Potential

Potential is a mechanic added in version 1.1.0. It acts as a representative value of the player's best and recent performances. It generally does not affect gameplay, with the following few exceptions:

Unlocking World Mode Map 2-3 (see Singularity § Challenge)
Unlocking SAIKYO STRONGER [FTR]

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 representing distinct potential ranges, and one for those who have "Show Potential" disabled under Settings.

As potential is strongly dependent on which songs are owned and inflates upon the release of new song packs, descriptions become obsolete over time and are hence not provided.

Icon
From	0.00	3.50	7.00	10.00	11.00	12.00	12.50	--
To	3.49	6.99	9.99	10.99	11.99	12.49	∞	--

Mechanics

Early research credit goes to choka_noah and is posted here with their permission.

There are three relevant quantities to the Potential, each explained in its own section.

Chart Constant

The chart constant is an internal value assigned to a chart, 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.

Additionally, they also determine how much Steps are gained when completing songs in World Mode.

Score Modifier

The score modifier is a value computed from your score in a round. It can be positive or negative, depending on whether your score is above or below 9,500,000.

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 is distorted for small values

Play Rating

The play rating, previously called chart potential, is an intermediate value used to calculate your potential. In each round, it is calculated by adding the chart constant and the score modifier, then rectified to zero if the result is negative:

{\text{Play Rating}}=\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 play rating of 8.5 which gets saved in your recent/best entries.

Calculation

At the end of each round, your play rating is recorded under your Recent Entries (with a few exceptions later mentioned). If high enough, it might also be recorded under your Best Entries.

Best Entries: A list of 30 unique charts with the highest play ratings ever obtained. Charts can only appear once.
Recent Entries: A list of 10 plays with the highest play rating, out of the 30 most recent plays. Charts can appear more than once.

In total, there are 40 play ratings used to calculated your potential. Potential is the average of these 40 play ratings. 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 by reaching 0 Recollection Rate with the HARD skill effect.

Plays falling under any of these situations are only added to your recent/best entries if they cause an increase in Potential. As such, to maximise your Potential:

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

Maximum Potential

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

Best Entries

Since play ratings 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
10.0	4
10.1 ~ 10.9	23
11.0+	3

The total chart constant of these songs is 313.5, which results in a maximum total of:

313.5 + 2.0 \times 30 = 373.5

Recent Entries

Since play ratings in recent entries are not limited to one per chart, one can maximise the recent entries by obtaining a Pure Memory on Grievous Lady [FTR] 10 times. This results in a maximum 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{373.5 + 132.0}{40} \approx 12.63

This yields the highest possible Potential one can currently obtain: 12.63.

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 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
2.4.5	12.60	9.9	11.33	8.4	144	Filament Senkyou	24 Nov 19
2.4.7	12.60	9.9	11.33	8.4	145	Avant Raze	9 Dec 19
2.4.9	12.60	9.9	11.33	8.4	146	BATTLE NO.1	15 Jan 20
2.5.0	12.63	10.0	11.33	8.4	150	La'qryma of the Wasteland Einherjar Joker IZANA SAIKYO STRONGER	21 Jan 20
2.5.2	12.63	10.0	11.33	8.4	151	world.execute(me);	21 Feb 20