Hidden Power calculation

Hidden Power is a Normal-type move. However, the real type of Hidden Power is determined by a Pokémon's IVs and may be one of 16 types, excluding Normal- and ???-types. Its power varies from 30 to 70 and is also determined by the user's IVs as well.

Type

Let us consider an example Pokémon, like Pikachu with this set of IVs:

	Hit Points	Attack	Defense	Speed	Sp.Attack	Sp.Defense
	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:

HP_type=Floor[(a+2*b+4*c+8*d+16*e+32*f)*15/63]

where a,b,c,d,e,f are calculated in this way:

• a=1 if the Individual Value of HP is odd. If not, a=0
• b=1 if the Individual Value of Attack is odd. If not, b=0
• c=1 if the Individual Value of Defense is odd. If not, c=0
• d=1 if the Individual Value of Speed is odd. If not, d=0
• e=1 if the Individual Value of Special Attack is odd. If not, e=0
• f=1 if the Individual Value of Special Defense is odd. If not, f=0

Which simply means that every element of the sum in the brace is the remainder of division of corresponding IV and 2, multiplied by appropriate power of 2 (2⁰ in case of a and 2⁵ in case of f). The sum may range from 0 (when all IVs are even) to 63 (when all IVs are odd), inclusively. It is worth mentioning that the computed sum may be easily calculated by putting its variables a,b,c,d,e,f together in reverse order and interpreting this as a number in the binary system, which then needs to be reverted to decimal system:

fedcba₍₂₎ = 32f+16e+8d+4c+2b+a ₍₁₀₎

The summed value is then multiplied by 15 and divided by 63, to be sure that the number representing Hidden Power Type will range form 0 to 15, inclusively (16 values in total). The calculated number is then rounded down (floor[]), which simply means that only integral part of the calculated number is considered.

The resulting number will correspond to a type; utilize the table below.

In our example, we get:

	Hit Points	Attack	Defense	Speed	Sp.Attack	Sp.Defense
	30 0	31 1	31 1	31 1	30 0	31 1

HP Type = Floor[(0 + 2 + 4 + 8 + 0 + 32)*15/63] = Floor[46*15/63] = Floor[10.952] = 10, which means that our Pikachu has a Grass-type Hidden Power.

Damage

Damage of the Hidden Power is calculated in a very same manner like its type, using the following formula:

HP_Power = Floor[((u+2*v+4*w+8*x+16*y+32*z)*40/63)+30]

• u=1 if the Individual Value of HP divided by 4 has a remainder of 2 or 3. If not, u=0.
• v=1 if the Individual Value of Attack divided by 4 has a remainder of 2 or 3. If not, v=0.
• w=1 if the Individual Value of Defense divided by 4 has a remainder of 2 or 3. If not, w=0.
• x=1 if the Individual Value of Speed divided by 4 has a remainder of 2 or 3. If not, x=0.
• y=1 if the Individual Value of Special Attack divided by 4 has a remainder of 2 or 3. If not, y=0.
• z=1 if the Individual Value of Special Defense divided by 4 has a remainder of 2 or 3. If not, z=0.

Like before, the sum may range from 0 to 63, inclusively. The calculated number is then multiplied by 40 and divided by 63 to make sure that the fraction will not exceed 40. Then, the number is increased by 30 and rounded down, making Hidden Power's power a number ranging from 30 to 70, inclusively.

In our example, we get:

	Hit Points	Attack	Defense	Speed	Sp.Attack	Sp.Defense
	30 1	31 1	31 1	31 1	30 1	31 1

HP Type = Floor[((1 + 2 + 4 + 8 + 16 + 32)*40/63)+30] = Floor [(63*40/63)+30] = Floor[70] = 70, which means that our Pikachu's Hidden Power's power is 70

	Hit Points	Attack	Defense	Speed	Sp.Attack	Sp.Defense
	30	31	31	31	30	31

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 32⁶=2³⁰, which is more than one billion possibilities. But let us consider two Pokémon with one different IV:

	Hit Points	Attack	Defense	Speed	Sp.Attack	Sp.Defense
	30	31	31	31	30	31

and

	Hit Points	Attack	Defense	Speed	Sp.Attack	Sp.Defense
	26	31	31	31	30	31

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 possibilities of IV:

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 4⁶=2¹²=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 number (in this case 10).

Percentage distribution of different variations of Hidden Power

Due to the fact that both Hidden Power's type and its power are the products of rounding down, chances of getting a Pokémon with certain Hidden Power are not equal, as one might have thought, and are different for every Hidden Power's type and damage value.

As it was stated before, the number of theoretically different Hidden Powers is 4096, which is the result of multiplying theoretical values of possible types (64) and powers (also 64). It means that every of 64 "types" comes into 64 "powers". After rounding down, however, the number of 64 "types" is reduced to 16 and the number of 64 "powers" to 41.

Trivia

• Although Hidden Power is listed as a Normal-type move, somewhat ironically it is impossible to get a Normal-type Hidden Power. However, the reasoning behind this is due to the statistical impossibility of it.

External links

Many Pokémon related sites prepared web-based calculators, which allows to compute Hidden Power of a Pokémon with given IVs:

• Psypoke's Hidden Power Calculator
• Legendary Pokémon calculator