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at level +2 affection, pokemon will gain x1.2 exp
at level +4 affection, a pokemon will be able to avoid 100% accuracy hits, endure ko's sometimes multiple times a turn, and have a chance to shake off a status condition
at level +5 affection gives a higher crit hit chance
level 2 is need to evolve eevee into sylveon
i suppose those are pretty good benefits, but frankly, i never really felt the need to take the time to do it, but thats just me