Individual Values or IVs (Also called Determinant Values or DVs for short) are values that determine the stats of a Pokémon. These are comparable to Genes, and are the reason for the difference in power from one Pokémon to the next, trained or otherwise.
Each of the battle stats have a certain number assigned to them that range from 0 to 31. These come into calculation within the base stats of a Pokémon which determine the number for each individual stat. These IVs are determined when it is generated by the game, which is often random and at the start of a wild battle, given to the player by an NPC or when an egg is received from the Pokémon Day Care.
 Generation I
In Generation I there were only 4 IVs that were available: Attack, Defense, Speed, and Special. Each of these increased their respective stat and the HP IV culminated from the IVs stored in the other 4 stats. In this generation the IVs could only range from 0 - 15 (or 0000 - 1111 in binary in which the HP IV took it's total from the final binary number from each stat. It took them from Attack, Defense, Speed, and Special, in that specific order, in order to create it's own Individual Value).
The IVs were determined with this formula:
HP = (((IV + Base + (√EV / 8) + 50) * Level) / 50) + 10
Other Stat = (((IV + Base + (√EV / 8) * Level) / 50) + 5
 Generation II
In Generation II, the IV mechanics remained the same from Generation I to maintain compatibility. Previously, there were only four IVs available: Attack, Defense, Special and Speed but that changed to six, spliting Special into Special Attack and Special Defense and the HP getting its own IV.
 Generation III
Starting with this Generation, Individual Values could now range from 0 to 31 instead of 0 to 15.
Additionally, natures were introduced, which also play a factor into how Statistics are distributed, many of which increase one Statistic by 10% whilst reducing another by the same 10%. The exception to this would be Pokémon with a Bashful, Docile, Hardy, Quirky or Serious nature, which do not receive any Statistic adjustments due to these natures being neutral in that regard.
From this Generation going forward, the basic IV formula is as follows:
HP = [IV + (2 x Base) + EV/4 + 100] x Level/100 + 10
Other Statistic = ([IV + (2 x Base) + EV/4] x Level/100 + 5) x Nature
 Generation IV
 Generation V
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