Meta Battle Subway PokeBase - Pokemon Q&A
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The title says it all.

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No it doesn't. Do you mean one pokemon with a base stat total, or 6 pokemon for each base stat?

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If you want the highest Base Stat Total, then Mega Mewtwo (both X and Y) are tied at 780 each. Ignoring the Mega's, then a lot of legendaries hit 680: Lunala, Solgaleo, Hoopa (Unbound), Lugia, and Mewtwo.

If you want it for each of the given stats, then keep reading.
HP: Wobbuffet with base 190.

Attack: Mega Mewtwo X with base 190, or if you ignore Megas, then it is Deoxys-Attack with base 180.

Defence: Mega Slowbro with base 190, or if you ignore Megas, then it is Deoxys-Defence with base 160.

Special Attack: Mega Mewtwo Y with base 194, or if you ignore Megas, then it is Deoxys-Attack with base 180.

Special Defence: Deoxys-Defence with base 160.

Speed: Deoxys-Speed with base 180.

So in other words, the Deoxys forms win overall!

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Thank you SO much!!! :)