Bustin out the math for the Wu Kong vs Tarlak Debate.
First we will start with some assumptions.
Wu Kong gives +185% attack and a 32% chance to miss - let’s assume this is the true percentage and that there is no funny business going on (my experience is that this percentage is spot on). Wu Kong will also stack with other buffers. So Wu + Bold Tusk will yield + 233%
Tarlak gives +100% and always hits (and stacks up to 160% with other buffers) Tarlak Plus Bold Tusk gives +148%.
Stacking With Ares gives +239% and +154% respectively.
So the math to compute the true attack power is this:
If your hero has a base attack power (AP) of 900 (like my melendor):
With Wu By himself - new AP = 900 * (1+1.85) = 2,565
With Tarlak By himself - new AP = 900 * (1+1.00) = 1,800
Wu + BoldTusk AP = 900 *(1+ 1.85 + 0.48 ) = 2,997
Wu + Ares AP = 900 *(1+ 1.85 +0.54) = 3,051
Tarlak + BoldTusk AP = 900 *(1+ 1.00+0.48) = 2,232
Tarlak + Ares AP = 900 *(1+ 1.00+0.48 ) = 2,286
So this is our baseline - but we want to include Wu’s miss percentage and then determine which combo is better.
I wrote some code and simulated a bunch of trials.
I assumed 100 tile attacks, factored in Wu’s Hit Percentage and came up with a value for the attack of each combo. Since Wu’s will vary I ran this trial 10,000 times to get a mean value.
Then I compared the constant value for attacks with tarlak as ratio to the mean for attacks with Wu.
The results were surprising.
With WuKong by himself vs Tarlak By himself Wu Kong does 96.7% of the damage that Tarlak will do.
But when you start stacking - this percentage grows.
Wu+BoldTusk does only 91.31% of the damage of Tarlak + BoldTusk
Wu+Ares does only 90.76% of the damage of Tarlak + Ares
So you lose about 3.3% of potential damage with just the two heros.
This loss drops to almost 10% if you stack with a buffer at 54%!
This actually makes sense - since you are changing the numerator and denominator of a ratio by the same amount. Even though you add a constant to both, the ratio starts to diverge the bigger this offset becomes.
Even though I simulated this with trials and counting, closed form solutions are derivable from just the raw percentages of the heros.
The Ratio of Wu’s attack to Tarlaks is simply:
2.85 * 0.68 / 2 = 96.7%
The Ratio of Wu’s + Bold attack to Tarlak + Bold is simply:
(2.85+0.48) * 0.68 / (2 +0.48)= 91.31%
The Ratio of Wu’s + Ares attack to Tarlak + Ares is simply:
(2.85+0.54) * 0.68 / (2 +0.54)= 90.76%
Of course Wu has a variance (a probability of either more or less damage than the mean).
Since we are dealing with Normal distributions (using the Ares Wu combo)
68% of the time your attack will be within 7% of the mean.
95% of the time your attack will be within 14% of the mean.
99% of the time your attack will be within 21% of the mean.
So about ~10% of the time you use Wu and Ares you can get higher scores than with Tarlak and Ares.
But 90% of the time it will be lower, and potentially quite a bit lower.
Enough fun for now! Enjoy.