Oh yeah, limited runewords in SP - forgot about that one. No anni or torch either, right? I don't think I've done SP since Diablo I.

I'll make an attempt at synergies and mastery too, but I don't think I can do it as well as PhatTrumpet has. I'll try an overview then some numbers from a skill calculator.

Lets start plugging in some real numbers for skills and gear. I'll use the gear you're looking at, but I'll assume you can get a +2 skill, 20 FCR amy. So long as we're trying to optimize everything we may as well start with optimal gear. That will look something like this:

Helm: +2 skills, 20% FCR tiara

Ammy: +2 skils, 20% FCR

Weapon: 50% FCR Wizzy

Switch: CtA

Amour: Vipermagi 30% FCR +1 all skills

Shield: Lidless Wall 20% FCR +1 all skills

Gloves: Magefist 20% FCR +1 fire skills

Rings: 2x 10% FCR

Belt: Arachnid Mesh 20% FCR +1 all skills

Boots: whatever

Total FCR = 200%

Total + all skills = 7

Total + fire skills = 8

There are 110 skill points possible at level 99.

You have to spend 3 points in the lightning tree (static, telekinesis as a prereq and teleport).

In the cold tree there are 5 prereq's for frozen orb. You'll also put 20 points into frozen orb. You could get up to +7 to the cold tree so that means 10 hard points invested in cold mastery for a total of 35 skill points in the cold tree.

On fire side it does start getting tricky. There are 4 prereq's for fireball and metoer (counting firebolt as only a prereq for now) and 1 point in warmth is pretty much required. You'll also max fireball and meteor (they synergize each other and both can be used as a main skill - trust me on this for now). We'll also start with 1 point in fire mastery, just to get that initial 30% boost. That's 46 points total in the fire tree so far.

So before we really start balancing firebolt vs. fire mastery we have a total of 84 skill points spent. In a perfect world we'd have 26 more skill points to spend (at level 99), but that's still not enough to max both firebolt and fire mastery.

Trying to max damage you end up with a multi-variable equation. Lets start by walking through the max fireball (FB) damage equation from sort of an intuitive angle. The more points we put into firemastery, the more damage our fireball does - easy enough so far. The more points we put into fireball synergies (meteor and firebolt) the more fireball damage goes up as well. And of course the more points into fireball, the more damage it does. In a perfect world we'd just max everything and not worry about it, but we just don't have that many skill points. We also already have fireball and meteor maxed out. We also know what our +fire skills total will be, so we really only have to worry about 2 aspects of this equation, FM and Fbolt. This will kinda simplify everything.

So far we have 21 fireball synergy points (20 from meteor and 1 from Fbolt, the +to skill gear doesn't matter for this). We also have an slvl FM of 9 (1 hard point, 8 from equipment). Our goal was "FireBall synergies (i.e. FireBolt and Meteor) has to be 10-11 greater than the displayed FM slvl." Right now we are 12 point greater (21-9).

From here, this gets to be part art, part math. Say you did't get the +2 skills on your ammy or circlet. (Not counting that you would have to put more points into cold mastery.) Your FM slvl would be 4 points lower, but the FB synergies would still be at 21. A difference of 16 (21-5). So just as Frostburn said, this is all very item dependant.

I hope you're with me up up to the FM slvl and FB synergy point and how we calculate the arithmatic difference between them. If I lost you anywhere before this, let me know.

At this point we'll need to break out some math. Here's the formula for spell damage.

[final damage] = [base spell damage] * [total synergy bonus] * [total mastery and gear bonus]

The final damage term is obviously what weâ€™re trying to maximize here. Furthermore, because weâ€™ve assumed that the skill itself is already maxed out, the base damage term is actually a constant and can be eliminated from the equation. We also don't have any gear bonus (that would be +% fire damge from something like eschuta or a facet.) Thus, the way to maximize the final damage term is to maximize the product of total synergy bonus and total mastery.

