Does Guard Spec. affect accuracy

The Power of an attack directly correlates to how much damage you deal, because its presence in the damage formula is entirely multiplicative. So, an attack with 120 power will do twice as much damage as one that has 60 power. The same goes with your corresponding attack stat: a Pokemon with 100 Attack will do twice as much damage as one with 50 Attack when using the same attack on the same target.

STAB has operated consistently since Gen 1 so this applies to all of the games. It increases the Power of an attack by 50% if it matches one of your types. 60 becomes 90, for instance.

Technician increases the Base Power of an attack by 50% if its Power is 60 or less. So the most you get is boosting an attack at 60 power to 90. This occurs before STAB is calculated, so your Power would be 90 for STAB, boosting it to 135.

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