Do gym badges really raise your Pokemons stats?

Question

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?

Answer 1

Badges DO affect in-battle stats. The "badge effect" gets calculated and temporarily added when you enter a battle, so it doesn't affect permanently your stats; nonetheless it does exist.
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 is 1/8, i.e badge-boosted stats are 9/8 normal stats.

Answer 2

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

1. At the gyms where a stat increase, you will have gained EVs in that stat (therefore slightly increased that stat). For example at Vermilion Gym in R/B/Y you fight Voltorb, Pikachu and Raichu who all give EVs in Speed. This doesn't match up to all gyms though.
2. It's possible the games hinder your real stats early on. So when you get hit, your defense is slightly lower than the actual number suggests.

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).

Comments

Interesting theories though... it's just always sounded a bit fishy to me when they said that they raise a certain stat of  your Pokemon.