View source for Hidden Power (move)/Calculation

In the Pokémon games, {{m|Hidden Power}} is a {{type|Normal}} move when the type is displayed, such as in battle and on status screens. However, the actual type of Hidden Power is determined by the Pokémon's [[individual values]], and through calculation, can be set as one of the sixteen other natural types and with a power between 30 and 70.

The type of Hidden Power can be checked in [[Veilstone Game Corner]]'s prize house in {{game|Platinum}}, the [[Celadon Game Corner]] in {{game|HeartGold and SoulSilver|s}}, in [[Mistralton City]]'s Pokémon Center in {{game|Black and White|s}}, and at the [[PWT]] in [[Pokémon Black and White Versions 2|Pokémon Black 2 and White 2]]. There remains no in-game way to determine the power level directly, however.

==Generation II==
===Type===
Consider an example Pokémon, like Pikachu with this set of IVs:

{{Hidden Power calculation/II|14|15|15|15|14}}

The type is determined by taking the two {{wp|least significant bit}}s of the Attack and Defense IVs, then {{wp|Concatenation|concatenating}} these two values in that order.

Mathematically, this is the equivalent of:
:[[File:HPtypeII.png]]

Where a represents the Attack IV and b represents the Defense IV.

The resulting number will correspond to a type as marked below.

{| class="roundy" style="background: #{{platinum color}}; border: 3px solid #{{platinum color light}}; {{roundy|10px}}"
! style="background: #{{platinum color light}}; {{roundytl|10px}}" | Number
! style="background: #{{platinum color light}}; {{roundytr|10px}}" | Type
|-style="background-color: #{{Fighting color}}; color:#FFFFFF" align="center"
| 0
| {{typecolor|Fighting}}
|-style="background-color: #{{Flying color}}; color:#FFFFFF" align="center"
| 1
| {{typecolor|Flying}}
|-style="background-color: #{{poison color}}; color:#FFFFFF" align="center" 
| 2
| {{typecolor|Poison}}
|-style="background-color: #{{Ground color}}; color:#FFFFFF" align="center" 
| 3
| {{typecolor|Ground}}
|-style="background-color: #{{Rock color}}; color:#FFFFFF" align="center" 
| 4
| {{typecolor|Rock}}
|-style="background-color: #{{Bug color}}; color:#FFFFFF" align="center" 
| 5
| {{typecolor|Bug}}
|-style="background-color: #{{Ghost color}}; color:#FFFFFF" align="center" 
| 6
| {{typecolor|Ghost}}
|-style="background-color: #{{Steel color}}; color:#FFFFFF" align="center" 
| 7
| {{typecolor|Steel}}
|-style="background-color: #{{Fire color}}; color:#FFFFFF" align="center" 
| 8
| {{typecolor|Fire}}
|-style="background-color: #{{Water color}}; color:#FFFFFF" align="center" 
| 9
| {{typecolor|Water}}
|-style="background-color: #{{Grass color}}; color:#FFFFFF" align="center" 
| 10
| {{typecolor|Grass}}
|-style="background-color: #{{Electric color}}; color:#FFFFFF" align="center" 
| 11
| {{typecolor|Electric}}
|-style="background-color: #{{Psychic color}}; color:#FFFFFF" align="center" 
| 12
| {{typecolor|Psychic}}
|-style="background-color: #{{Ice color}}; color:#FFFFFF" align="center" 
| 13
| {{typecolor|Ice}}
|-style="background-color: #{{Dragon color}}; color:#FFFFFF" align="center" 
| 14
| {{typecolor|Dragon}}
|-style="background-color: #{{Dark color}}; color:#FFFFFF" align="center; color:#FFFFFF" align="center" 
| 15
| {{typecolor|Dark}}
|}

In our example, we get:

HPtype=4*('''15 mod 4''')+('''15 mod 4''')='''4*3'''+3='''12+3'''='''15''', which means that our Pikachu has a {{type|Dark}} {{m|Hidden Power}}.

===Damage===
The damage of the Hidden Power is calculated using the following formula:

:[[File:HPPowerII.png]]

* The variables v through y (the "damage bits") represent the {{wp|most significant bit}} of each IV. If a variable is less than eight, this bit is 0; otherwise, it is 1.
:* v and w depend on the Attack and Defense stats respectively.
:* x depends on the Speed stat.
:* y depends on the Special stat.
* Z is equal to the Special stat when the Special stat is less than or equal to 3; when the Special stat is greater than 3, Z is equal to 3.

Hidden Power's power is therefore a number ranging from 31 to 70, inclusively. 

