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The only other scenario I can think of is that you're running a super-expensive umbral build, which needs points only Steel Charge can provide.
i never run CP since i can alredy 1 shoot everything around level 100
For team play and very long runs it should be used as in a lot of cases it helps A LOT when team is organized and with a proper reason, like fighting something with armor.
Talking about Grineer Arbitrations for example, also and it can be directly seen in your ESO score as 4 CP's beat any other combo.
Answer to it is simple, armor scaling is exponential and if you are looking at the enemy who has 3000 armor - reducing 30% is not giving you 30% more damage, it is only gonna reduce enemy's damage reduction by ~4%, from 91% to 87-ish percent.
So yeah, pretty good for organized high level play, meh for random play and overshadowed by Steel Charge's extra capacity which lets you make AN INSANE Umbral builds that negate any need for CP in a random mission.
Even after the buff, physique is terrible. Use Rejuvination instead.
i use CP on all frames.
alt auras are :
growing power : nearly useless when killing mobs offscreen (and one shotting all mobs with a non status chance mean i don't trigger this often and i won't bother checking my buff every single kill i make and wait for the buff to cast an ability) so i don't equip that
energy siphon : completely useless with zenurik
power donation on speed nova and dead eye on chroma (i always run chroma with a sarpa) though
you math is wrong.
let's say you do 10000 dmg on an enemy that have 3000 armor (equivalent to a bailliff 54 or a trooper 112).
Without CP :
foe has (3000 / 3000+300 ) 90.91% dmg reduction. You do (1-0.9091 * 10000) 909 dmg
With one CP :
foe has (1-0.3 * 3000) 2100 armor that is (2100 / 2100+300) 87.5% dmg reduction. You do (1-0.875 * 10000) 1250 dmg.
With two CP :
foe has (1-0.6 *3000) 1200 armor that is (1200 / 1200+300) 80% dmg reduction. You do (1-0.8 * 10000) 2000 dmg.
That is an increase of 37.5% (1250-909 / 909) with a single CP, +120% (2000-909 / 909) with two CP and +450% with three CP.
From the wiki : "This limit is 3/7 or ≈+42.86% for one CP, 3/2 or +150% for two CPs and 9 or +900% for three CPs."
you should not think about the dmg reduction (90.91 - 87.5 = 3.81%) but rather on the damage taken (0.125 / 0.0901 = 37.5%).
Maybe with Saryn you'd use Growing Power or Energy Siphon instead because your 1 will strip the armor of enemies anyway.
Oh yeah and Power Donation if you play Speed Nova.
It's true that Corrosive Projection does not really do anything against enemies with armor, but those enemies are also completely irrelevant. The only enemies that are actually relevant in higher levels are the ones with armor thanks to how it scales on higher levels.
(Also 2/3 is not really true, Corrupted enemies exist too)
On 2 CP's we are already looking better.
But Steel Charge beats it for melee, and if you have a a buffer frame it beats it too because with Steel Charge you can actually make use of Umbral Set and gain more than with regular loadout.
So my math is right, you just pointed out a different PoV on it, 350/10000 is those ~4% I said.
Thing is, in regular random play we will almost never meet enemies with such armor, and in team play for long runs you either use 4 CP's or you rip.
strange thing is, when it is augmented armor sortie my team mates always like to avoid CP.
With Steel charge (same 10000 dmg and 3000 armor) you'll do 1442 dmg. With one CP instead you'll do 1250 dmg.
So yes, steel charge is 15.3% better in this case, but it only works when attacking with melee (and +15%, i wouldn't say that it "rapes" CP).
CP works for ALL sources of damage and scales way better, but only versus armored foes (and i dare say those are the only tough mobs in the game).
Your math/PoV is wrong, with a single CP you're doing +37.5% more damage, not 4%. You calculated 350 / 10000. That's just a meaningless calculation.
Running with a CP, you do 1250 damage. You were previously doing 909 without CP. So you are doing (1250-909) +341 flat damage. That is a (341/909) 37.5% increase. In other words, you are doing 1250 with and 909 without, you get (1250/909) 137.5% of your damage when running a single CP.
Compare Mesa's shatter shield vs all other damage reduction abilities from any other frame.
Mesa's SS is -95%, any other ability is -90% (desolate hands, splinter storm, shield of shadows, warding halo, null star, etc). Mesa is actually twice (+100%) as tough as any other frame (except mirage that also has -95% iirc) when just looking at those defensive skills, not just 5%.
Mesa takes 5%, other frames take 10%. Mesa takes half of the damage compared to the others. That is the exact same reasoning/calculation but it's easier to understand and visualize.