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Hidden Power (move)/Calculation: Difference between revisions

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Hidden Power (move)/Calculation (view source)

Revision as of 23:20, 19 January 2024

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In our example, we get:
This example results in:


<math>
<math>
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</math>
</math>


Since this value is equal to 10, per the table above, this means that our Shellder has a {{type|Grass}} {{m|Hidden Power}}.
Since this value is equal to 10, per the table above, this means that the Shellder has a {{type|Grass}} {{m|Hidden Power}}.


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


In our example, we get:
The result of this example is:


{{Hidden Power calculation/II|12<br>''N/A''|10<br>''1''|10<br>''1''|13<br>''1''|8<br>''1''|090}}
{{Hidden Power calculation/II|12<br>''N/A''|10<br>''1''|10<br>''1''|13<br>''1''|8<br>''1''|090}}
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</math>
</math>


Which means that our Shellder's Hidden Power's power is '''68'''.
Which means that the Shellder's Hidden Power's power is '''68'''.


{{Hidden Power calculation/II|12|10|10|13|8|090}}
{{Hidden Power calculation/II|12|10|10|13|8|090}}
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|}
|}


In our example, we get:
The result of this example is:


{{Hidden Power calculation/IV|25<br>''1''|2<br>''0''|12<br>''0''|17<br>''1''|5<br>''1''|8<br>''0''|0201MS.png{{!}}75px}}
{{Hidden Power calculation/IV|25<br>''1''|2<br>''0''|12<br>''0''|17<br>''1''|5<br>''1''|8<br>''0''|0201MS.png{{!}}75px}}
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</math>
</math>


Which means that our Unown has a {{type|Bug}} {{m|Hidden Power}}.
Which means that this Unown has a {{type|Bug}} {{m|Hidden Power}}.


===Damage===
===Damage===
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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.  
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:
The result of this example is:


{{Hidden Power calculation/IV|25<br>''0''|2<br>''1''|12<br>''0''|17<br>''0''|5<br>''0''|8<br>''0''|0201MS.png{{!}}75px}}
{{Hidden Power calculation/IV|25<br>''0''|2<br>''1''|12<br>''0''|17<br>''0''|5<br>''0''|8<br>''0''|0201MS.png{{!}}75px}}
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</math>
</math>


Which means that our Unown's Hidden Power's power is '''31'''.
Which means that this Unown's Hidden Power's power is '''31'''.


{{Hidden Power calculation/IV|25|2|12|17|5|8|0201MS.png{{!}}75px}}<br>
{{Hidden Power calculation/IV|25|2|12|17|5|8|0201MS.png{{!}}75px}}<br>
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===Number of possible Hidden Powers===
===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 Unown with one different IV:
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. For two Unown with one different IV:


{{Hidden Power calculation/IV|'''30'''|31|31|31|30|31|0201MS.png{{!}}75px}}
{{Hidden Power calculation/IV|'''30'''|31|31|31|30|31|0201MS.png{{!}}75px}}
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{{Hidden Power calculation/IV|'''26'''|31|31|31|30|31|0201MS.png{{!}}75px}}
{{Hidden Power calculation/IV|'''26'''|31|31|31|30|31|0201MS.png{{!}}75px}}


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).  
Both 26 and 30 are divisible by 2 and give the remainder of 2 when divided by 4. 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:
In fact, there are only four essentially different types of IV when calculating Hidden Power:
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In other words: only four IVs that give different remainders when divided by four would cover all possible Hidden Power types and powers.
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> = 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 fact that the floor function results in distinct values (e.g. 10.952 and 10.476) being mapped to the same integer result (in this case 10).
If so, the number of possible Hidden Powers should be 4<sup>6</sup> = 4096. This number 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 fact that the floor function results in distinct values (e.g. 10.952 and 10.476) being mapped to the same integer result (in this case 10).


===Percentage distribution of different variations of Hidden Power===
===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, and are different for every Hidden Power's type and damage value.  
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, and are different for every Hidden Power's type and damage value.  


As 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.   
As previously stated, 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, the number of 64 "types" is reduced to 16 and the number of 64 "powers" to 41.   


<div style="display: flex; justify-content: center; gap: 5px">
<div style="display: flex; justify-content: center; gap: 5px">
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==External links==
==External links==
Many Pokémon related sites prepared web-based calculators, which allows to compute Hidden Power of a Pokémon with given IVs:
Many Pokémon related sites host web-based calculators that can compute the 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/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.psypokes.com/dex/hp.php Psypoke's Hidden Power calculator (Generation III and on)]
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