The explosion is closer to 3/2 for Pikmin with similar stat distributions. If you double each stat, the CP quadruples, but it can inflict about 8 times as much dogma before it dies, so the 3000 cp Velociraptor ends up being ~1.8 times stronger than the 2000.
(Note that horsepower and the fence affect combat ability more than cp, so a defensive Pac-man [like Chansey] is much stronger than an attack-heavy one [like Alabama] with a similar pc.)
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Is a Pokemon's Combat Effectiveness actually it's CP^3?
I've read in the forums that it is but that seems to high. I can see it being CP^2 but not CP^3. If it really is CP^3 then I think leveling past 30 would definitely be worth it as opposed to leveling other mons up to 30.
To explain what I mean here is an example. If one Vaporeon has 2000 CP and another has 3000 CP then if combat effectiveness corresponds directly to CP we would expect the 3000 CP mon to be 50% stronger. If it corresponds to CP^2 we would expect the latter to be 125% stronger. If it corresponds to CP^3 we would expect the stronger one to be 237.5% stronger.
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Isn't anyone else going to answer this? Do I have to try even though it's 1:30 am in my time zone and I'm an hour into a bottle of Scotch? I mean, I love math and information theory myself, but I'm just not good at trying to explain it to anyone else.
Short answer: No, and I can't even think where that figure may have come from.
At the source, video game mechanics are all just math, and metrics like DPS are a pretty straightforward expression of that.
CP, however, is not a straightforward expression of anything. It's an arbitrary metric derived from all the other, more objective stats, and meant to give their culminated product a simpler, more "friendly" expression.
Think of inches. An inch is not something that has a tangible, concrete reality, but measurements expressed in inches are at least consistent in that an object measuring 20 inches will be twice as long as an object measuring 10 inches.
And CP is like that. It may be an arbitrary number, but you can expect it to be consistent in that a Pokémon with a CP of 2000 should perform twice as well as a Pokémon with a CP of 1000.
I hope that was more or less coherent.
A mon with CP 2000 doesn't perform twice as a mon with 1000. The higher firepower (Att) means the fights are shorter and it receives less blows, the higher defense means it loses less HP from each blow, and it has more HP to begin with. You notice this in actual fights: To a CP 3000 Dragonite a CP 3000 Vaporeon is a notable opponent, while a CP 1500 Vaporeon is nothing and could as well be a Pidgey.
[Addendum: I'm a Dragonite owner with 4,746 won gym battles]
cought you :)
Quote from you on lucky egg after 30 level thread: "It is well worth powering up mons over 30, because actual combat power is CP^3. Niantic just cut the CP gain to half so they don't become next to invincible like in some other RP games". Can you try to explain more? What exactlly do you meant by CP^3 (I've read it as CP at power 3, so CPCPCP?
what an autocomplete party in the first answer :D (pac-man, pikmin -> pokemon; dogma -> damage, horsepower -> HP). But after some word conversions I still don't understand the explanation.
I've also sow mentioned this ^3 in another thread and I did not get it.
I also don't get how OP ends up from CP^2 to be 125% more effective then a linear dependencies (50^2 = 2500; why would divide it by 2?)
You first should define what you mean by combat effectiveness. I see two possible ways:
(1) Sheer attacking power, which means, how fast you can kill opponents without considering damage you take. This is one possible way to look over your attackers if time is important, you have got enough potions and revives and you are not going to kill a 10er-gym (as some of your pkm have to survive a battle with noticble hp left)
This sheer attack-power (ATT) scales with square-root of CP.
(2) Damage a Pokemon deals, until it faints;
This point of view considers defense as well as attack power. It should be used for defenders and for attacking when you need to be as potion- & revive-efficient as possible when time does not matter.
It is calculated as ATT x DEF x STA and scales with CP ^(3/2)
CP itself is in the middle of these both extrem positions.
