Actually, as the number of rays is defined in terms of lvl, it is not considered a variable.
Consider that in mathematics x is commonly touted as the only variable as y, z and any other "variable" values are defined in terms of x. This hard definition in terms of x cause them to be concerned as constants for all intensive purposes.
However, x cannot always be defined by a particular value of y, z, or any other defined constant as they may pass through the same value many times at different values of x. Take, for instance, any trig function, such as sine or cosine(x) where y occelates between -1 and 1 infinitely in both directions.
Furthermore, if what you claim were true, this would mean that a 7 the lvl caster using scorching ray could increase from 2 rays at 4d6 dmg each (totaling 8-48 dmg) to 3 rays at 6d6 dmg each (totaling 18-108 dmg). This would far outstrip any other spell which could normally deal 8d6 dmg that was empowered, now dealing 12d6 (totaling 12-72 dmg).
Definition of a variable in this case should most logically follow the mathematical definition of such, or the system breaks.
That said, if you had an ability such as a bloodline arcana that increased the damage dealt PER DIE ROLLED, that additional dmg would be increased by 50%, as, dispute being defined in terms of another variable, it is specifically called out in the feat as a "bonus to that roll".
Besides, the number of rays does not count as a bonus to the variable numeric effect of any given ray's damage; it is an effect of it's own right.
The number of missiles or rays is not a variable--it is a static number. The only variables in this context are dice.
The damage of a Fireball is not a variable because your caster level adds more dice, but because dice provide variable results.
As for #1, there are not two valid methods, there is only one:
(Variables) x 1.5
So, for your example, the correct way to deal with 2d8+10 is to actually roll 2d8, add 10, then multiple the result. If I rolled average (9), I'd heal 19 normally, or 27 when Empowered.
Multiplying the dice before rolling is not correct--a spell with an odd number of dice will create wonky results (as you showed by turning 9d8 into 13d8).
Yes, in the real world the number of rays/missile is a variable because it changes depending on caster level. But as far as the game is concerned, it is not a variable - variables are dice rolls.
It doesn't matter if a 7th level caster casts Scorching Ray 1 time, 10 times, 100 times, or 1000 times - he'll still get 2 rays each time. What does change each time is the damage of the ray.
Claiming that caster level dependent features of spells are variable is like claiming that the slope of a line in the generic equation y=mx+b is a variable because different lines have different slopes. In reality, it is a constant since for any given line that value is the same. Many lines can have the same slope and still be different just as many casters can have the same caster level and be different. The variables for a spell are only the independent variables of the spell, or the features of the spell that change every time the spell is cast regardless of caster level. If we assume CL dependent features change, a 6d6 fireball that has a range of 640 ft becomes a 9d6 damage fireball (with +50% damage rolled) that goes 760 ft since number of dice, range, and damage rolled are all "variables". Other spells will also find things like duration increased and the target limit increased since they are also based on caster level. It doesnt stand up to scrutiny.
Also, look at the last three words of the first sentence of the empower spell feat if you dont believe me. Im on a phone and cant show it easily myself, but the feat specifically calls out it increases bonuses "to the dice rolls". From the wording of that statement, it can be conclusively determined that "variable, numeric effects" are in farct "dice rolls"
Edit:Left out important words
Variables are something that can vary. My caster level will not vary. It is constant until I level up, as an example. The only thing that varies are dice rolls with a spell. At level 10 you will get 10 dice for fireball. The variable is what numbers come up.
If you want to ignore the people that know the rules feel free to google 3.5 and empower. There are articles about the game rules, and those rules were most transported to PF. Empower is one that did not change. You also check the developer comments on this site.
In short if you roll it then it is a variable. Otherwise its not.
The book is not written in legalese. Trying to claim a feat allows you to empower caster level show a gross lack of understanding of the game. Now either you are right or "everyone" else is wrong.
However if you must insist.
Do Empower Spell and Maximize Spell affect d20 rolls
made as part of a spell’s effect (such as an attack roll or
dispel check)?
No. Any attack roll, saving throw, skill check, dispel check,
or any other d20 roll required to adjudicate a spell’s success or
failure is not considered a “variable, numeric effect” of the
spell and thus is unaffected by feats such as Empower Spell or
Maximize Spell.
Caster levels which affect dispel checks would figure into these "D20" rolls, and they work just like they did in 3.5.
Caster level is not variable at the time of casting, and therefore no caster level dependent variables are variable at the time of casting either.
This precludes any caster level dependent variable, other than the "bonuses to those dice rolls" specifically called out in the associed text, from being affected by empower metamagic.
If this were ruled otherwise a CL8 caster using an empowered fireball would modify his 8d6 fireball as follows:
CL8 x 1.5 = CL 12
12d6 fire dmg x 1.5 = 18d6
I highly doubt that this is what was intended, and I doubt that you will convince even a simple majority of this idea.
