CA Buff brake down so you can understand The CA Buff

WHY is your Counter Attack level 36?

SHORT ANSWER:
I think the buff is most useful for me given my leveling strategy and the doubler buff that I use. I am sometimes have to buy Counter Attack 72 so let me know if you have it! See below for a more detailed explanation....


HOW DOES COUNTER ATTACK WORK?

Uses 0.25% extra stamina (per point) to add 0.25% to both attack and damage. (Both values are rounded up, vs. creature only)

WHY WOULD I USE IT?
You would use CA if you needed to increase your damage just a bit to go from 2 hits to 1 hit, or possibly from 3 hits to 2 hits...

WHAT ARE THE BEST VALUES OF COUNTER Attack

It depends

Lets assume you are using Doubler 500. That is 11X stamina for 11X EXP/gold.

Since stamina always rounds up with Counterattack. 11.2 stamina, 11.5 stamina and 11.99 stamina would all round up to 12 stamina used.

If you have any value up to 36 in CA (using doubler 11X) you will be using 12 stamina because:

X * (1 + P * 0.0025) = S
where:
X is the value of the doubler you are using
P is the number of points in CA
S = amount of stamina used.

11 * (1 + 36 * 0.0025) = 11.99 which will round up to 12.

36 points in counter attack will give you:
36 * .0025 = 9% more attack and damage.

Any value under 36 gives you less than a 9% increase in damage for the same 12 stamina. Therefore you maximize the damage increase per increase in stamina by choosing 36.

If u had 37-72 points in Counter Attack then you will use 13 stamina since:

11 * (1 + 72 * .0025) = 12.98 which will round up to 13.

The same logic applies. It makes sense to use CA 72 and get the maximum increase in damage for the increase in stamina cost. The following values maximize damage for the stamina used.

EDIT FOR Doubler 750
level 25 uses 17 stamina and gets you 6.25% more damage and attack.
level 50 uses 18 stamina and gets you 12.5% more damage and attack.
level 75 uses 19 stamina and gets you 18.75% more damage and attack.
level 100 uses 20 stamina and gets you 25% more damage and attack.
level 125 uses 21 stamina and gets you 31.25% more damage and attack.
level 150 uses 22 stamina and gets you 37.5% more damage and attack.
level 175 uses 23 stamina and gets you 43.75% more damage and attack.
EDIT ENDS

For doubler500

level 36 uses 12 stamina and gets you 9% more damage and attack.
level 72 uses 13 stamina and gets you 18% more damage and attack.
level 109 uses 14 stamina and gets you 27.25% more damage and attack.
level 145 uses 15 stamina and gets you 36.25% more damage and attack.
You wont max damage but:
level 175 uses 16 stamina and gets you 43.75% more damage and attack.


CAN YOU SHOW ME THE MATH?

If you are using different doubler values then the optimal Counter Attack values exist.

You can use:
X * (1 + P * 0.0025) = S and round down to solve for yourself

X is the doubling power (doubler 450 X = 10, Doubler 4X, then X=4, etc)
P = the number of points
S = stamina u wish to use. (For doubler 10X u would use 11, 12, 13 for values. For150 you would use S values = 5, 6 or 7)

Rearrange the equation to solve for P.

P = (S / X - 1) / 0.0025 and ALWAYS round down

In the above example to maximize points per stamina use by substitution. I use Doubler X11, and need just a little more damage to 1 hit. So if I only want my stamina cost to go to 12 I solve as follows:

P = (12/11 - 1) / 0.0025
P = (1.090909 - 1) / 0.0025
P = .090909 / 0.0025
P = 36.36
ROUND DOWN
P = 36.

For those who have not reached grade 9 math or who have otherwise forgotten or ignored their math education, here is the chart for doubler 4X and 10X which are the most likely doubers that will be used.

For DOUBLER 10X

40 points uses 11 stamina and gets you 10% more damage and attack
80 points uses 12 stamina and gets you 20% more damage and attack
120 points uses 13 stamina and gets you 30% more damage and attack
160 points uses 14 stamina and gets you 40% more damage and attack
You wont max damage but:
175 points uses 15 stamina and gets you 43.75% more damage and attack

For Doubler 4X
100 points uses 5 stamina and gets you 25% more damage.
You wont max damage but:
175 points uses 6 stamina and gets you 43.75% more damage and attack


WHAT IS THE BEST STRATEGY?
It makes sense to use the lowest power counter attack as possible to get the necessary improvement. Since the goal is to 1 hit (or go from 3 hit to 2 hit) and use as little stamina as possible then there is an optimal strategy at different levels and this will usually mean that lower counter attack values are better. If you are already 1 hitting then counter attack will hurt you since you will get no benefit and be using more stamina. If you can get from 2 hits to 1 hit using counter attack 36 that will save you one round of combat for every kill. If 36 wont do it but 72 will then use CA72. But if 36 is good enough then any value over 36 is a mistake.

Someone else using counter attack 175 when CA 36 would have done... They would be getting the same benefit of 1 hitting but would be using 16 stamina instead of 12 per kill. That means that you save 4 stamina per kill using CA36 compared to CA175. Since you are killing 1000s of creatures, that 4 stamina per kill will really add up.


HOW DOES COUNTERATTACK COMPARE TO WITHER AND OTHER 1 HIT STRATEGIES?

