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I know that same-type-attack-bonus (STAB) increases the damage of same type moves, but does it increase the amount of energy gained(to fill up the charge bar) when using quick moves of the same type?

Some websites seem to suggest so (rankedboost etc.)?

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According to this site, when either attacking or training a gym,

Energy gained per hit points loss -2 HP = +1 energy

Due to the fact that there is a Same-Type Attack Bonus mechanic in the game that increases damage, one can infer that the higher damage dealt by STAB moves leads to higher energy gains.

EDIT:

Thanks to Eikre's explanation in the comments, my previous answer actually applies to bonus energy being gained from taking extra damage due to the STAB bonus.

Therefore, there does not seem to be a bonus in energy gain for inflicting more damage with STAB moves. In addition, you can see exactly how much energy you would gain for any given attack here.

  • @downvoter, care to explain something I missed? – Vemonus Sep 8 '16 at 15:36
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    Pokemon gain energy from losing their own HP, not from inflicting HP damage. Though your answer is, in a way, technically correct, it's also misleading. – Eikre Sep 8 '16 at 15:37
  • @Eikre Oh, seriously? Do you have a reference? I'll update my answer if that's true. – Vemonus Sep 8 '16 at 15:39
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    It's an implication observed in your reference, if you would care to read it. It is also more explicitly described here. – Eikre Sep 8 '16 at 15:43
  • Ah okay, I misread my own reference then. I guess this answer needs an overhaul so allow me to fix it. Thanks for pointing this out. – Vemonus Sep 8 '16 at 15:44

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