Actually the fact that nobody "but you" reads it that way is pretty much all I need to know. No I am not being contentious. I just fail to believe that out of the hundreds of gamers I have interacted with over the years, including ones such as myself who have been said to have a good understanding of the game, that you have it right.
Not only that, but you would also have to explain how empower is only +2 for increasing spells, and maximize is a +3 since maximize should be better than empower.
So what does maximize do for caster levels?
On top of that how does maximize and empower now work when used together.
Maximize Spell (Metamagic)
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.
You are the one basically saying the rest of us have it incorrect. The proof of burden is on you.
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I hate to do this, but I think the devs need to look at this one.
When empowering a spell such as scorching ray or magic missile, is the number of rays or missiles considered a "variable numeric effect" of that spell?
I think you all know where I stand on this, but I encourage you to FAQ this either way as otherwise wolfen and a few others will attempt to exploit this.
The number of rays and missiles is fixed by caster level, which is not a variable.
The amount of damage is the variable.
Magic missile is even used as the base example for how empower works, and the example only references the damage die, and "not" the number of missiles.
edit:The example from 3.5 was taken out but otherwise it reads the same.
But Dominigo it does state that range, duration, damage, area, and saving throws are all caster level dependant variables. It even states in the empower spell feat: Saving throws and opposed rolls are not affected. If it specifically states that a saving throw, which is a caster level dependant feature, is not effected by this ability which shows they considered it a modifiable variable. Also with the last portion of the first sentence "including bonuses to those dice rolls". This just states that you must include the extra bonuses gained via feats, abilitys, or caster level dependant effects to the calculations.
Ex: By using your exact reasoning if I go to cast an Empowered Cure Moderate Wounds I would get ((2d8)*1.5)+10) as the +10 is a level derived variable or "constant" and should not be increased.
And it does not even come close to reading "variable = dice roll". It specifically states ALL (variable and numeric) effects are increased, INCLUDING (not exclusively to) bonuses to those dice rolls (which may not be variables such as with specializations or the constant +1 bonus to magic missile).
First off, let me say saving throws aren't based on CL in any way. It is based on your characters stats and the spell's level. A 20 Int level 20 wizard casts Charm Person exactly as potently as a 20 Int level 1 wizard (without any feats, of course).
Second, yes, it does directly say that the "variables" are dice rolls. Look at the sentence. The variable effects are what are increased. Also, any bonus to those dice rolls are increased. Which dice rolls are these? Nothing before it said dice rolls. Well, they must mean those variable effects from the first half of the sentence. Sounds to me like those "variable effects" are "dice rolls". There isn't really anything else those "dice rolls" can be.
Alright, now, lets run with your logic. Let's run it straight into the Maximize Spell feat.
Maximize spell states (from the PRD):
" 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."
Ok, the same as Empower except I put it at its maximum value. It even has the caveat at the end like Empower stating what it doesn't apply to. Great.
So this will set all those variables you have mentioned above that to their maximum value. Awesome. So let's look at the spell haste. Here are some of the details:
School transmutation; Level bard 3, sorcerer/wizard 3
Casting Time 1 standard action
Components V, S, M (a shaving of licorice root)
Range close (25 ft. + 5 ft./2 levels)
Targets one creature/level, no two of which can be more than 30 ft. apart
Duration 1 round/level
Ok, so here is what I have gathered (from you) about how this works. Range is a variable (it can change), so we set it to its maximum value. Well, there isn't any cap listed, so how high can it go? Well, mathematically speaking, it can go forever. There isn't a limit to caster level, after all (which is not increased, of course! Only variables based on it). So the range is now infinite. If you have line of effect, you can hit it.
Next is targets. Well, there are two limits: number of creatures and distance. The distance is set, so everything must remain that close together buuuuut the number of targets isn't, so just like with the range it goes to its cap of infinity. As long as everything is together, they all get it!
Finally, there is the Duration and as luck would have it, its also a variable set by level! So we get to set it to its maximum value as well which, as it has no cap, is infinite. So now we have a Haste that lasts forever, affects as many targets as you can get in a 30 ft diameter circle, and can be cast on anything not physically blocked. Awesome!
Extending this logic, spells like Shield, Mage Armor, Heroism, Jump, Resist Energy, Life Bubble, etc (this is a long list!), can become permanent until dispelled by simply applying Maximize spell. Now you may say "for +3 spell levels, thats fair! His Mage Armor wasn't really infinite until level 7 anyway!" Well, this is where the magic items come in. A lesser Maximize rod only costs 14,000 gold, and will let you make 3 buffs at spell level 3 lower a day become permanent. According to WBL, a character could afford this by level 6! That means at level 6, a wizard can make any spell he can cast with a non constant duration last forever since almost no spells cap duration.
Some spells become even more problematic than before. That guard giving you problems? Hit him with a nice Maximized Sleep spell. If he fails that save, he will sleep until he starves to death (literally)!