Depending on your math skills, theres a few ways to think about this. I've been out of college for years now, so a good part of that calc is starting to fade away. I'm also kinda visual. I think of it as trying to maximize the area under two different slopes.

It's not this simple, but the concept is kinda like this. Remember the story problems about a farmer trying to make a fence that has the most interior space for his animals. (I'm sure there's variations, but this one sticks in my mind.) The farmer only has so many pieces of fence, lets say 20. Lets also say each piece is 1 meter long (1 yard if you prefer English measurements). He can put 9 on each side, and 1 piece on each end. something like this.

Code:

```
- - - - - - - - -
| |
- - - - - - - - -
```

But then he ends with only 9 x 1 = 9 sq meters of internal area. If instead he makes it with 5 sections on each side and end. something like this.

Code:

```
- - - - -
| |
| |
| |
| |
| |
- - - - -
```

This way he ends up with 5 x 5 = 25 sq meters of internal area.

You optimize two products by keeping them relatively close to each other. We'll use this principle when it comes to multiplying synergy damage and mastery damage. Weâ€™ve simplified the equation down to:

[final damage] = [base spell damage] * [total synergy modifier] * [total mastery modifier]

or,

= [base spell damage] * [1 + (X / 100)] * [1 + (Y / 100)]

Now for synergies we get 14% for each level and for mastery we get 7% for each level. The base spell damage for a level 20 fireball with +8 to fire skill is: 326 - 361 (Ã¸343.5) That would make the formula something like this:

= [343.5] * [1 + (X * 14%)] * [1 + (Y * 7%)]

But that neglects the fact that the first point into FM starts you at 30%, not 7%. So we have to make it something like this.

= [343.5] * [1+(X* 14%)] * [1 + (30% + (Y-1) * 7%)]

Lets make sure this work so far. We have 21 points in synergy and 9 point in mastery so:

= [343.5] * [1+(21* 14%)] * [1 + (30% + (9-1) * 7%)]

= [343.5] * [1 + 2.94] * [1 + (30% + (8 * 7%))]

= [343.5] * [1 + 2.94] * [1 + (.30 + .56)]

= [343.5] * [3.94] * [1.86]

= 2517.3054

The skill calculator says:

Fire damage: 2392 - 2649 (Ã¸2520.5)

Iâ€™m within a few points, so unless someone sees a math error somewhere, Iâ€™m gonna call this close enough.

Q: wait, I thought he said we should keep the products close to each other. He has the synergy mod about twice as high as the mastery mod. And this is almost an optimized balance to start with. (12 point difference instead of 10 or 11)

A: well, the synergy mod is increasing at 2x the rate of the mastery mod 14% vs. 7%. So yeah, we want the synergy % to be greater than the rate of the mastery %, but we canâ€™t totally forget mastery. Going back to the fence problem above. It would be kinda like the farmer using two different sized pieces of fence. If he could buy fences for the sides that were twice as long as the pieces he had to use for the top and bottom, but he was still limited to 20 pieces of fence. The highest internal area would come from a rectangle that was longer than it is wide. Donâ€™t worry, I wonâ€™t walk you through another story problem.

OK, time to start optimizing. Lets assume level 90 (101 total skill points or 17 points to spend after the 84 we already spent) then you'll see that there's a simple pattern for any extra points you get for leveling after that. We also want the FB synergies to be 10 or 11 higher than the FM slvl. So lets put 8 points into FB synergies (firebolt) and 9 into FM.

