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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:

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 To 0.00 3.50 7.00 10.00 11.00 12.00 12.50 -- 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

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:

$\text{Play Rating}=\max\left\{\text{Chart Constant}+\text{Score Modifier},0\right\}$

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.

The formula for potential is as follows:

$\text{Potential}=\dfrac{S_R+S_B}{40}$

• $S_R$is the sum of all Play Ratings in Recent Entries.
• $S_B$is the sum of all Play Ratings in Best Entries.

This formula applies even when not all entries are filled. Potential is displayed up to two decimal points, with any more being truncated.

There are 2 special cases wherein Potential cannot decrease:

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 3
10.1 2
10.2 2
10.3 4
10.4 2
10.5 6
10.6 5
10.7 2
10.8 1
11.0 1
11.1 1
11.2 1

The total chart constant of these songs is 314.1, which results in a maximum total of:

$314.1 + 2.0 \times 30 = 374.1$

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:

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

Result

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

$\frac{374.1 + 132.0}{40} \approx 12.65$

This yields the highest possible Potential one can currently obtain: 12.65.

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 20 Mar 17
1.0.10 10.82 6.5 9.62 4.0 23 12 Apr 17
1.0.11 11.13 7.4 9.71 4.5 29 11 May 17
1.1.0 11.35 7.8 10.02 5.5 34 2 Jun 17
1.1.2 11.49 8.2 10.07 5.5 40 23 Jun 17
1.1.3 11.56 8.4 10.25 5.5 42 18 Jul 17
1.1.4 11.62 8.6 10.32 6.0 49 10 Aug 17
1.1.6 11.65 8.6 10.39 6.0 51 25 Sep 17
1.5.0 12.09 9.1 10.68 6.5 60 3 Nov 17
1.5.2 12.10 9.1 10.68 6.5 62 24 Nov 17
1.5.3 12.11 9.2 10.79 7.3 64 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 29 Apr 18
1.6.4 12.28 9.5 10.91 7.4 80 1 Jun 18
1.6.6 12.28 9.5 10.92 7.5 82 22 Jun 18
1.7.0 12.38 9.6 11.00 7.6 91 16 Jul 18
1.7.2 12.39 9.6 11.05 7.7 94 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 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 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 21 Mar 19
2.0.3 12.49 9.8 11.27 8.3 123 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 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 8 Oct 19
2.4.3 12.60 9.9 11.32 8.4 142 26 Oct 19
2.4.5 12.60 9.9 11.33 8.4 144 24 Nov 19
2.4.7 12.60 9.9 11.33 8.4 145 9 Dec 19
2.4.9 12.60 9.9 11.33 8.4 146 15 Jan 20
2.5.0 12.63 10.0 11.33 8.4 150 21 Jan 20
2.5.2 12.63 10.0 11.33 8.4 151 21 Feb 20
2.5.3 12.63 10.0 11.33 8.4 152 9 Mar 20
2.6.0 12.65 10.0 11.33 8.4 155 25 Mar 20

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