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  • IVs, or Individual Values, are those things that influence stats. An IV of 31 is considered a perfect (flawless) IV and an IV of 0 is considered bad. The rater always gives you the highest IVs for a Pokémon and you know they're perfect if they "can't be beat"; the same rater then mentions any 0 IVs, or says nothing else if there are none.

    More on IVs.
    Not a breeding thing, but related, here are Effort Values.

    EDIT: I see now I was beaten to answering, but the links may prove helpful.
    Hello! Randomly decided to lend my help. An IV is an 'Individual Value' and plays a key role in determining how high a Pokemon's stat can be when they reach level 100. Another key fact is that there are also 'EV's or 'Effort Values', these are earned either by beating wild Pokemon, using items such as HP UPs or with super training, and also help increasing a stat to a certain degree. IVs are randomly assigned when you get an egg/receive a Pokemon. Some natures hinder or help increase the maximum points of a stat, while some natures are 'neutral' and don't do anything to a Pokemon's stats. An IV can range from 0 to 31 per stat. If a Pokemon has 31 IVs in a stat, that stat is considered perfect. And a Pokemon with 6 IVs of 31 is denominated 'flawless', whereas a Pokemon with 5 or 4 IVs is considered 'semi-flawless'. IVs can be inherited thru breeding if you do it the right way. and with the right parents (parents with perfect stats tend to give perfect offspring somewhat easily compared to using random parents). EVs can be distributed across all stats, every stat can have a maximum of 255 EVs, but overall a Pokemon cannot have more than 500-something (forgot the exact number) EVs across all of its stats. Several held items such as the Power Brace help a Pokemon to gain EVs quicker, and some berries increase happiness in exchange of reducing EVs. Some punching bags of super training can even reset all of a Pokemon's EVs! Competitive players like to administrate their EVs in two specific stats on a generally flawless Pokemon in order to achieve maximum performance for them in battle.

    And that's about it, hopefully I made myself clear but if you have any more doubts I can gladly answer them :3
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