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+--- Thread: Combined effect of masteries and synergies (/thread-10821.html)
Combined effect of masteries and synergies - Methraton - 07-10-2003
I was messing around with the character pack that's available through diabloii.net and tried to understand how masteries and synergies for the sorc worked. I concentrated on the fire skill tree (why ? I guess I love to play with fire).
First, I'll list the synergies from that tree so you won't need to go to arreat summit (wich may contain errors) or write them down. That's what is shown on the mouse over in-game. I know that the the mouse over numbers might contain errors too... but I needed my numbers from somewhere !!!
Code:
Fire bolt -Fire ball +16%
-Meteor +16%
Inferno -Warmth +12%
Fire ball -Fire bolt +14%
-Meteor +14%
Enchant -Warmth +9%
Meteor -Fire bolt +5%
-Fire ball +5%
-Inferno +3% average fire damage (non-impact damage)
Hydra -Fire bolt +3%
-Fire ball +3%Then I looked at fire mastery wich gives +30% fire damage for the first skill point then only +7% fire damage for all other skill points after that (maybe it changes after 20, I didn't test it).
With those numbers in mind, I figured that fire mastery may not be the best skills to pump your primary damage dealing spell. Sure, everyone should put that first point in mastery to get the 30% bonus but after that, what do you do?
For exemple, if I want to pump Fire bolt, the numbers show that it's better to put points in Fire ball and Meteor than mastery (14% > 7%). So I tested some combination using only the maximum damage. Here are the results:
Fire bolt (20) + Fire ball (0) + Fire mastery (0)
60 + 0 + 0 = 60 (this 60 comes from the screen)
Fire bolt (20) + Fire ball (20) + Fire mastery (0)
expected -> 60 * (1 + 3,2) = 252
screen -> 254 (close enough for me)
Fire bolt (20) + Fire ball (0) + Fire mastery (20)
expected -> 60 * (1 + 1,63) = 157,8 (screens says 159)
screen -> 159 (close enough for me)
Fire bolt (20) + Fire ball (20) + Fire mastery (20)
expected -> 60 * (1 + 3,2 + 1,63) = 349,8
screen -> 668 (doh!)
There is a problem here when you look at the damage when both synergy and mastery are in effect. Through trial and errors, I guessed the formula to be :
(60 * (1 + 1,63)) * (1 + 3,2) = 662,76 I suppose it's close enough
(60 * (1 + 3,2)) * (1 + 1,63) = 662,76 It makes sense since multiplication is associative
Let's test it backward :
668 / (1 + 3,2) = 159 -> 159 / (1 + 1,63) = 60,45 ~ 60
I suppose this is the formula and that the differences are due to rounded values or decimals that don't show on the mouse-over numbers.
The big formula for firebolt is :
60 * (1 + 0.3 + (m - 1) * 0.07) * (1 + n * 0.16)
where m is the number of skill points in fire mastery and n is the number of skill points in fire ball. m > 0 because I suppose everyone will put at least point in fire mastery for the 30% bonus.
Now, another important question, if I max Fire bolt (20 points in it) and I have only 20 other points to split between Fire ball and Fire mastery, what is the optimum set up ?
By observation, you have to find the value of m and n in the formula that gives the maximum for the product (1 + 0.3 + (m - 1) * 0.07) * (1 + n * 0.16) where m > 0 to maximize your damage output. I wrote a small program to calculate the possibilities. Here are the results :
Fireball = 19 Mastery = 1 DAMAGE = 315
Fireball = 18 Mastery = 2 DAMAGE = 318
Fireball = 17 Mastery = 3 DAMAGE = 321
Fireball = 16 Mastery = 4 DAMAGE = 322
Fireball = 15 Mastery = 5 DAMAGE = 322
Fireball = 14 Mastery = 6 DAMAGE = 320
Fireball = 13 Mastery = 7 DAMAGE = 317
Fireball = 12 Mastery = 8 DAMAGE = 313
Fireball = 11 Mastery = 9 DAMAGE = 308
Fireball = 10 Mastery = 10 DAMAGE = 301
Fireball = 9 Mastery = 11 DAMAGE = 292
Fireball = 8 Mastery = 12 DAMAGE = 283
Fireball = 7 Mastery = 13 DAMAGE = 272
Fireball = 6 Mastery = 14 DAMAGE = 259
Fireball = 5 Mastery = 15 DAMAGE = 246
Fireball = 4 Mastery = 16 DAMAGE = 231
Fireball = 3 Mastery = 17 DAMAGE = 214
Fireball = 2 Mastery = 18 DAMAGE = 197
Fireball = 1 Mastery = 19 DAMAGE = 178
Fireball = 0 Mastery = 20 DAMAGE = 157
It's getting late now, I can't think anymore... I'll let someone else find the conclusion (if there is one). I think it has something to do with the ratio (Number of skill points in Fireball / Number of skill points in Fire mastey) wich should match with the ratio (Fireball bonus per skill / Mastery bonus per skill point) but I'm not sure at all. (. I know that for Fire bolt you can also pump meteor for more damage... but I wanted to keep the test simple)
Hope it helps... :blink:
Methraton
Combined effect of masteries and synergies - Obi2Kenobi - 07-10-2003
But then you might get more damage from, say, 15 to all rather than maxed fire bolt and fire ball and 10 in mastery. :D
Combined effect of masteries and synergies - Brista - 07-10-2003
Methraton,Jul 10 2003, 05:02 AM Wrote:Fire bolt (20) + Fire ball (20) + Fire mastery (20)Try this formula instead:
expected -> 60 * (1 + 3,2 + 1,63) = 349,8
screen -> 668 (doh!)
-> 60 * (1 + 3,2) * (1+1,63) = 662.8 (close enough)
In other words the mastery is multiplicative with the synergy bonus