In our example, we get:

{{Hidden Power calculation/II|14<br>''N/A''|15<br>''1''|15<br>''1''|15<br>''1''|14<br>''1''}}

HP Power = Floor[(5*(1 + '''2*1''' + '''4*1''' + '''8*1''') + 3)/2+31] = Floor[(5*('''1 + 2 + 4 + 8''') + 3)/2+31] = Floor[('''5*15''' + 3)/2+31] = Floor[('''75 + 3''')/2+31] = Floor['''78/2'''+31] = Floor['''39+31'''] = '''Floor[70]''' = '''70''', which means that our Pikachu's Hidden Power's power is '''70'''

{{Hidden Power calculation/II|14|15|15|15|14}}
{| class="roundy" width="650px" style="border: 2px solid #{{Dark color light}};" 
|- style="text-align:center;" 
| bgcolor="#{{Dark color}}" style="width: 33%; {{roundyleft|10px}}" |[[Hidden Power (move)|<span style=color:#000>Hidden Power:</span>]]
| bgcolor="#{{Dark color}}" style="width: 33%" | <span style=color:#000>Type:</span><br>'''[[Dark_(type)|<span style=color:#000>Dark</span>]]'''
| bgcolor="#{{Dark color}}" style="width: 33%; {{roundyright|10px}}" | <span style=color:#000>Power:</span><br>'''<span style=color:#000>70</span>'''
|}

==Generation III and on==
===Type===
{{

Consider an example Pokémon, like Pikachu with this set of IVs:

{{Hidden Power calculation/IV|30|31|31|31|30|31}}

Hidden Power's type of a Pokémon with given IVs is represented by a number, calculated with this formula:

:type = (def % 2) + ((spd % 2) * 2) + ((spatk % 2) * 4) + ((spdef % 2) * 8)

Another way of expressing this is that the type is derived from the least significant bits of the Special Defense, Special Attack, Speed and Defense IVs, in order from most to least significant bit of the result; i.e.:
:type = (def & 1) + ((spd & 1) << 1) + ((spatk & 1) << 2) + ((spdef & 1) << 3)

The resulting number will correspond to a type as marked below.
{| class="roundy" style="background: #{{platinum color}}; border: 3px solid #{{platinum color light}}; {{roundy|10px}}"
! style="background: #{{platinum color light}}; {{roundytl|10px}}" | Number
! style="background: #{{platinum color light}}; {{roundytr|10px}}" | Type
|-style="background-color: #{{Fighting color}}; color:#FFFFFF" align="center"
| 0
| {{typecolor|Fighting}}
|-style="background-color: #{{Flying color}}; color:#FFFFFF" align="center"
| 1
| {{typecolor|Flying}}
|-style="background-color: #{{poison color}}; color:#FFFFFF" align="center" 
| 2
| {{typecolor|Poison}}
|-style="background-color: #{{Ground color}}; color:#FFFFFF" align="center" 
| 3
| {{typecolor|Ground}}
|-style="background-color: #{{Rock color}}; color:#FFFFFF" align="center" 
| 4
| {{typecolor|Rock}}
|-style="background-color: #{{Bug color}}; color:#FFFFFF" align="center" 
| 5
| {{typecolor|Bug}}
|-style="background-color: #{{Ghost color}}; color:#FFFFFF" align="center" 
| 6
| {{typecolor|Ghost}}
|-style="background-color: #{{Steel color}}; color:#FFFFFF" align="center" 
| 7
| {{typecolor|Steel}}
|-style="background-color: #{{Fire color}}; color:#FFFFFF" align="center" 
| 8
| {{typecolor|Fire}}
|-style="background-color: #{{Water color}}; color:#FFFFFF" align="center" 
| 9
| {{typecolor|Water}}
|-style="background-color: #{{Grass color}}; color:#FFFFFF" align="center" 
| 10
| {{typecolor|Grass}}
|-style="background-color: #{{Electric color}}; color:#FFFFFF" align="center" 
| 11
| {{typecolor|Electric}}
|-style="background-color: #{{Psychic color}}; color:#FFFFFF" align="center" 
| 12
| {{typecolor|Psychic}}
|-style="background-color: #{{Ice color}}; color:#FFFFFF" align="center" 
| 13
| {{typecolor|Ice}}
|-style="background-color: #{{Dragon color}}; color:#FFFFFF" align="center" 
| 14
| {{typecolor|Dragon}}
|-style="background-color: #{{Dark color}}; color:#FFFFFF" align="center; color:#FFFFFF" align="center" 
| 15
| {{typecolor|Dark}}
|}

In our example, we get:

{{Hidden Power calculation/IV|30<br>''0''|31<br>''1''|31<br>''1''|31<br>''1''|30<br>''0''|31<br>''1''}}
:type = 1 + (1 * 2) + (0 * 4) + (1 * 8) = 11, which means that our Pikachu has an {{type|Electric}} {{m|Hidden Power}}.

===Base Power===
Base power of the Hidden Power is calculated in a manner very similar to that of its type, using the following formula:
:power = floor(((1 + ((hp / 2) % 2) + 2*((atk / 2) % 2) + 4*((def / 2) % 2) + 8*((spd / 2) % 2) + 16*((spatk / 2) % 2) + 32*((spdef / 2) % 2)) * 5) / 8 + 30)
where ''hp'' is the HP IV, ''atk'' is the Attack IV, ''def'' is the Defense IV, ''spd'' is the Speed IV, ''spatk'' is the Special Attack IV, ''spdef'' is the Special Defense IV, and ''%'' is the [[wp:Modulo_operation|modulo operator]] (i.e. x % y = the remainder of x / y).

