Are offensive and defensive EV's balanced?

Question

When dividing EV's, many powerful Pokemon max out their respective offense stat, then HP for bulk, or speed for.... speed.
BUT, with the way damage and stats are calculated, is it worth it to invest in defenses assuming that is what your Pokemon is for?

What my question really boils down to is this:
If a Pokemon's Special attack stat is maxed out. 31 IV's, nature and 252 EV's.
And my Pokemon's Special Defense stat is the same way.
Would their attack do more, the same, or less damage, if the two stats were at their minimum, i.e. both at 0 IV's, bad nature and 0 EV's.

Comments

I'm pretty sure it does - I have nothing to prove it though.

Answer 1

No, they aren't balanced due to the way damage and stats are calculated. The lower investments in offensive and defensive EVs/stats involve more damage. If you want to learn more about this, take...

Professor Scraf's Damage Course

BaseDamage = (2 × Level) ÷ 5 + 2) BasePower ([Sp]Atk ÷ [Sp]Def) ÷ 50 + 2
This mumbo-jumbo is the formula of damage calculation in the games as of Black and White.

Let's take two Pokemon battling, like Typhlosion and Alazakam. Both are Level 100, no status conditions, no weather, no crits.

Typhlosion has its maximum SpAtk stat with a beneficial nature of 348, and Alakazam has its maximum SpDef stat of 317 in Gen6. Typhlosion uses a non Fighting-, Bug-, Fire-, Dark-, Ghost- , or Psychic-Typed Move with a Base Power of 90. Let's plug this all in:

BaseDamage = (2 x 100 [level] ÷ 5 + 2) x 90 x (348 ÷ 317) ÷ 50 + 2

Now, we have all solid numbers. Yay! Let's finish this calculation:

BaseDamage = (42) x 90 x (1.0977917981072555205047318611987) ÷ 50 + 2
BaseDamage = (3780) x (1.0977917981072555205047318611987) ÷ 50 + 2
BaseDamage = (3780) x (1.0977917981072555205047318611987) ÷ 50 + 2
BaseDamage = (4149.6529968454258675078864353311) ÷ 50 + 2
BaseDamage = (4149.6529968454258675078864353311) ÷ 50 + 2
BaseDamage = (82.993059936908517350157728706622) + 2
BaseDamage = 84.993059936908517350157728706622 (84)

And the Smogon calculator gives us... 71-84 damage.

Applying in the Random factor formula *D' = (D (100-R)) ÷ 100** where D' is the new damage, R is a number that is between or is equal to 0 and 15 and D is the BaseDamage, we have a minimum damage of 71.4 (71) when R is 15.

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Now let's try minimum investment of 200 SpAtk for Typhlosion and 175 SpDef for Alakazam. Same move used.

BaseDamage = (2 x 100 ÷ 5 + 2) x 90 x (200 ÷ 175) ÷ 50 + 2
BaseDamage = (200 ÷ 5 + 2) x 90 x (1.1428571428571428571428571428571) ÷ 50 + 2
BaseDamage = (42) x 90 x (1.1428571428571428571428571428571) ÷ 50 + 2
BaseDamage = (3780) x (1.1428571428571428571428571428571) ÷ 50 + 2
BaseDamage = (4320) ÷ 50 + 2
BaseDamage = (86.4) + 2
BaseDamage = 88.4 (88)

And the Smogon calculator gives us... 74-88 damage

Applying the Random Damage Formula with R = 15, we have a minimum of 74.8 (74) damage.

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So, since the formula is ([Sp]Atk ÷ [Sp]Def) and through the way stats are derived from BSTs, lower investments result in more damage. Everything explained here.

Comments

Thank you professor. lol

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I DUWIKE MUMBA-JUMBA ;~;

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I kinda wanna calculate the max amount of damage that can be dealt through hax and stuff

Like

Shuckle with Power Swap/Switch (whatever it's called) using a powerful move on a Pokemon with an 8x weakness with Forest's Curse

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Well database can sort Pokemon by stat. Lets see what the lowest defensive Pokemon is with an 8x weakness and go from there.

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Well Shuckle learns no fire, ice or flying type moves. So we need a pokemon that is already quad weak to bug or poison. Poison only has two advantages, grass and fairy, so we cant use that because grass cant be added, so we need to find something that is quad weak to bug and not already part grass. Bug has advantages against grass, dark and psychic, and since we can't have something with grass, we need a dark-psychic type. This did not exist until Generation six with the addition of the famous contrary superpower "will get you through story mode but actually sucks competitively" inkay and malamar.

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But first, lets look at the old method
It used rollout's final blow on a combee, a pokemon with base defense 11 lower than inkay's. The base power of the new move used must be greater than the old one. Rollout's last use had 480 power. With a 4x weakness that gave it astounding 1920 power. I'm ignoring STAB because both moves have it, and I don't want to do unnecessary math, no matter how simple. Shuckle's strongest bug type move is bug bite, a 60 power move. Wait what? I guess that's it. At an 8x weakness, that's an ironic 480, the base power of Shuckle's rollout with normal damage. Ugh. So it looks like with the addition of forest's curse, the highest possible damage has yet to change. Unless however, there is a way to change one of shuckle's moves to another type. Although, like I said, there is only one type combo that actually has an 8x weakness right now, which is inkay after forest's curse getting hit by bug. Now the problem with this is although there are new abilities and moves for changing move type in Gen 6, to the best of my knowledge, no move that is not a bug-type move can become one as of now. So it appears that poor Combee will be famous for being the best punching bag in all of the pokemon world.

But wait. What is this? If we sort pokemon by attack power, it appears that the second highest attack stat is mega heracross, a pokemon capable of using the move mega horn! A 120 power bug type move. With 8x weakness that becomes 960. Unfortunately, that is only double max rollout, still half of the power we needed to match shuckle, not to mention mega heracross is weaker than power-swapped shuckle anyway. Well it was worth looking into, and due to a comment limit, this one comment has gotten way too long. Although this was fun to look into and explain, unfortunately the results are unchanged. The dual-helping-hand-attack-maxed-ev-trained-iv-bred-specific-nature shuckle using the fifth rollout and getting a critical hit on a defense-minimized-zero-ev's-iv-bred-specific-nature combee still remains unbeatable. Except sonic boom. Nothing does more damage than sonic boom.

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Jesus Christ. You did your research.