Hi I'm a gm and had a problem last week.
One of my players had the meta magic feat Empower and used it on magic missile.
He argued he would get more missiles instead of 50% more damage on target hit. I ruled against it, but promised to look into it
He is level 7 and would get 4 missiles normally and instead of 50% more damage he would get an extra 2 missiles for a total of 6 missiles.
I don't really know if it would be game breaking, I'm not good at the math part of pathfinder.
Can you help me?
Your player is wrong. Empower only affects variable numbers which are represented by the die. The number of missiles created by the spell based on caster level is not variable.
The correct way to apply empower spell is to take the damage, in this case its (4(1d4+1))*1.5.
This is further clarified in its interaction with maximize spell
An empowered, maximized spell gains the separate benefits of each feat: the maximum result plus half the normally rolled result.
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.
A missile of magical energy darts forth from your fingertip and strikes its target, dealing 1d4+1 points of force damage.
The missile strikes unerringly, even if the target is in melee combat, so long as it has less than total cover or total concealment. Specific parts of a creature can't be singled out. Objects are not damaged by the spell.
For every two caster levels beyond 1st, you gain an additional missile - two at 3rd level, three at 5th, four at 7th, and the maximum of five missiles at 9th level or higher. If you shoot multiple missiles, you can have them strike a single creature or several creatures. A single missile can strike only one creature. You must designate targets before you check for spell resistance or roll damage.
Empower spell increases the numeric variables which the number of missiles is not.
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.
So as per the rules only the damage of the magic missiles is increased. You would do that for each target hit, as missiles can be spread among several targets. The more the missiles are spread the more likely it is you lose damage by rounding. Maybe that is why your player would rather increase the number of missiles.
To your sub-question about breaking the game: Changing how empower affects will, most likely, not break the game (but that might be subjective) but it can very well have unwanted side effects. That can be avoided by using the feat as written (increasing the damage).
Examples:
