future charts in the game.
	11.00~11.99	Anyone with this rank likely has hard cleared all Future charts, with many of them being Pure Memories.
	12.00~12.49	One would have to attain Full Recall or Pure Memory on most level 9+ charts to reach this rank.
	12.50+	A rank held by the most skilled, most consistent players in the world.
	--	A rank held by those who have disabled their potential. Potential still gets updated even when disabled, only not displayed.

Mechanics

Note: Most of the research credit goes to choka_noah and is posted here with their permission.

There are several relevant quantities to the Potential:

Chart Constant - a value inherent to a chart, rounded to the nearest 1 decimal point.
Score Modifier - a value based on score.
Chart Potential - a value obtained by adding the Chart Constant and Score Modifier, lower-bounded at 0.
Recent Entries - a list of 10 plays with the highest chart potential, out of the 30 most recent plays (charts can appear more than once, hence "plays").
Best Entries - a list of 30 unique charts with the highest chart potential obtained on, of all time (charts can only appear once).

Potential is the average of the 40 total chart potentials in recent entries and best entries. It is displayed up to two decimal points, with any more being truncated.

There are 2 special cases wherein Potential cannot decrease:

Obtaining EX rank.
Losing in the middle of a song due to the HARD skill effect.

Plays falling under any of these situations are only updated in the recent entries if they cause an increase in Potential.

As such, the approach to maximize one's Potential is to:

Avoid grades below EX when online (for recent entries).
Maximize score in songs with higher chart constants (for best entries).

Chart Constant

The chart constant is an internal value assigned to a song, which is a more precise representation of its difficulty than its difficulty level. It is currently unknown how these values are determined or calculated.

Chart constants for various songs, as well as the methods used to obtain these values, are detailed in Songs by Chart Constant.

In addition to determining Potential gain/loss from a song, they also determine how much Steps are gained when completing songs in World Mode. As chart constants are stored on the online server, Potential does not change and World Mode is inaccessible when not connected.

Score Modifier

The score modifier is a value computed from your score. It can be positive (reward) or negative (penalty), depending on whether your score is above or below 9,500,000. For a score of 9,500,000, the score modifier is exactly zero.

Below is a table showing the formula for calculating the score modifier for various score ranges.

Score	Score Modifier
≥ 10,000,000	$2.0$
9,950,000 ~ 9,999,999	$1.5 + \dfrac{\text{Score} - 9,950,000}{100,000}$
9,800,000 ~ 9,949,999	$1.0 + \dfrac{\text{Score} - 9,800,000}{400,000}$
≤ 9,800,000	$\dfrac{\text{Score} - 9,500,000}{300,000}$

Below are score modifiers for some notable scores:

Grade	Score	Score Modifier
EX	10,000,000	2.0
	9,950,000	1.5
	9,800,000	1.0
AA	9,500,000	0.0
A	9,200,000	-1.0
B	8,900,000	-2.0
C	8,600,000	-3.0

Score Modifier Plot — Graph distorted for small values

Chart Potential

The chart potential, known internally as rating, is an intermediate value used to calculate the potential. It is simply the sum of the chart constant and the score modifier, and rectified to become zero if the result is negative.

\text{Chart Potential}=\max\{\text{Chart Constant}+\text{Score Modifier},0\}

For example, Sayonara Hatsukoi [FTR] has a chart constant of 6.5, so if you obtain a Pure Memory, the corresponding score modifier is 2.0. This results in a chart potential is 8.5 which gets saved in your recent/best entries.

Maximum Potential

Calculation

In order to attain the maximum Potential, you need to have the highest possible chart potential for best entries and recent entries.

Best Entries:

Since chart potentials in best entries are limited to one per song, one can maximise the best entries by obtaining a Pure Memory on 30 charts with the highest chart constants:

Chart Constant	Number of Songs
9.9	2
10.0	4
10.1 ~ 11.0	22
11.1+	2

The total chart constant of these songs is 312.2, which results in a maximum best entries total of:

312.2 + 2.0 \times 30 = 372.2

Recent Entries:

Since chart potentials in recent entries are not limited to one per song, one can maximise the recent entries by obtaining a Pure Memory on Grievous Lady [FTR] 10 times. This results in a maximum recent entries total of:

\bigl[11.2 \text{ (Chart Constant)} + 2.0 \text{ (Score Bonus)}\bigr] \times 10 \text{ (Plays)} = 132.0

Result:

Adding the total recent Potential and the total best Potential, then dividing by 40 and rounding down gives:

\frac{372.2 + 132.0}{40} \approx 12.60

This yields the highest possible Potential one can currently obtain: 12.60.

History

This section lists the maximum possible Potential on every version of Arcaea where new songs were added. The values for versions before the potential system was introduced (1.1.0) are also shown here. The "Minimum CC" is the lowest Chart Constant that affected the maximum potential in each version.