Compare Counter Attack to your chance of 1 hitting.
IF you are already 1 hitting 100% of the time, you do not want this buff. It will just cost you stamina.
IF this buff can not get you 1 hits then you do not want this buff. It will just cost you stamina.
IF you are sometimes 1 hitting then the value of counter attack is diminished and it is worse the higher the level of CA you use.
IF it always gets you from 2 hits to 1 hit you may want the buff but it still depends on stamina cost and your max stamina.

There are many ways to 1 hit a 2 hit zone. Deathwish, Wither, PS, CH, or maybe ignite, blood thirst, assist or shatter armor etc etc.

Lets compare wither350 potion and use Doubler X10 for arguments sake:
Wither gets you 70% 1 hit kills so:
7 times out of 10 you use 10 stamina and 3 times out of 10 you use 20 stamina.
That is a total of 130 stamina for 10 kills or an average of 13 stamina per kill.

If you look at the doubler 10X chart above you will notice that that is the same as using CA120 and 1 hitting all the way. As such, any value of CA over 120 would be worse in terms of stamina use and any value under 120 would be better in terms of stamina use if you can get 1 hit kills. If you need CA 175 to get 1 hit kills you will be 1 hitting the entire way BUT you will be using 160 stamina per 10 kills. That means that someone using Wither 350 is leveling more efficiently by a value of 3 stamina per kill (1000 kills X 3 = 3000 stamina.... value that as you will).

Using both Wither 350 and CA together is either a waste of a Wither potion or a waste of stamina. If CA gets you 1 hits then why use a wither potion? That said, wasting a wither potion is not the worst mistake you can make. If a Wither potion gets you 1 hits, then why spend more stamina with counterattack? That is a terrible mistake.


HOW DO I KNOW WHAT IS BEST?

A rough guide would be to determine you chances of 1 hitting using various strategies.

Wither 350 gets you 70% 1 hits
Wither 175 gets you 35% 1 hits
Death Wish 175 gets you 5.25% 1 hits
(they do not add! Wither 350 + DW 175 is not 75.25% chance of 1 hitting it is 71.575% 1 hitting)

Regardless, 75-80% 1 hitting can probably be attained without using CA if you use all the best potions and buffs.

K * S + (1-K) * 2S

Where K is the chance of 1 hitting as a decimal and S is the stamina cost per combat round)

vs

K2 * S2


Where K2 is the percent of times you will 1 hit and this value should = 1
and S2 is the Stamina cost using counter attack

If Equation 1 is less than equation 2, do not use CA.
If Equation 2 is less then eq 1 then use CA

In other do not use CA if:
K * S + (1-K) * 2S < K2 * S2

But use CA if
K * S + (1-K) * 2S > K2 * S2

and if
K * S + (1-K) * 2S = K2 * S2

Then it doesn’t really matter (or it matters on which buffs are available or cheaper... but the difference is minor unless you can save a wither potion). Since the current optimal choice is to use Wither 350 plus other buffs to get you 1 hits, you can probably 1 hit over 70% of the time. In that case K * S + (1-K) * 2S will be less than K2 * S2 for using doubler 11 if CA36 or 72 will work but not for higher values. For doubler 12 CA40 or 80 are viable and for doubler 4X only 100 makes sense. Having CA values other than 36, 40, 72, 80 or 100 therefore is probably not a good strategy compared to a wither 350 potion.

The only other thing to consider is that if Wither 350 plus EW1000 may cost you 10-15 FSPs. 10 FSPs could be converted directly to 250 stamina, so if CA is not exactly perfect that is OK, especially if your max stamina is so low that you can’t get good value out of a Wither potion...

SO
lets assume Doubler 10 and 70% success rate on killing with wither. (makes math easy)

That means you will use 7 X10 stamina plus 3 X 20 stamina or 130 stamina for 10 kills or 13 stamina per kill.

Using CA40 (best with doubler 10X) you use 11 stamina per kill
Using CA80 you use 12 stamina per kill
Using CA 120 you use 13 stamina per kill
Using CA160 u use 14 stamina per kill.

In effect CA120 is the same as Wither350 (minus the cost of the wither potion) when using Doubler 10X. If however you have DW and PS CH getting you 1 hits as well, then wither is still a little better. With 80% 1 hits using DW Wither, PS CH then the math falls to 8 at 10 and 2 at 20 so then the cost is only 12 per kill using wither. The likely value is twelve point something so CA40 is good, CA80 is probably a little better and CA120 is probably a little worse, but since u save 8 or 9 FSPS on the wither potion i would still be willing to say that CA values up to 120 are worth it.

The other problem is what if 1 level CA40 is best then the next CA80 then the next Wither would be better, then back to 80... that is irritating.



The Same math works with CA36 and CA72 getting you a bit of a bonus...

7 kills at 11 and 3 kills at 22 = 143 for 10 or 14.3 stamina using Wither 350.
8 kills at 11 and 2 at 22 is 132 for 10 or 13.2 stamina using wither 350 plus other buffs.

level 36 costs you 12
level 72 costs you 13
level 109 costs you 14

The same logic applies. Level 36, 72 or 109 may be viable strategies. better or equal to wither 350 if you can use the same level buff all the way and it is better if you can minimize the buff level.


LAST THOUGHTS
CA175 is handy for SEs and Elites and such...