How do IVs affect a Pokemon's combat in Pokemon Go?

Just found out there are hidden Individual Values (Attack, Defense and Stamina) for a pokemon in Pokemon Go. How do these value affect the combat performance in gym?

Attack Value: A Vaporeon with a Water Gun has 6 attack points, does a higher attack value makes this Vaporeon's Water Gun more powerful so the Water Gun will get rid of more than 6 HP of the opponent's HP? Or does a higher attack value make this Vaporeon to response faster when you click the screen to attack or swipe to dodge?

Defense Value: Does a higher defense value gives more HP or simply better defense so a 6 point Water Gun attack can only get rid of half or less of the HP?

Stamina Value: Does a stamina value gives more HP or it makes the stamina bar to fill up quicker in gym battle?

• Stamina I can say for sure has an effect on a Pokemon's hp. That's the reason why for example you can have 2 Ratata with the same CP but different HP. – VanBuzzKill Aug 14 '16 at 3:29
• I forgot the source, but in the subreddit SilphRoad there once posted the formula of usage for such. – Dadan Aug 14 '16 at 13:52

Let me do a brief introduction to Individual Values.

Each type of pokemon has different base values for Attack, Defense and Stamina. However, each Pokemon is also randomly assigned a 0-15 bonus to each of them. These bonuses are called IV's (Individual Values). They represent genetic variance, in that some pokemon are just genetically superior to others.

Base stats are obtained from base Gen 6 stats:

BaseStamina = 2 * Hp
BaseAttack = 2 * ROUND(Atk0.5 SpA0.5 + Spe0.5)
BaseDefense = 2 * ROUND(Def0.5 SpD0.5 + Spe0.5)

Hp, Atk, Def, SpA, SpD, Spe are all the base values in Gen 6.

Then each value is obtained adding the base stat and the relative IV (with a common multiplier):

HP = (BaseStamina + IVStamina) * Multiplier
Attack = (BaseAttack + IVAttack) * Multiplier
Defense = (BaseDefense + IVDefense) * Multiplier

This means that IVs only grant you a bonus for each stats.

Does a higher attack value makes Water Gun more powerful?
Definitely yes. Stats in Pokemon Go are like stats in the classic series, a higher Attack deals higher damage.

Does a higher attack value make Pokemon to response faster?
I don't think so, moveset has the biggest impact upon DPS (damage per second) and it has nothing to do with IVs.

Does a higher Defense value gives more HP or simply better defense?
As you can see from the formulas above, HP depends on `BaseStamina + IVStamina`. So a higher Defense will give your Pokemon a better defense when attacked, like in the classic series.

Does a Stamina value gives more HP or it makes the Stamina bar to fill up quicker in gym battle? Same answer as the previous question, HP is affected by `BaseStamina + IVStamina`.
I can't tell you anything about the Stamina bar, at the moment.