In our example, we get:

{{Hidden Power calculation/IV|30<br>''1''|31<br>''1''|31<br>''1''|31<br>''1''|30<br>''1''|31<br>''1''}}
:power = floor(((1 + 1*1 + 2*1 + 4*1 + 8*1 + 16*1 + 32*1) * 5) / 8 + 30), which means that our Pikachu's Hidden Power's power is '''70'''

===Number of possible Hidden Powers===
As there are 6 IVs, ranging from 0 to 31 (32 in total), the number of different possible Hidden Powers should be 32<sup>6</sup>=2<sup>30</sup>, which is more than one billion possibilities. But let us consider two Pokémon with one different IV:

{{Hidden Power calculation/IV|'''30'''|31|31|31|30|31|Ani025MS.png}}

and

{{Hidden Power calculation/IV|'''26'''|31|31|31|30|31|Ani025MS.png}}

As we see, both 26 and 30 are divisible by 2 and give the remainder of 2 when divided by 4. So, in both cases the algorithms will interpret the IVs of those Pokémon in the same way, returning Grass-type Hidden Power with 70 power. It means that for the mentioned algorithms an IV of 30 is treated in the same way like IVs of 2, 6, 10, 14, 18, 22 and 26 (8 in total).

In fact, there are only four essentially different types of IV when calculating Hidden Power:

{|border="0" style="border-collapse: collapse; " cellspacing="1" cellpadding="3" 
|-
|1.
|IV that gives a remainder of 0 when divided by 4 - has damage bit 0 and type bit 0:
|0, 4, 8, 12, 16, 20, 24, 28
|-
|2.
|IV that gives a remainder of 1 when divided by 4 - has damage bit 0 and type bit 1:
|1, 5, 9, 13, 17, 21, 25, 29
|-
|3.
|IV that gives a remainder of 2 when divided by 4 - has damage bit 1 and type bit 0:
|2, 6, 10, 14, 18, 22, 26, 30
|-
|4.
|IV that gives a remainder of 3 when divided by 4 - has damage bit 1 and type bit 1:
|3, 7, 11, 15, 19, 23, 27, 31
|}

In other words: only four IVs that give different remainders when divided by four would cover all possible Hidden Power types and powers.

If so, the number of possible Hidden Powers should be 4<sup>6</sup>=2<sup>12</sup>=64*64=4096. This number, however is again far too large, as the real number of possible variations of Hidden power is simply 16*41=656, as Hidden Power exists in 16 types and has 41 different powers. The significant difference between 656 and 4096 is explained by the function ''floor[]'', which reduces theoretically different numbers (for example 10.952 and 10.476) to the same integer, or whole number (in this case 10).

===Percentage distribution of different variations of Hidden Power===
Due to the fact that Hidden Power's power is the product of rounding down, the chances of getting a Pokémon with a certain Hidden Power base power are not equal, as one might have thought, and are different for every Hidden Power's damage value. 

As stated before, the number of theoretically different values for base damage is 2<sup>6</sup> = 64, since there are two possibilities for each bit. After rounding down, however, the number of 64 "powers" is reduced to 41.

{| style="background: #{{normal color}}; border: 3px solid #{{normal color dark}}; {{roundy|10px}}"
|+ '''Percentage distribution of Hidden Power's powers'''
! style="text-align: center;" style="background:#{{normal color light}}; {{roundytl|5px}}" | Powers
! style="text-align: center;" style="background:#{{normal color light}};" | Qty
! style="text-align: center;" style="background:#{{normal color light}}; {{roundytr|5px}}" | %
|- style="background: #fff;"
| 30, 32, 34, 37, 39, 42, 44, 47, 49,<br />52, 54, 57, 59, 62, 64, 67, 69, 70
| 18 × 64
| 1.5625% each
|- style="background: #fff;"
| 31, 33, 35, 36, 38, 40, 41, 43, 45, 46, 48, 50,<br />51, 53, 55, 56, 58, 60, 61, 63, 65, 66, 68
| 23 × 128
| 3.125% each
|-
|
| 4096
| 100%
|}

==Trivia==
* Although Hidden Power is listed as a Normal-type move, it cannot damage as a Normal-type attack.
* In Generation II, the calculation of the type and power of Hidden Power is completely independent of the HP IV.

==External links==
Many Pokémon related sites prepared web-based calculators, which allows to compute Hidden Power of a Pokémon with given IVs:
* [http://www.psypokes.com/gsc/dvguide.php Psypoke's Hidden Power calculator (Generation II)]
* [http://www.psypokes.com/dex/hp.php Psypoke's Hidden Power calculator (Generation III and on)]
* [http://www.legendarypokemon.net/javacalc.html Legendary Pokémon Hidden Power calculator (Generation III and on)]  

{{Project Games notice|game mechanic}}

[[Category:Game mechanics]]

[[ja:めざめるパワー計算法]]