IVs

What are IVs?
IVs, or Individual Values, are points that every Pokemon has in every stat, they range from 0-31.

Every Pokemon has it's IVs set when it's caught or hatched, there's only 1 way to change them.

What do they do?
The IV of a stat adds the corresponding number of points to that stat, for example if a Pokemon has an IV of 31 in Attack, it will add 31 points to the Attack stat at lv100.

They also determine Hidden Power type but that's for another page.

Competitive Pokemon typically need a max IV of 31 in all the stats they use (often all but the stat their Nature will be lowering anyway) to make them the most effective they can be.

Viewing IVs
IVs can't be viewed by their exact number, but you can see a general range by using the "Judge" function on the PC (obtained by hatching 20 eggs then speaking to a trainer at the Battle Tree entrance)

A stat labeled "Best" means an IV of 31 in that stat, "Fantastic" being 30, and "No Good" being 0, any other labels will typically be useless as they range from 1-29.

Inheritance
When breeding, an egg will always inherit 3 of the IVs from either of it's parents, if either parent holds a Destiny Knot this becomes 5 guaranteed to inherit.

This is how most competitive Pokemon are obtained, by having parents with max IVs of 31 in most stats, it doesn't take long for those perfect IVs to pass to an egg in all the right stats, this is most easily done by breeding with a Ditto that has perfect IVs in all 6 stats.

Changing IVs
Sun/Moon introduced the first means of actually changing IVs, Hyper training will increase any IV (that isn't already at it's max) to 31, however it will not affect Hidden Power type or make it possible for that Pokemon to pass those IVs to eggs, they will still pass their original IVs to eggs.

Terms
To simplify things since only max IVs of 31 are of value in competitive battling, people use terms like "6IV" or "5IV" to refer to how many stats have a perfect IV of 31 in them.

When higher isn't perfect
Under most circumstances a max of 31 is best, however there are cases where having an IV of 0 in a stat is better.

Trick Room

 * Pokemon on Trick Room (TR) teams want an IV of 0 in Speed to make them slower.

Gyro Ball

 * As with TR, Gyro Ball users want the lowest speed possible.

Special Attackers

 * Special Attackers want 0 in Atk to reduce unnecessary damage from Confusion self hits and Foul Play.

Beast Boost

 * For certain sets on Ultra Beasts, certain stats are needed to be lower for the sake of raising a desired stat with Beast Boost, such as Stakataka with a lonely nature and Def IV no higher than 13.