Firebolt: 9

Fireball: 20

Meteor 20

FM: 10

with +8 from gear

for a difference of 29 (FB synergies) â€“ 18 (FM slvl) = 11

Skill calculator says:

Fireball:

Fire damage: 4113 - 4554 (Ã¸4334)

[Synergy] Fire Bolt: +126% Fire damage (14% / Lvl)

[Synergy] Meteor: +280% Fire damage (14% / Lvl)

[Mastery] Fire damage: +149%

Meteor:

Fire damage: 9230 - 9681 (Ã¸9455.5)

Fire damage per second: 962 - 1024(Ã¸ 993)

Fire length: 17.4 Seconds

[Synergy] Fire Bolt: +45% Fire damage (5% / Lvl)

[Synergy] Fire Ball: +100% Fire damage (5% / Lvl)

[Synergy] Inferno: +3% Fire damage per second (3% / Lvl)

[Mastery] Fire damage: +149%

Say we didnâ€™t know about the whole 10-11 point difference thing and put all those points into FM.

Firebolt: 1

Fireball: 20

Meteor 20

FM: 18

with +8 from gear

for a difference of 21 (FB synergies) â€“ 26 (FM slvl) = -5

Fireball:

Fire damage: 3923 - 4344 (Ã¸4133.5)

[Synergy] Fire Bolt: +14% Fire damage (14% / Lvl)

[Synergy] Meteor: +280% Fire damage (14% / Lvl)

[Mastery] Fire damage: +205%

Meteor:

Fire damage: 9460 - 9922 (Ã¸9691)

Fire damage per second: 1178 - 1254(Ã¸ 1216)

Fire lenght: 17.4 Seconds

[Synergy] Fire Bolt: +5% Fire damage (5% / Lvl)

[Synergy] Fire Ball: +100% Fire damage (5% / Lvl)

[Synergy] Inferno: +3% Fire damage per second (3% / Lvl)

[Mastery] Fire damage: +205%

Our Fireball went down about 200 points and our Meteor went up about 240 points. Not perfect, but workable, arguably better if you like Meteor over Fireball. Letâ€™s see what happens if we put all the points into Fbolt instead of FM.

Firebolt: 18

Fireball: 20

Meteor 20

FM: 1

with +8 from gear

for a difference of 38 (FB synergies) â€“ 9 (FM slvl) = 29

Fireball:

Fire damage: 3838 - 4249 (Ã¸4043.5)

[Synergy] Fire Bolt: +252% Fire damage (14% / Lvl)

[Synergy] Meteor: +280% Fire damage (14% / Lvl)

[Mastery] Fire damage: +86%

Meteor:

Fire damage: 8161 - 8560 (Ã¸8360.5)

Fire damage per second: 718 - 764(Ã¸ 741)

Fire lenght: 17.4 Seconds

[Synergy] Fire Bolt: +90% Fire damage (5% / Lvl)

[Synergy] Fire Ball: +100% Fire damage (5% / Lvl)

[Synergy] Inferno: +3% Fire damage per second (3% / Lvl)

[Mastery] Fire damage: +86%

No matter which of the above examples you compare this to, damage goes down.

Q: I thought damage would go up because weâ€™re getting more synergy bonus (14%), and we only some mastery bonus (7%). Doesnâ€™t the extra 14% mods make up for the lack of 7% mods?

A: No, remember weâ€™re trying to maximize the product of two numbers. The best way to maximize the product of two numbers is to keep them somewhat close to each other. Going back to the fence analogy, you made the fence too long and skinny â€“ thereâ€™s very little internal space.

OK, this should be enough to show the point of all this and draw some conclusions. Try to keep your FB synergies about 10-11 points above your FM slvl. If you donâ€™t have perfect gear, or arenâ€™t sure what you will end up with â€“ error on the side of putting more points into FM than FB. (i.e. make your FB synergies about 10 points higher than FM slvl with the gear you think you will reasonably find. If later on you add some more +skill items and you end up with a higher FM slvl, itâ€™s no big deal.) Even at only 5 points higher FB synergies compared to FM slvl your fireball damage will only decrease by less than 100 points (and your Meteor damage will go up anyway). This is really where the art comes in more than the math. Not knowing how much + skill items you'll end up with has a bigger impact on how much CM to use.