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Does the level of evolution affect the final result of EV training?

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Lets say that I am EV training a Doublade, and it has Maxed EV's in a stat at level 36 . The first scenario would be that I evolve it to Aegislash at level 40, and the second is that I evolve it at level 50. Will the stats between the two Aegislash differ at level 100? Thank you very much.

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No matter what level you choose to evolve your Pokemon, EVs for a certain stat will always stay the same. The stat itself, however, is subject to change due to the different evolution stages having different base stats.

If your Doublade has maxed EVs in a certain stat, then the EVs will stay maxed, but it will change according to Aegislash's base stats.

Here's a situation:
Doublade #1:

  • This Doublade has 252 EVs in special attack (assuming 31 IVs and neutral nature) at level 36, which gives a special attack stat of 71.
  • When you level it up to level 40 as a Doublade, its special attack stat will then be 78.
  • Upon evolution via dusk stone, it still has 252 EVs in special attack, but since Aegislash (shield form) has a higher base special attack stat than Doublade, its new special attack stat at level 40 is 82.

If this Aegislash were leveled to level 50, it would have a special attack stat of 102.

Doublade #2:

  • This Doublade has the same EVs, IVs, and Nature as the last one at level 36, giving it a special attack stat of 71.
  • When you level this one up to level 50, its special attack stat will be 97 as well.
  • Upon evolution via dusk stone, it still has 252 EVs in special attack, but since Aegislash (shield form) has a higher base special attack stat than Doublade, its new special attack stat at level 50 is 102.

Since this Pokemon is at level 50 already, its special attack stat at level 50 is 102.

As you can see from this, both methods produce the same results. Hope this helps :)

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If its EVs are not fully maxed out, will the remaining ones be randomly assigned upon evolution, as Dedenne said?
Thank you so much.
No... evolution doesn't give EVs or randomize the ones you currently have :/. Like I said in the answer, stats, not EVs, are all recalculated upon evolution based on their base stats.

Although it does sometimes speed the process up if you EV train the EVs you want onto a pre-evolution. Just make sure to use something to determine what you want the stats to be in the future so you know what you're getting.