PokéBase - Pokémon Q&A
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Sorry to lump multiple questions into one like this, but asking them separately seemed like it'd clog up the questions and activity. So, let's say I Supremely Train a Surskit in Super Training on X, meaning he's beat the target time on every course.

Now let's say I trade him with a friend of mine to Y. If the friend checks him in Super Training, will he still be Supremely Trained?

And let's say I put him into Pokémon Bank, then take him back out in X. Will he still be Supremely Trained?

And finally, let's say I transfer him to Alpha Sapphire via Pokémon Bank. Will he be Supremely Trained in Alpha Sapphire too?

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Well, this doesn’t answer your question, but in Let’s Go, if your Pokémon is trained in any AVs, it will lose it’s AVs if transferred to home.
I have no idea what AVs are I don't think. Are they like EVs? XD
XD, Well, in Let’s Go, EVs were replaced with AVs, to make it more simple. AVs only exist in Let’s go. You can give your Pokémon candies, not rare candies, strength and smart candies and whatnot. Giving it one candy will give it one AV. One AV is one stat point. A Pokémon can have 200 AVs in one stat.
And you can have 200 AVs in each stat.
Oh, interesting. Thanks. :3
Np! My guess why your Pokémon loses it’s AVs upon transferring to Home is because AVs don’t exist in any other game and if you Pokémon kept the stat boosts, it would be way to overpowered.

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The 30 Super Training bitfields are still part of the data structure even up to at least US/UM (where they can't possibly be relevant for anything other than a data consistency check, due to the inability to go back to XY at that point). Once you get them, they will be preserved even through transfer to another game or Pokemon Bank.

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So yes to it keeping its Supremely Trained status? I'm sorry I'm a bit dim. XD
OK I think I figured it out, thanks! :3