Honestly, I've always used the roll then divide by half, though I'm pretty sure the rules imply that it's supposed to be 9d6 - or, at least, that's what I've seen in printed things.
Empower Spell (Metamagic)
Source PRPG Core Rulebook pg. 122
You can increase the power of your spells, causing them to deal more damage.Benefit: All variable, numeric effects of an empowered spell are increased by half including bonuses to those dice rolls.
Saving throws and opposed rolls are not affected, nor are spells without random variables. An empowered spell uses up a spell slot two levels higher than the spell's actual level.
That doesn't really tell us, but I'm pretty sure I've seen NPCs use the higher dice number. That said when I look a maximize spell it reads differently to me.
Maximize Spell (Metamagic)
Source PRPG Core Rulebook pg. 130
Your spells have the maximum possible effect.Benefit: All variable, numeric effects of a spell modified by this feat are maximized. Saving throws and opposed rolls are not affected, nor are spells without random variables. A maximized spell uses up a spell slot three levels higher than the spell's actual level.
An empowered, maximized spell gains the separate benefits of each feat: the maximum result plus half the normally rolled result.
Bold part mine.
To me, that reads like you roll up the result, then divide it by two, then add the maximum amount you could roll to quotient you just created. Basically, I don't know. I'm sure there are people who do, and can say better, but this is what I've got based on my ability to read things.
¯\_(ツ)_/¯
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To me, that reads like you roll up the result, then divide it by two, then add the maximum amount you could roll to quotient you just created.
Yes.
Empowered: Roll the dice as normal, add all your bonuses to that, calculate the total, then multiply the total by 1.5 (rounding down) = Damage.
Maximized: Replace each rolled die with its maximum, then add all your bonuses to that, calculate the total = Damage.
Empowered + Maximized: Roll the dice as normal, add all your bonuses to that, calculate the total, then multiply the total by 0.5 (rounding down), then add the maximum of every die to the empowered damage = Damage.
If there are different types of damage (fire, acid, bludgeoning, force, ...) involved, then do the respective calculation for each damage type separately. Exception: If a spell says something like "half that damage is fire, the other half acid", then you calculate the total damage as if it were one damage type, and then you split the damage into its parts as even as possible - have the player/GM/chance distribute any remainders (no rounding in this case).
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for whatever it's worth, I've always just rolled, because I like rolling huge piles of dice!
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Darn it, I made a mistake and rushed it here. Let's do this whole thing with proper mathematical formulas.
First, you need to put every damage bonus into one of those two categories: "dice bonus" vs "flat bonus".
Example for dice bonus: typical sorcerer bloodline arcanas.
Example for flat bonus: typical alchemical power components, Havoc of Society trait
Let "X" be the sum of your normal dice roll (only dice, no bonus).
Let "MAX" be the possible maximum of your dice roll.
Let "n" be the number of dice you roll.
Let "D" be the sum of all your dice bonuses (for a single dice).
Let "F" be the sum of all your flat bonuses.
Then you can calculate your damage as follows:
Normal Damage = (X + n*D) + F
Maximized Damage = (MAX + n*D) + F
Empowered Damage = (X + n*D)*1.5 + F
Empowered+Maximized Damage = (X + n*D)*0,5 + (MAX + n*D) + F
If there are different types of damage (fire, acid, bludgeoning, force, ...) involved, then do the respective calculation for each damage type separately. Exception: If a spell says something like "half that damage is fire, the other half acid", then you calculate the total damage as if it were one damage type, and then you split the damage into its parts as even as possible - have the player/GM/chance distribute any remainders (no rounding in this case).
Above is still valid.
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Of course, this begs the question: what about an empowered spell: confusion?
XD
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Of course, this begs the question: what about an empowered spell: confusion?
XD
Math is confusing too, isn't it? :D
Confusion cannot be Empowered or Maximized, because it does not have variable, numeric effects. The table with the d% roll is just put there for convenience, but is actually just the effect of the Confused condition.
It really does not matter because the end result is the same. In either case your average damage is 31.5.
As to the second part of your question empowered spell specifically states that it increases any bonuses to those dice rolls. That makes it pretty clear that your bonus damage from your bloodline is also increased.
With your bloodline bonus the average damage you will do at 6th level is 40.5 before save.
Empower gives bonus dice. So 9d6 for an Empowered 6d6 spell is correct.
Nope.
The number of dice you roll for a fireball is always the same (for a given character at a given level).
The result of those dice is numeric and variable. Hence the result of those dice is multiplied by 1.5.
This is also important for spells like magic missile which does d4 + 1 damage. If you roll a 3, doing 4 damage, empower raises it to 6. But if you multiplied the # of dice rolled you'd get 1.5 dice, rounded down to 1 die. Same with cure spells that do xd8 + caster level healing. The "+caster level" is also multiplie by 1.5 for a empowered version.
A maximized empowered 10th level Fireball does 60 +(10d6/2) but that's needlessly complicated and every group I've come across just says to roll half the normal number of dice. Personally I see no reason an Empowered Maximized 10d6 spell couldn't just do 90 points of damage.
Only because the rules say not to
An empowered, maximized spell gains the separate benefits of each feat: the maximum result plus half the normally rolled result.
But I agree, its not game breaking to just do 90. Its on average 15 more damage to a creature with a failed save, and 8 more damage on save.
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Empower gives bonus dice. So 9d6 for an Empowered 6d6 spell is correct.
Nope.
The number of dice you roll for a fireball is always the same (for a given character at a given level).
The result of those dice is numeric and variable. Hence the result of those dice is multiplied by 1.5.
This is also important for spells like magic missile which does d4 + 1 damage. If you roll a 3, doing 4 damage, empower raises it to 6. But if you multiplied the # of dice rolled you'd get 1.5 dice, rounded down to 1 die. Same with cure spells that do xd8 + caster level healing. The "+caster level" is also multiplie by 1.5 for a empowered version.
It makes a difference every time you have an odd number of dices. In Pathfinder you normally round fractions down, so increasing the dices give us a sequence of 1,3,4,6,7,9, etc. instead of 1+50%, 2+50%, 3+50%, etc.
Variance change too. The more dices you roll, the narrow and higher is the center part of your gaussian curve, i.e. the higher the chance of rolling an average result.If you have a relevant bonus to the value of the single die the difference increase, as adding dices make you lose the equivalent of half of one dice+bonuses half of the time.
Sure, it is a small difference, even with the right bloodline, traits, and feats probably less than 10 points, but as a GM I have seen plenty of NPC service long enough to make one more attack or sequence of attacks, or flee, or activate the gizmo, so many times because they had a few hit point remaining that I know that it can make a difference.