Potential

Potential is a mechanic added in version . It serves as a rating that quantifies a player's overall skill, based on the average of their 10 best recent performances and 30 best overall performances (see Calculation). A player's Potential value is displayed next to the partner icon at the top of the screen. It generally does not affect gameplay or content unlocks, with a few exceptions.
==Mechanics==
Early research credit goes to choka_noah and is posted here with their permission.
Depending on a player's performance after a song play, their Potential may increase, decrease, or stay the same. Performance is quantified via a Play Rating that depends on the score modifier for that play (which is determined solely by the score), and the chart constant for that particular chart (which depends only on the chart).
These quantities are explained in more detail below.
=== Chart Constant ===
The chart constant is an internal value assigned to a chart, which is a more precise representation of its difficulty than its displayed difficulty level.
Chart constants for various songs, as well as the methods used to obtain these values, are detailed in Songs by Level.
=== Score Modifier ===
The score modifier is a value computed from the score after a song play. It can be positive, zero, or negative, depending on whether the final score is above, equal to, 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
9,800,000 ~ 9,999,999	1.0 + \dfrac{\text{Score} - 9,800,000}{200,000}
≤ 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
EX+ 	9,900,000 	1.5
EX 	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, quantifies a player's performance for a specific song play. Play Ratings are used to calculate a player's Potential, as well as the total steps gained if the play is in World Mode. After a song play, 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\}
e.g. Sayonara Hatsukoi [FTR] has a chart constant of 7.0. Obtaining a Pure Memory will give a score modifier of 2.0. This results in a Play Rating of 9.0.
=== Calculation ===
After each song play, the Play Rating is recorded under a player's Recent Entries (with exceptions). High enough Play Ratings will also be recorded under a player's Best Entries.
;Best Entries
:The 30 highest Play Ratings attained over a player's entire play history. Charts can only appear once, i.e. for multiple high Play Ratings on the same chart, only the highest will appear in Best Entries.
;Recent Entries
:The 10 highest Play Ratings out of the 30 most recent plays. Charts are only included once, i.e. for multiple recent Play Ratings on the same chart, only the highest will be included. (prior to v3.0, multiple recent Play Ratings on the same chart could appear in Recent Entries)
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, with unfilled entries being set to 0. The displayed Potential is truncated to two decimal points.
There are 2 special cases for which Potential cannot decrease:
* Obtaining EX rank or above.
* Losing by reaching 0 Recollection Rate with a HARD Gauge.
Plays falling under either of these situations are only added to the recent/best entries if they cause an increase in Potential.
==Ranks==
There are nine different icons for the Potential rating: eight representing distinct potential ranges, and one for when "Show Potential" is disabled under Settings.
Icon	 	 	 	 	 	 	 	 	
From	0.00	3.50	7.00	10.00	11.00	12.00	12.50	13.00	--
To 	3.49	6.99	9.99	10.99	11.99	12.49	12.99	∞ 	--
== Unlocks ==
The following songs and World Mode maps/chapters have Potential-based unlock requirements:
== Maximum Potential ==
:Main article: Misc Trivia § Maximum Potential
The maximum possible Potential can be attained by achieving a Pure Memory on the 30 charts with the highest Chart Constant, with 10 of these happening within the 30 most recent plays.
==Gallery==
potential down.png|Potential down, keep and up (credit to the Japanese wiki)
method_1.jpg|Derive chart constant by method 1 (credit to the Japanese wiki)
potential_rating.png|Potential ranks (credit to the Japanese wiki)
Potential.jpg|Potential ranks (including comparisons with pre 1.5 system, credit to the Japanese wiki)
Category:Game Mechanics