Arcane Energize theory-craft Questions

[(XBOX)castanzacrew]

Let's say that I have 6 arcane energizes, which is enough to achieve a Rank 3 Arcane Energize on a syandana or helmet. At Rank 4 (max rank), according to the wiki, there is a 40% chance of energize proc'ing from energy pickup, Rank 3 has a 30% chance, Rank 2 has a 20% chance, and Rank 1 has a 10% chance. If I were to take the 6 energizes that I have and split them up, installing 3 on a syandana and 3 on a helmet, thus resulting in 2 items that contain a Rank 2 energize each, and If i were to then use both of the Rank 2 energizes (each with an activation chance of 20%) on a single frame (using a syandana with a Rank 2 energize, and a helmet with a Rank 2 energize), wouldn't the overall chance of proc'ing arcane energize total to 40%? In other words, wouldn't the chance of either one activating be the sum of their individual proc chance? So 20% chance from the syandana, plus 20% chance from the helmet, totaling to a 40% chance of either one activating every time an energy orb is picked up. Therefore, wouldn't two Rank 2 Energizes (6 arcane energizes total) be statistically equivalent to a full stack (10 arcanes) of Arcane Energize?

Going further down this line of thought. If I had 9 arcane energizes (only 1 away from a full set), then I could technically split them up into a Rank 3 (which is 6 arcanes) and a Rank 2 ( which is 3 arcanes), and If i installed the Rank 3 (30% proc chance) on a syandana and the Rank 2 (20% proc chance) on a helmet and equip both on a frame, wouldn't the total proc chance be 50%? Thus exceeding the 40% proc chance provided by a set of 10 arcanes?

A small note at the end, I am not advocating for splitting arcane sets up. I understand that having a full arcane set installed on a single item allows for a different arcane to be used on the other item, thus allowing for more diverse arcane combinations. I know that this method of splitting up arcanes into both the syandana and helmet forces you to only run a single arcane on a singe frame. What i really want to know is that if this idea is worth implementing if one does not have full sets of arcanes? (i also realize that this method would only work with a select few arcanes, energize being one of them.)

[Xion]

42 minutes ago, (Xbox One)castanzacrew said:

Also, are you saying that a Rank 2 Arcane Energize only gives half of the energy of a Rank 4? I thought that the energy return from Energize is always 25-100 energy, irrespective of the rank of the arcane?

Arcane Energize gives 25 energy at Rank 1 and 100 energy at Rank 4

[Xion]

With 6 Arcane Energize, if you have 2 Rank 2 Energizes, you'll actually have 20% x2 chance to proc Arcane Energize per Energy Orb. Giving the chance that both Energizes will actually proc from the same Energy Orb, which gives the same amount of energy as a rank 4 Energize

[(XBOX)castanzacrew]

45 minutes ago, Xionyde134 said:

With 6 Arcane Energize, if you have 2 Rank 2 Energizes, you'll actually have 20% x2 chance to proc Arcane Energize per Energy Orb. Giving the chance that both Energizes will actually proc from the same Energy Orb, which gives the same amount of energy as a rank 4 Energize

As I understand it, the probability of two arcanes activating at the same time would be the product of their proc chance. So in the case of two Rank 2 Energizes there is a 4% chance of both proc'ing at the same time. (20% x 20% = 0.2 x 0.2 = 0.04 = 4%)

Also, are you saying that a Rank 2 Arcane Energize only gives half of the energy of a Rank 4? I thought that the energy return from Energize is always 25-100 energy, irrespective of the rank of the arcane?

In the case of using 2 Rank 2 Energizes, there would technically be a 36% chance to get 25-100 extra energy per energy orb and a 4% chance to get 50-200 energy per energy orb, thus totaling to a 40% chance to get any amount extra energy between 25-200, right?

{ (Probability of Syandana OR Helmet Proc'ing) = (Probability of Syandana Proc) + (Probability of Helmet Proc) - (Probability of Syandana AND Helmet Proc'ing) }

Thus, 20% (syandana) + 20% (Helmet) - 4% (both) = 36% of only Syandana OR Helmet Proc'ing

Edited March 24, 2017 by (XB1)castanzacrew
Calculation Error

[(XBOX)castanzacrew]

30 minutes ago, Xionyde134 said:

Arcane Energize gives 25 energy at Rank 1 and 100 energy at Rank 4

Ah. You are correct. My mistake. I misunderstood information that was given to me. I should have checked the wiki to verify it.

I suppose the fact that the amount of energy given increases as the arcane increases in rank makes my entire proposition moot.

The only situation i could think of where it MIGHT be worthwhile to split up a set would be if I had 12 arcane energizes as two Rank 3s. Which would work out to provide a 51% chance for 75 energy and a 9% chance for 150 energy; But at this point, it wouldn't be worth it to split up a full set.

Thank you, Xionyde. You have solved this debacle of mine, which has been bothering me for quite some time.

[-TSA-warramssie]

yes .... probability of 2 not mutually exclusive events is Prop A + Prob B - Prob ( A and B) = 1/5 + 1/5 - ( 1/5 x 1/5) = 0.36

with your 6 arcane energizes you are maximizing their happening but not their effectiveness if splitting them up...careful!

--- here comes the crux : effectiveness of use which should tend to 1 (optimal result)

if we consider both factors : 36% for getting 50 energy and  30% for getting 75 energy .. which is in pure effectiveness (1-36/50) to (1-30/75) which is 0.28 to 0.6 in effectiveness... where 1 is the desired value , still a big difference ... so you are almost losing double energy efficiency giveback if splitting up arcanes