Combination of attack/crit stones for max DPS
A detailed aion guide into the game mechanics involved in a usage of crit stones and max DPS. This has been written by SesimoGraf of Aionsource and is a pretty indepth look at the game mechanics involved. We still haven’t understood all of it and we will give it a complete read once we get some free time on our hands. As of now, it definitely is worth having a read. The guide follows…
Discussions about attack and crit manastones seem to be quite popular. People want to find the way to maximize damage with the slots they can allocate to those two types of manastones. From what I understood the following distinction can be made:
- Attack stones add a fixed amount of damage/DPS to a weapon
- Crit stones add a percentage-based amount of damage/DPS to a weapon
The correctness of these 2 facts is important. If they aren’t true this whole post
is a fail. If they are actually true, the method here can be useful and adapted to
better knowledge, that will be coming steadily.
Now what we do is build a simple model of how DPS could be affected by the manastones. This model is inaccurate with a 100% probability, but it doesn’t matter for the purpose of this post… read on.
First we say that a weapon has a certain amount of DPS and attack/crit stones add boni on top of it. Attack stones are additive, crit stones multiplicative. Some abbreviations are used.
weapon_base_dps : w_dps
dps_increase_per_attack_stone : ba
dps_factor_per_crit_stone : bc
Then a player has a certain amount of manastone slots he can socket. The number of stones of each type he should optimally socket is what he tries to find out. Here are the variables:
number_of_manastone_slots : N
num_socketed_attack_stones : na
num_socketed_crit_stones : nc
The number of manastones that can be socketed will be a constant for each individual case we look at. Once we know that we should socket a certain amount of attack stones, the number of crit stones is simply the number of remaining free slots.
Thus we can eliminate one variable by substitution:
nc = N – na
This leads us to a function of one variable on the number of attack stones (na) that we want to maximize for DPS. The value of na must be inside the interval 0 <= na <= N ; the domain of the function.
Total DPS = f(na)
= (w_dps + na * ba) * (1 + nc * bc)
= (w_dps + na * ba) * (1 + (N – na) * bc)
To find the optimal combination of stones to put in the available sockets we must find the maximum of the function f(na). In the old days we would take the first derivative of f(na) and find where it is zero. Now we can use WolframAlpha. So let’s imagine an example, build a query string for WolframAlpha and then let it do the work
for us.
We take a hypothetical weapon with w_dps=150 and set the other variables arbitrarily to ba=4, bc=0.02 and N=20. This is our template string to make the queries, where we put in the concrete values for all the examples we want:
Template for WolframAlpha query: maximum (w_dps + (x * ba)) * (1 + ((N - x) * bc)) for 0 <= x <= N
Filling in the values from above gives the string…
maximum (150 + (x*4)) * (1 + ((20 – x) * 0.02)) for 0 <= x <= 20
…that we feed into the “beast”: Wolfram|Alpha query
It tells us that the maximum is at x=16.25, so this means we should get the best DPS by socketing 16 attack stones and only socket 4 slots with crit stones. At least for the chosen example with fictional numbers.
We could continue to play with the numbers and certainly come to some interesting conclusions. Let’s just make one last example where we keep the old numbers and only replace dps with the value 225. Here is the second query and link:
maximum (225 + (x*4)) * (1 + ((20 – x) * 0.02)) for 0 <=
x <= 20
The result is now x~=6.875 which means only 7 attack stones, but 13 crit stones. It’s not surprising that the optimal number of attack stones has decreased, since they only add a fixed amount of DPS, whereas the crit stones benefit from the larger factor (w_dps=225 instead of 150). If we further increase the weapon dps value, then x will go to 0, meaning all crit stones is optimal.
Once the right formulas for the added DPS of attack and crit manastones are known, we can use basic math and tools such as WolframAlpha to find the optimal numbers in terms of expected damage. Coming to an end and to summarize:
Conclusion: In some cases the maximum damage/DPS of a weapon will be achieved with a combination of both attack and crit stones. This post shows a method to calculate the optimal proportion, using a hypothetical model that will be obsolete once the exact mechanics are known.
Original Link: http://www.aionsource.com/forum/mechanic-analysis/39452-combination-attack-crit-stones-max-dps.html
Author: SeismoGraf
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