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Wobbuffet

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#202

ATK

106

DEF

382

STA

Lvl 50Max CP

1160

Lvl 40

1026

Lvl 25Weather Boost

733

Lvl 20Raids/Eggs

586

Lvl 15Research

440

Stage 1

Stage 2

Moves

Fast

Counter

Splash

Charm

Charge

Mirror Coat

Return

purified

PvE Analysis

Wobbuffet has the third highest HP in the game. That being said, it doesn’t have the other stats to back up the HP pool like Blissey does. Its low CP allows it to remain in gyms for very long periods of time without being affected by CP depreciation, but it doesn't threaten its attackers very well. 
Best PvE Offensive Moveset
Counter + Return*Best
Wobbuffet has one "viable" moveset, and that is Counter + Return
Charm has decent damage as well.
Mirror Coat is objectively terrible.
Splash should not be considered.
Best PvE Defensive Moveset
Charm + Return*Best
Charm is better for defense due to its superior damage output.
Counter is more likely to be resisted by Ghost-type attackers. 
Return is better for defense.
Mirror Coat gets STAB but is still quite bad. 

PvP Analysis

Counter + Return* and Mirror Coat
Wobbuffet has only one real option, and this is it. Counter is arguably one of the best fast moves for PvP, and helps cover Wobbuffet's weakness to Dark-type Pokemon. Wobuffet's only real charge move is Return, which is obtained by purifying a Shadow Wobuffett. Mirror Coat is a very poor move, but benefits from STAB and costs moderately less energy. 
The more recent addition of Charm is an interesting option for Wobbuffet, but its horrible energy generation is discouraging. 
Great League3 / 5
Wobbuffet has two good things going for it: having the third best Stamina stat in the game (at a whopping 382), and having access to a good fast move: Counter. A disappointing maximum CP of only 1160 leaves Wobbuffet behind most competitors, even in Great League. The lack of additional moveset options including powerful STAB moves means Wobbuffet can't really threaten its opponents, but having incredible bulk allows Wobbuffet to win through wars of attrition and outlasting its opponent. 
Should this game go beyond Level 50, Wobbuffet's incredibly defensive stat distribution can allow it to make leaps in viability as it reaches closer to the Great League CP cap.
Ultra League0 / 5
Hi Wobbuffet. Bye Wobbuffet. 
Master League0 / 5
In days past in the main series, Wobbuffet was a contender in the strongest formats due to its unique combination of Shadow Tag + Encore. Its opponents could not flee while Wobbuffet locks them into one move. Those who attack Wobbuffet are swiftly taken care of by either Counter, Mirror Coat, or Destiny Bond. Those who don't attack Wobbuffet allow Wobbuffet to freely switch into a threatening set up sweeper. Wobbuffet could even use Safeguard to protect its teammates from any status moves used by the trapped Pokemon. ﻿
﻿
Anyways, that's just about it for main series competitive Wobbuffet lore. It's a shame it'll never replicate that kind of role here in Pokemon GO.

Great League	3 / 5
Wobbuffet has two good things going for it: having the third best Stamina stat in the game (at a whopping 382), and having access to a good fast move: Counter. A disappointing maximum CP of only 1160 leaves Wobbuffet behind most competitors, even in Great League. The lack of additional moveset options including powerful STAB moves means Wobbuffet can't really threaten its opponents, but having incredible bulk allows Wobbuffet to win through wars of attrition and outlasting its opponent. Should this game go beyond Level 50, Wobbuffet's incredibly defensive stat distribution can allow it to make leaps in viability as it reaches closer to the Great League CP cap.
Ultra League	0 / 5
Hi Wobbuffet. Bye Wobbuffet.
Master League	0 / 5
In days past in the main series, Wobbuffet was a contender in the strongest formats due to its unique combination of Shadow Tag + Encore. Its opponents could not flee while Wobbuffet locks them into one move. Those who attack Wobbuffet are swiftly taken care of by either Counter, Mirror Coat, or Destiny Bond. Those who don't attack Wobbuffet allow Wobbuffet to freely switch into a threatening set up sweeper. Wobbuffet could even use Safeguard to protect its teammates from any status moves used by the trapped Pokemon. Anyways, that's just about it for main series competitive Wobbuffet lore. It's a shame it'll never replicate that kind of role here in Pokemon GO.