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HP vs Def IV's on imbalanced base stats

Am I correct in thinking that the HP IV on a Cloyster matters a lot more than its Defense IV? If the 0-15 values are added to the base stat value of the pokemon, the difference between 323 and 337 should make a lot less difference for tankiness than the difference between 100 and 115, because when they're multiplied together the percentage difference is what really matters.

For math people: if tankiness is HP*Def, the partial derivative w.r.t HP is Def, and vice versa, so each point in a stat is worth more the higher your other stat is (with indifference only when the two stats are equal).

Other imbalanced pokemon for whom this would matter would be Chansey/Wigglytuff/Snorlax (Def more valuable), Onix (HP more valuable), and to a lesser extent Alakazam/Magneton (HP). Am I missing any?

I partially wonder in order to feel better about the only Chansey I have, caught at 15/11/0 atk/def/hp, which I haven't powered up at all but which might not be so bad after all.

Asked by PlentiCool8 years 3 months ago

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You're correct in that IVs make a bigger difference on smaller stats, since it's the relative increase that the IV gives which matters.

On Chansey the biggest boost is going to be having 15 attack IV, since it's a 1.25x increase to it's base attack and therefore a 1.25x increase in max CP compared to a 0 attack IV Chansey.

15 stamina is only a 1.03x increase to base stamina and therefore only a (1.03^0.5) = 1.01488916x (or 1.5%) increase in max CP, so even though your Chansey only has 26/45 IVs, it's going to have about 97.5% max CP compared to a perfect one, because it's got the best possible IV distribution despite it's total IVs being pretty average.

The CP formula does a decent job at combining all 3 stats for how effective something is going to be. Pure "tankiness" is only relevant if you're going for a timeout with Chansey/Blissey. Otherwise, you need to factor in how much damage you're putting out.

One thing you can definitively conclude from the CP formula is that the proportional increase in CP per IV point in Attack, Defense, and HP is 1/BaseAttack, 1/(2BaseDefense), 1/(2BaseStamina), respectively.

So at least in terms of CP, your Chansey having a low StaminaIV is pretty negligible since it has such a high BaseStamina.

One thing you can definitively conclude from the CP formula is that the proportional increase in CP per IV point in Attack, Defense, and HP is 1/BaseAttack, 1/(2BaseDefense), 1/(2BaseStamina), respectively.

Not 2x base stamina / def, it's the square of it, since stamina and def are square rooted in the CP formula not halved. ^0.5 and x0.5 aren't the same

^2 = power of 2 i.e. squared
^0.5 = power of 1/2 therefore square root.

CP(A,D,S)=A\sqrt{DS}

So using a linear approximation,

dCP/dS (ie, how much CP changes based on a small change in Stamina) is A\sqrt{D}/(2\sqrt(S)) = CP/(2S) dS.

How nice is to see "analytical math" (this is a mot a mot translation from the name in my mother language, might be calculus in eng.?) applied to a favorite game :). Thanks! More than 15 years since I studied it, right now I'm just able to understand while reading, not able to apply it on my own :)

Thanks to you and androgynous for tying this question to how CP does capture the importance of balancing stats. I just emphasize HP vs Def because they do literally the same thing (barring potion usage), which is keep you alive longer, so a 15/10/15 wigglytuff or chansey will perform exactly the same as a 15/15/0 one (hp ~= 3*def).

Unless I'm missing your point, I don't think it's true that a higher defense IV will "keep you alive longer" - I've been looking at spreadsheet matchups and very often the defense IV makes no difference (see my post below) whereas the stamina IV always makes a difference - which I grant will only be relevant in the tiny percent of fights that go the distance...

Everyone else has answered better than I can but I want to say something.

All of this is the reason that I don't like people giving IV as a %, as you can miss a large part of the equation.

Alakazam as an example, with 33% IV can have a massively different CP at any given level depending on the distribution of the %. If it makes it 15 to Stamina, it is going to be a huge difference in CP compared to if it was 15 to attack. At level 30, it could be around a 10% difference in HP, or more - and that can be the difference between a win and a loss in a fight.

I have a Snorlax that has around 60% IV compared to a 70% IV...but the 60% one has max attack IV (15), and the 70+% IV has 0 to attack. When at the same level, the 60% one has a lot more CP than the 70% one. There are more examples, with many mentioned in the OP.

It is worth considering when deciding which to evolve or power up.

Just wanted to add my 2 stardust worth...

Been thinking a lot about this recently (in the context of prestigers), but I suspect HP may be more relevant in actual play.
Here's why: the Damage formula considers the Attack/Defense as a modifier, but then takes the floor() of the final result. Mathematically this results in many cases where the damage taken is identical over the entire range of defense IV's (0-15 = same damage taken).
However, there is always a linear increase in the total HP as the stamina IV increases, roughly 9-10 HP at level 30.
Sure, a 10 HP increase to a Chancey is a tiny percent increase, but could spell the difference between timing out or not if it will require a couple of extra attacks. And to a glass canon fighter, 10 HP is likely very useful, especially if the damage it takes is the same regardless of 0 DEF or 15 DEF.
In any individual matchup, there may be break points where a 1-pt increase in Defense IV results in 1-pt less damage, that's clearly the "sweet spot" if it can be determined in advance...

I agree that making them into whole numbers throws off the nice smooth concept I was portraying. However, since we can't know which point of DEF will cause that 1-less dmg/hit (a huge effective HP difference in a chansey/wigglytuff fight), we have to think about it AS IF it was smoothly distributed, but in probabilistic terms. Instead of actually making attackers deal a little bit less damage, this is interpreted as the % chance that each point of def will cause 1 less damage. Then the rule of thumb still holds true that DEF is worth more on low-DEF mons: the chance that floor(ATK/50) is different from floor(ATK/51) is higher than floor(ATK/150) vs floor(ATK/151)--regardless of what ATK is.

Really, though, they should just make fractional damage a thing, because it shouldn't be a huge-difference-or-no-difference situation.

You're absolutely right. This is even more striking with a Chansey, who's stamina IV can be ignored entirely. If you have a chansey with 15/11/0, I'd ignore that 0 and just consider the 15/11, which is 26 out of 30 (87%).

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