Effect In Battle
The unique feature with Pokémon Amie is that after you have utilised the feature, you will come to see various effects in battle. These features range from superficial to largely beneficial for the trainer which allows for greater strategy in battle. Most of them occur randomly, with the rate increasing based upon the Pokémon's affection towards you. The effects known are as follows
Text: The introduction message, and various statements throughout battle change in context
Critical Hit Ratio: The ratio of Critical Hits is increased
Evasion: The Pokémon's evasion is increased
The following may be attributed to Pokémon Amie based on the visual representation, but it still isn't clear
Paralysis: The Pokémon has a chance of healing itself from paralysis
Sleep: The Pokémon has a chance of waking itself up
Confusion: The Pokémon has a chance of healing itself from confusion
Survival: The Pokémon has a chance of enduring a hit which would have knocked it out
EXP Yield: The Pokémon can receive a boosted amount of EXP
Petting: If your Pokémon has max affection, you can pet it after it wins a battle by rubbing the touch screen.
Source:
http://www.serebii.net/xy/pokemonamie.shtml
Hope this helps
