In terms of straight damage, chelona is better. If you are keeping goetia +2 on just for a "chance" of a set proc, you are losing damage potential. Goetia +2 head has its uses still, dont get me wrong, but the consistent damage increase from chelona justifies its use imho.
This would be a much easier argument to make (or to refute) if we knew the actual proc rate of the set bonus, and how it varies with each piece, but we don't. I would happily math this out completely if I had all the information, and I strongly suspect that Goetia would come out ahead - but we're missing some key information.
What we DO know is that the Chelona's over Goetia +2 will give roughly a 3% increase in "normal" damage (depending on a number of factors). The general belief about the Goetia set bonus is that damage bonus is twice the percentage of mp conserved when conserve mp procs. That would put the upper bound of the Goetia set bonus at around 14%, if the bonus always kicked in (based on an approximate 7% mp savings on average). How often it actually procs, and how much that would be reduced by taking away the hat are unknowns to me at this point. But it should be fairly apparent that if even a fraction of this potential 14% is realized, then the damage potential of the Goetia hat is greater than Chelona's.
How about doing it this way: assuming that Chelona's gives a 3% increase in damage over Goetia +2 hat and the set bonus gives a 14% bonus, calculate the rate at which the set bonus would have to activate to give the same average damage as Chelona's.
Let D = expected damage while wearing Goetia +2 hat.
Let X = rate at which set bonus activates without Goetia +2 hat (X is less than 1.0)
Let Y = increased rate at which set bonus activates with Goetia +2 hat (Y is less than 1.0)
X + Y <= 1.0
The two pieces would have the same average damage over time when:
D * 1.14 * (X + Y) + D * (1 - X - Y) = D * 1.03 * 1.14 * X + D * 1.03 * (1 - X)
1.14 DX + 1.14 DY + D - DX - DY = (1.03 * 1.14) DX + 1.03 D - 1.03 DX
1.14 DY - DY = (1.03 * 1.14) DX + 1.03 D - 1.03 DX - 1.14 DX - D + DX
(1.14 - 1) DY = (1.03 * 1.14 - 1.03 - 1.14 + 1) DX + (1.03 - 1) D
0.14 DY = (1.03 * 1.14 - 1.17) DX + 0.03 D
0.14 Y = (1.03 * 1.14 - 1.17) X + 0.03
Y = [(1.03 * 1.14 - 1.17) X + 0.03] / 0.14
Y = (0.0042 X + 0.03) / 0.14
Y = 0.03 X + 0.03 / 0.14 = 0.03 X + 0.2143 (approx)
Since the Goetia +2 hat set bonus is represented by the left side of the equation, Goetia +2 will win out when Y is greater than 0.03X + 0.2143.
One trivial conclusion that this equation gives:
- If X is 0 and Y is 0 (Goetia +2 is the only piece and the set, thus not providing any set bonus activation), Y is less than .2143, thus Chelona's wins.
The conclusion that I found surprising is that if the Goetia +2 hat is one of only two pieces of the +2 set, that would make X = 0, and Y would have to be at least 21.43% for the set bonus to win out. Given Byrthnoth's post on the suspected activation rate at this point, it seems highly unlikely for the addition of the Goetia +2 hat to increase the activation rate of the set bonus sufficiently to beat out the consistent damage increase of Chelona's, if average damage over time is the primary goal
Granted, this ignores the increased damage that the Goetia +2 hat can give by shortening casting time (and thus letting you cast your best nukes more often). But needing the set bonus to proc an additional 21.43% of the time from equipping just one more piece of the set seems like rather large disparity to overcome. Other than the assumptions I had based these calculations on (3% increased damage for Chelona's, 14% extra damage from set bonus), can anyone see any errors in my calculations above?
Edit: needed to add "hat" to distinguish between when I was talking specifically about the +2 hat vs +2 set in general in a couple of spots. Edited, Jul 27th 2012 2:19pm by svlyons