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Not Stat Value, not BST; Base Stat.

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HP- 255
Blissey

Attack- 190
Mega Mewtwo X

Defence- 230
Shuckle and Mega Aggron

Special Attack- 194
Mega Mewtwo Y

Special Defence- 230
Shuckle

Speed- 180
Deoxys-S

Overall- 780
Mega Mewtwo X and Mega Mewtwo Y

Source

Hope I helped :)

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The highest base stat of any individual Pokemon is Blissey's 255 HP. One day we might see something break that, but we'll have to wait and see now.

Hope I helped.

Oh look, a Pokemon with higher HP: http://th04.deviantart.net/fs71/200H/i/2013/303/d/e/mega_evolution_blissey_by_idaida-d6qcvt8.jpg MEGA BLISSEY :DDDDDDDDDD

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You cannot get more than 255 on any stat because that is the maximum 8 bit number, which is what pokemon runs.