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What does "Battles Won" mean!?
I mean the line under some pokemon in gyms.
-Thank you in advance.
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Answers
For each Battle Won, it means that your Pokemon was responsible for them losing the fight. That means their final attacking Pokemon was defeated by your guy.
And I believe this is a permanent stat stored for each of your Pokemon, so wins collected from previous gyms will be added to your total for new gyms as well. It seems the number only goes up and will not ever decrease. :)