Version	Potential	Minimum CC	Potential (free)	Minimum CC (free)	Total Songs	Songs Added	Date Added
1.0.5	10.62	6.0	8.83	2.5	19	Release songs	8 Mar 17
1.0.9	10.72	6.5	9.26	3.5	21	Dement ~after legend~ , Dandelion	20 Mar 17
1.0.10	10.82	6.5	9.62	4.0	23	Infinity Heaven , Anökumene	12 Apr 17
1.0.11	11.13	7.4	9.71	4.5	29	Crimson Solace , Brand new world	11 May 17
1.1.0	11.35	7.8	10.02	5.5	34	Chronostasis, Kanagawa Cyber Culvert, DataErr0r, Cross†Soul, Your voice so... feat. Such	2 Jun 17
1.1.2	11.49	8.2	10.07	5.5	40	Dynamix Collaboration, Clotho and the stargazer	23 Jun 17
1.1.3	11.56	8.4	10.25	5.5	42	Ignotus, Impure Bird	18 Jul 17
1.1.4	11.62	8.6	10.32	6.0	49	Ambivalent Vision Pack, Harutopia ~Utopia of Spring~, Auxesia	10 Aug 17
1.1.6	11.65	8.6	10.39	6.0	51	Rabbit In The Black Room, Modelista	25 Sep 17
1.5.0	12.09	9.1	10.68	6.5	60	Vicious Labyrinth, One Last Drive, Dreamin' Attraction!!, Red and Blue	3 Nov 17
1.5.2	12.10	9.1	10.68	6.5	62	Surrender, Yosakura Fubuki	24 Nov 17
1.5.3	12.11	9.2	10.79	7.3	64	Reinvent, Syro	21 Dec 17
1.5.5	12.17	9.2	10.79	7.3	69	Lanota Collaboration	1 Feb 18
1.5.6	12.19	9.3	10.79	7.3	70	Metallic Punisher	16 Feb 18
1.5.7	12.20	9.3	10.85	7.4	71	Blaster	9 Mar 18
1.6.0	12.24	9.4	10.85	7.4	76	Binary Enfold	23 Mar 18
1.6.2	12.27	9.5	10.85	7.4	78	carmine:scythe, γuarδina	29 Apr 18
1.6.4	12.28	9.5	10.91	7.4	80	Cybernecia Catharsis, Be There	1 Jun 18
1.6.6	12.28	9.5	10.92	7.5	82	inkar-usi, Call My Name feat. Yukacco	22 Jun 18
1.7.0	12.38	9.6	11.00	7.6	91	Luminous Sky, Suomi, Bookmaker (2D Version), Illegal Paradise	16 Jul 18
1.7.2	12.39	9.6	11.05	7.7	94	Nhelv, dropdead, Fallensquare	13 Aug 18
1.7.4	12.39	9.6	11.09	7.7	95	LunarOrbit -believe in the Espebranch road-	31 Aug 18
1.7.5	12.40	9.7	11.11	7.7	97	Purgatorium, Alexandrite	17 Sep 18
1.8.0	12.42	9.7	11.11	7.7	102	Tone Sphere Collaboration	7 Oct 18
1.8.1	12.42	9.7	11.14	7.8	104	Astral tale, Rugie	8 Nov 18
1.8.2	12.42	9.7	11.14	7.8	105	Phantasia	29 Nov 18
1.8.3	12.42	9.7	11.14	7.8	106	Empire of Winter	22 Dec 18
1.9.0	12.46	9.7	11.14	7.8	111	Groove Coaster Collaboration	9 Jan 19
1.9.2	12.46	9.7	11.14	7.8	112	Libertas	11 Feb 19
1.9.3	12.46	9.7	11.14	7.8	113	Solitary Dream	9 Mar 19
2.0.0	12.49	9.8	11.19	7.9	120	Absolute Reason, Grimheart, ReviXy	21 Mar 19
2.0.3	12.49	9.8	11.27	8.3	123	SUPERNOVA, VECTOЯ, Dot to Dot feat. shully	2 May 19
2.1.0	12.54	9.8	11.27	8.3	126	CHUNITHM Collaboration	23 May 19
2.2.0	12.57	9.8	11.27	8.3	131	Adverse Prelude, Dreadnought	18 Jul 19
2.3.0	12.58	9.8	11.27	8.3	136	Sunset Radiance	22 Aug 19
2.3.2	12.59	9.9	11.27	8.3	137	Mirzam	5 Sep 19
2.4.0	12.60	9.9	11.28	8.3	140	GLORY : ROAD, Diode, FREEF4LL	8 Oct 19
2.4.3	12.60	9.9	11.32	8.4	142	Monochrome Princess, Heavenly caress	26 Oct 19