Huge necrobump, but my mind has been drawn back to this again. It really deserves to be finished. However, in direct reply to myself from two posts up, given other discussions, I decided to crunch some numbers. Specifically, I'm reworking the math that shows when Tiger Stole beats out Spike Necklace from the PLD's point of view.
This begins with milich's math. X is our current attack value. Y is the percent increase necessary to beat out Spike Necklace. All calculations assume that the mob is 7 levels higher, as per milich's original math.
[((X+5)/(X/1.25)-.35)-(X/(X/1.25)-.35)]/(X/(X/1.25)-.35) = Y
(X/(X/1.25)-.35)=(X/X)*1.25-.35)=.9
[((X+5)/(X/1.25)-.35)-.9]/.9 = Y
((X+5)/(X/1.25)-.35)-.9 = .9Y
(X+5)*1.25/(X)-.35-.9=.9Y
(1.25X+6.25)/X-1.25=.9Y
1.25X+6.25-1.25X=.9XY
6.25=.9XY
6.25/.9Y=X
X=6.94444/Y
Using the final equation, it's easy to see the Attack needed for the percentages being equal.
A note on percent increase:
I calculated the Spike Necklace as the following:
fSTR % increase for Base Damage is 1/starting Damage.Accuracy was calculated using 3 DEX * .5 = 1.5 * .5 again to get the hitrate increase. This will account for the average case between getting two extra Accuracy vs. one extra Accuracy based on current Dex. % increase is then calculated by taking this value and dividing it by some base accuracy.Summing these together gives the best case % increase for the Spike Necklace - this value is the Y value in the equation. So, without further ado, here's the results.
First, the case (25%) where fSTR doesn't increase base damage.
Accuracy Y X
50 1.5 463
60 1.2 556
70 1.1 648
80 0.9 741
90 0.8 833
95 0.0 999
Base Damage Accuracy Y X
15 50 8.2 085
60 7.9 088
70 7.7 090
80 7.6 091
90 7.5 093
16 50 7.7 090
60 7.5 093
70 7.3 095
80 7.2 097
90 7.1 098
17 50 7.4 094
60 7.1 097
70 7.0 100
80 6.8 102
90 6.7 103
18 50 7.1 098
60 6.8 102
70 6.6 105
80 6.5 107
90 6.4 109
19 50 6.8 103
60 6.5 107
70 6.3 110
80 6.2 112
90 6.1 114
20 50 6.5 107
60 6.2 111
70 6.1 114
80 6.9 117
90 5.8 119 So, a few notes.
First note: The 175 rule is VASTLY out of date for PLD (and is what I think Shintasama was pointing at earlier). This is mostly due to the effect that in the formula, the attack needed to overcome the % increase of the +STR/+DEX is inversely proportional that % increase. I have a hunch (I'll check it when I'm less tired) that this fact will be independent of mob level - the only thing that will change it is mob defense (and thus, the constant of proportionality), not the level correction which appears to normalize out of the formula.
Second note: Two handers get a different formula from one-handers, so the general rule shouldn't have been applied like it was by myself.
Third note: The higher the base damage the weapon, the more attack is needed to overcome the smaller increase from fSTR. As better swords become equipped, it's necessary to reevaluate.
Fourth note: As of this writing, it finally donned on me that we're also neglecting the attack boost from the spike necklace as well. Since that will only increase Y, it will only FURTHER decrease the attack at which Spike Necklace is useful.
It looks like, as a general rule, the lower your base damage is, the sooner you should put on the spike necklace. PLD is probably in the portion where we're quickly going to break into it. IMO, it's probably in the low hundreds.
Edited, Dec 4th 2009 12:27am by Dracoth