Do stats actually get raised by Gym Badges?

Question

In Pokemon FireRed and Pokemon LeafGreen, you get badges for defeating Gym Leaders, just like in any other Pokemon game. However, upon receiving the badges, it sometimes tells you that a stat of all of your Pokemon has been raised. Supposedly, the Boulder Badge gives raises your Pokemon's Attack, the Thunder Badge raises your Pokemon's Speed, the Soul Badge raises your Pokemon's Defense, and the Volcano Badge raises your Pokemon's Special Attack and Special Defense.

Additionally, according to Bulbapedia, the respective gyms in the Johto and Hoenn regions also give your Pokemon the same benefits (1st badge increases Attack, 3rd badge increases Speed, etc). However, I don't believe this is mentioned in-game.

I'm curious as to if these badges actually do raise the stats of your Pokemon. If so, by what value?

Answer 1

The stats for a Pokémon are based on:

• The base stats
• The IV for a Pokémon (depends on the one you caught)
• The EVs gained while training a Pokémon (depends which types of Pokémon you battle)
• The nature of a Pokémon

The relevant formulas are:

and

for the first and second generation, and:

and

for the third and fourth generation.

As you can see, nowhere is there any mention of having a gym badge in these formulas.

The theory as to why the game tells you there is a stat boost that, in my opinion, holds the most ground, is that the EVs you get from battling the gym leader's Pokémon match the stat that they tell you gets raised.

Source for theory
Source for stats

Answer 2

The above answer is only true for link battles and generations 4 and following. In previous generations, this boost does exist and affects all in game battles. The boost is 12,5% in generations 1 and 2, 10% in generation 3.