Do gym badges really raise your Pokemons stats?

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Like the question says, do gym badges really raise your Pokemons stats when they say?I mostly remember this only occurring in the older games, but in my Emerald for example, the Petalburg gym leader (your father) gives you the Balance Badge after defeating him.He explains how he’s proud of you blah blah blah, and says that the badge apparently raises the Defense of your Pokemon.

Do those badges really raise your Pokemons stats?(And of course I don’t mean raise physically, but maybe in battles your Pokemon recieves a boost?

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BadgesDOaffect in-battle stats. The “badge effect” gets calculated andtemporarilyadded when you enter a battle, so it doesn’t affect permanently your stats; nonethelessitdoesexist.If you are interested the ASM code that checks badge-flags and edit temp stats accordingly is at 0xEE19-0xEE57 (0F:6E19-6E57) in a Pokemon Blue (U) cartridge.The “badge effect” coefficient is1/8, i.e badge-boosted stats are 9/8 normal stats.

There isn’t anything in the damage formula that takes gym badges into account so I don’t think that a gym badgeactuallyincreases stats in any way. There are two theories I know of:

All mentions of this have been removed from Diamond/Pearl onwards, so now the gym badges do not directly affect stats (aside from any EVs you might gain).