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I know that IVs increase a stat up and one down.
But how do you know HOW MANY IVs Pokemon has? I know they have 31 possible IVs on each stat, but I have heard on Pokemon trading site people say, "There Pokemon has the max *IVs!" Also in X/Y the guy in the Pokemon station says a possible of 6 things, and will tell you what they have "Good potential."
Additionally isn't the increase in one stat decrease in another the result of a Pokemon's nature? Also, I read the section here, and many other Pokemon sites and I still don't get them. Sorry for the long question I just wanted to be better at Pokemon!
Thanks to everyone who answers!

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IVs do not put a stat up and one down, that's natures (they increase one by 10% and decrease another by 10%). Before I answer this, you need to fully understand what IVs are.

  • Each stat (Attack, Defence, etc.) on the Pokemon has an IV value, ranging from 0-31.
  • One IV represents one stat point.
  • Characteristics ("Likes to eat", "Likes to run", etc.) tell you which stat has the highest IV value in that particular Pokemon.

So with that in mind...

  1. How do you know how many IVs a Pokemon has?
    Yeah that's the thing. You can't. IVs are hidden completely by the game apart from the IV checkers (in Kiloude City in X/Y), and characteristics mentioned earlier, but they are vague and don't tell you the specific figures. To get a fairly accurate idea of its IVs, try an IV calculator. You'll need to know its EVs and such though, so it might not be useful.
  2. I have heard on Pokemon trading site people say, "their Pokemon has the max 6 IVs!"
    They're just referring to to how the Pokemon has perfect IVs in all 6 stats. They just worded it badly.
  3. Also isn't the up in one stat down in another the Pokemon's nature?
    That's correct. One goes up by 10%, one goes down by 10%. Also, some natures increase and decrease the same stat, which means it makes no difference.

Also, some info from Bulbapedia on the IV judge and what he says:

>"Incidentally, I would say its greatest potential lies in its (highest stat here)." (this is him telling you which stat has the highest IV value)

>(If the Pokémon has two or more equally good best stats, then he will add one of the following lines:)
"But its Attack stat is good, too."
"Hmm. And its Defense stat is good, too."
"Although its Sp. Atk stat is equally good."
"Its Sp. Def stat seems just as good, though."
"And, well, its Speed stat is good, too."

>To describe the value of the Pokémon's highest IV(s), he will use one of the following lines:
IV range of 0-15: "It has rather decent stats, I'd say. That's how I judge it."
IV range of 16-25: "It's definitely got some good stats. That's how I judge it."
IV range 26-30: "This Pokémon has some fantastic stats. That's how I judge it."
IV of 31: "Stats like those... They simply can't be beat! That's how I judge it."

If you have any more questions, comment.

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Umm.. the link leads to this page.  Also what exactly does the guy in kiloude city tell you?  For example, he tells me my Starmie has above average potential overall and it's greatest potential lies in its defense stat.  This pokemon has fantastic stats. What iv's would that mean it has?
Just edited and fixed the link :)
So yeah basically he's telling you Starmie's Defence has the highest IV value, and that value is somewhere between 26 and 30.
And then fizz happened. +1
Oh ok I think I get it! So a pokemon can have 0 ivs in a stat, and it would be rare to have a perfect 31 in a stat and very rare to have more than one stat have 31.  Thanks!
Yeah pretty much! There are breeding techniques around that help you breed "perfect" Pokemon with 31 IVs in every stat, but they are very tedious and take a lot of time.
I might do a few pokemon in max iv's on certain stats.  I'll probably do my main battle team plus a few others.  But that's another question ;)
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Thanks for the link, but I wanted to know HOW iv's work.