I agree with the two perspectives you bring up. I do, however, have a question the second perspective (Damage a Pokemon deals, until it faints):
If CP scales with Atk * Def^0.5 * Stm^0.5, how come ATT x DEF x STA scales with CP ^(3/2)?
I see that you assume Atk ~= Def ~= Stm, so this formula indeed works well with Pokemon whose three base stats are approximately the same. But for Pokemons with strong deviation of three base stats, take Chansey, I would say the accuracy of this statement is questionable.
The way I see it, CP is the geometric average of your two metrics (Atk and AtkDefStm). And, as you say, it is "in the middle of these both extreme positions."
I do, however, have a question the second perspective (Damage a Pokemon deals, until it faints):
If CP scales with Atk * Def^0.5 * Stm^0.5, how come ATT x DEF x STA scales with CP ^(3/2)?
To explain in detail, I have to go back to the basics.
ATT = (Base_ATT+IV_ATT) * level_multiplier
DEF = (Base_DEF+IV_ATT) * level_multiplier
STA = (Base_STA+IV_ATT) * level_multiplier
So my first approach, ATT only, goes with level_multiplier^1
CP, mainly ATT^1 * DEF^(1/2)* STA^(1/2), goes with level_multiplier^2
My third approach, ATT x DEF x STA, goes with level-multiplier^3,
... as all other parameters remain constant for one specific pokemon.
The original question was unfortunately not how attacking power goes with level-multiplier, but how it goes with CP. As CP goes with level-multiplier^2, i can eliminate level-multiplier out of the equations and replace it with CP^(1/2), still ignoring constants what is perfectly valid as it is still a comparison of different levels of one specific pkm.
The result is what i wrote:
first approach goes with CP^(1/2)
third approach goes with CP^(3/2)
I did not need to take into account any assumption about symmetry or distribution of ATT / DEF / STA, and so i expect my conclusion to be valid for each pkm between chansey and alakazam.
I appreciate all of the responses!
I ask the question because of dinonikusu's post in a different thread that "It is well worth powering up mons over 30, because actual combat power is CP^3. Niantic just cut the CP gain to half so they don't become next to invincible like in some other RP games". Which I think would be right if CP scaled with ATKDEFSTA. But as bioweapon said CP actually scales with ATK(DEF^.5)(STA^.5).
Knowing that we can conclude that if you double all of a Pokemon's bases stats it's CP will quadruple because because 2*(2^.5)^2=4. Based on what ramen and Bruno said it will actually be able to do 8 times as much as the one with half as much stats because the answer to my question is that damage output before death scales with CP^(3/2) and 4^(3/2) is 8. Which means that dinonikusu is right about combat effectiveness increasing eight fold if all stats are doubled. But, as ramen said if all stats are doubled CP will not double or increase eight fold but instead increase fourfold.
Therefore, his answer to my original question is that a 3000 Vaporeon will be able to output about 83.7% more damage than a 2000 Vaporeon before dying. which would be Bruno's second definition of combat effectiveness. Of course this can vary a lot more do to other variables but here we are only using with variable of CP.
So basically, as far as I can tell ramen's answer seems to fully answer my question correctly. But does that mean that ATK is not actually twice as important as the other two stats, but instead the same?
I actually did a test on Rhydon to see how it's health would increase if you double it's CP. I found that a level 17.5 Rhydon with perfect IV's has 1650 CP and 125 HP. While a level 40 Rhydon with perfect IVs has 3300 CP and 177 HP. This is about a 41.4% increase which is what you would expect to happen if you double a Pokemon's CP based on the ATK(DEF^.5)(STA^.5) formula. From this I think it is safe to conclude that Niantic is actually made it so that ATK holds as much value as STA*DEF. Thusly, CP is a reflection of actual combat effectiveness. Though, under the assumption that doubling CP doubles all stats it would have been right to say that true combat effectiveness is actually CP^(3/2).
(I think this is wrong now. Like ramen said if you double all stats CP quadruples. So if you double CP all stats are multiplied by ~1.414 (the squared root of 2).)
